@Preamble{
"\let \k = \c" #
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)}\fi" #
"\ifx \undefined \cprime \def \cprime{$'$} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" #
"\ifx \undefined \polhk \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}}\fi" #
"\ifx \undefined \url \input{path.sty} \fi"
}
@String{ack-mjn = "Mark J. Nigrini"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{j-ACCOUNT-HIST-J = "Accounting Historians Journal"}
@String{j-ACCOUNT-RES = "Accountability in Research"}
@String{j-ACCOUNT-REV = "The Accounting Review"}
@String{j-ACCOUNTANCY = "Accountancy: The journal of the {Institute
of Chartered Accountants in England and
Wales}"}
@String{j-ACTA-ARITHMETICA = "Acta Arithmetica"}
@String{j-ACTA-ASTRONAUT = "Acta Astronautica"}
@String{j-ACTA-PHYS-POL-B = "Acta Physica Polonica B"}
@String{j-ADV-APPL-STAT = "Advances and Applications in Statistics"}
@String{j-ADV-COMPLEX-SYST = "Advances in Complex Systems"}
@String{j-ADV-MATH = "Advances in Mathematics"}
@String{j-ADV-QUANTUM-CHEM = "Advances in Quantum Chemistry"}
@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}
@String{j-AEROBIOLOGIA = "Aerobiologia"}
@String{j-AM-DOC = "American Documentation"}
@String{j-AM-J-APPL-SCI = "American Journal of Applied Sciences"}
@String{j-AM-J-ECON-SOCIOL = "The American Journal of Economics and
Sociology"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-J-MATH-MANAGE-SCI = "American Journal of Mathematical and
Management Sciences"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-J-PSYCHOLOGY = "The American Journal of Psychology"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANALYST = "The Analyst"}
@String{j-ANIM-BEHAV = "Animal Behaviour"}
@String{j-ANN-APPL-PROBAB = "Annals of Applied Probability"}
@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical
Mathematics (Tokyo)"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-PHYS = "Annals of Physics"}
@String{j-ANN-PROBAB = "Annals of Probability"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-APPL-ECON-LETT = "Applied Economics Letters"}
@String{j-APPL-FINANC-ECON = "Applied Financial Economics"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-AQUAT-BOT = "Aquatic Botany"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ARKHIMEDES = "Arkhimedes"}
@String{j-ASIA-PAC-MATH-NEWSL = "Asia Pacific Mathematics Newsletter"}
@String{j-ASLIB-PROC = "ASLIB Proceedings"}
@String{j-ASTROPART-PHYS = "Astroparticle Physics"}
@String{j-ATMOS-ENV = "Atmospheric Environment"}
@String{j-AUDITING = "Auditing: A Journal of Practice \& Theory"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIOINFORMATICS = "Bioinformatics"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BIOSYSTEMS = "Biosystems (A6E)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BMC-BIOINFORMATICS = "BMC Bioinformatics"}
@String{j-BOLL-UNIONE-MAT-ITAL = "Bollettino della Unione matematica italiana"}
@String{j-BRAIN-COGN = "Brain and Cognition"}
@String{j-BULL-INST-MATH-STAT = "Bulletin --- Institute of Mathematical
Statistics"}
@String{j-C-R-ACAD-SCI-I = "Comptes rendus de l'Acad{\'e}mie des
sciences. S{\'e}rie I, Math{\'e}matique"}
@String{j-C-R-ACAD-SCI-PARIS-SER-AB = "Comptes Rendus Hebdomadaires des
S{\'e}ances de l'Acad{\'e}mie des Sciences.
S{\'e}ries A et B"}
@String{j-C-R-BIOL = "Comptes Rendus Biologies"}
@String{j-CACM = "Communications of the ACM"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics = Journal
canadien de math{\'e}matiques"}
@String{j-CHANCE = "Chance: a magazine for people interested in
the analysis of data"}
@String{j-CHAOS = "Chaos (Woodbury, NY)"}
@String{j-CHAOS-SOLITONS-FRACTALS = "Chaos, Solitons \& Fractals"}
@String{j-CHEM-PHYS-LETT = "Chemical Physics Letters"}
@String{j-CHIN-PHYS-LETT = "Chinese Physics Letters"}
@String{j-COGN-SCI = "Cognitive Science"}
@String{j-COGNITION = "Cognition"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE = "Collnet Journal of
Scientometrics and Information Management"}
@String{j-COLLOQ-MATH = "Colloquium Mathematicum"}
@String{j-COMM-NONLIN-SCI-NUM-SIM = "Communications in Nonlinear Science and
Numerical Simulation"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMM-THEOR-PHYS = "Communications in Theoretical Physics"}
@String{j-COMMUN-DESIGN-Q-REVIEW = "Communication Design Quarterly Review"}
@String{j-COMMUN-MATH-STAT = "Communications in Mathematics and Statistics"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-COMM = "Computer Communications"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-MUSIC-J = "Computer Music Journal"}
@String{j-COMP-NET = "Computer Networks"}
@String{j-COMP-NET-AMSTERDAM = "Computer Networks (Amsterdam, Netherlands:
1999)"}
@String{j-COMP-STAT = "Computational Statistics"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
@String{j-COMPLEXITY = "Complexity"}
@String{j-COMPOS-MATH = "Compositio Mathematica"}
@String{j-COMPUT-AIDED-DES = "Computer-Aided Design"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-COMPUTING = "Computing: Archiv f{\"u}r Informatik und
Numerik"}
@String{j-CONTEMP-PHYS = "Contemporary Physics"}
@String{j-CRYPTOLOGIA = "Cryptologia"}
@String{j-DEC-SUPP-SYS = "Decision Support Systems"}
@String{j-DEMOGRAPHY = "Demography"}
@String{j-DEUTSCH-MATH-V = "Jber. Deutsch. Math.--Verein"}
@String{j-DISCRETE-CONTIN-DYN-SYST = "Discrete and Continuous Dynamical
Systems. Series A"}
@String{j-DISCRETE-DYN-NAT-SOC = "Discrete Dynamics in Nature and Society"}
@String{j-DISCRETE-MATH = "Discrete Mathematics"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii Nauk SSSR"}
@String{j-DOKL-MATH = "Doklady Mathematics"}
@String{j-DRUG-DISCOVERY-TODAY = "Drug Discovery Today"}
@String{j-ECONOM-LETT = "Economics Letters"}
@String{j-ECONOMIST = "The Economist"}
@String{j-EDPACS = "EDPACS"}
@String{j-ELECT-J-COMB = "Electronic Journal of Combinatorics"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECT-STUDIES = "Electoral Studies"}
@String{j-ELECTRON-COMMUN-PROBAB = "Electronic Communications in Probability"}
@String{j-ELECTRON-J-PROBAB = "Electronic Journal of Probability"}
@String{j-ELEK-INFO-KYBER = "Elektronische Informationsverarbeitung und
Kybernetik (EIK)"}
@String{j-ELEM-MATH = "Elemente der Mathematik"}
@String{j-EMPIRICA = "Empirica"}
@String{j-ENTROPY = "Entropy"}
@String{j-ESAIM-PROBAB-STATIST = "ESAIM: Probability and Statistics"}
@String{j-EUR-J-OPER-RES = "European Journal of Operational Research"}
@String{j-EUR-J-PHYS = "European Journal of Physics"}
@String{j-EUR-PHYS-J-A = "European Physical Journal A: Hadrons and
Nuclei"}
@String{j-EUR-PHYS-J-B = "European Physical Journal B: Condensed
Matter and Complex Systems"}
@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
Processing"}
@String{j-EUROPHYS-LETT = "Europhysics Letters"}
@String{j-EXP-MATH = "Experimental Mathematics"}
@String{j-EXPERT-SYST-APPL = "Expert Systems with Applications"}
@String{j-EXPO-MATH = "Expositiones Mathematicae"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORUM-MATH = "Forum Mathematicum"}
@String{j-FRACTALS = "Fractals"}
@String{j-FUNDAM-MATH = "Fundamenta mathematicae"}
@String{j-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"}
@String{j-GER-ECON-REV = "German Economic Review"}
@String{j-GLOB-FINANCE-J = "Global Finance Journal"}
@String{j-ICARUS-IJSSS = "Icarus: International Journal of Solar
System Studies"}
@String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"}
@String{j-IEEE-POT = "IEEE Potentials"}
@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-ELECTROMAGN-COMPAT = "IEEE Transactions on
Electromagnetic Compatibility"}
@String{j-IEEE-TRANS-FUZZY-SYSTEMS = "IEEE Transactions on Fuzzy Systems"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-NETWORKING = "IEEE\slash ACM Transactions on Networking"}
@String{j-IEEE-TRANS-NUCL-SCI = "IEEE Transactions on Nuclear Science"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
Distributed Systems"}
@String{j-IEEE-TRANS-RELIAB = "IEEE Transactions on Reliability"}
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization
and Computer Graphics"}
@String{j-IMA-J-APPL-MATH = "IMA Journal of Applied Mathematics"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-IMAGE-VIS-COMPUT = "Image and Vision Computing"}
@String{j-INF-CONTROL = "Information and Control"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INFO-PROC-MAN = "Information Processing and Management"}
@String{j-INFO-SCI = "Information Sciences"}
@String{j-INFO-SYS = "Information systems"}
@String{j-INT-ECON-REV = "International Economic Review"}
@String{j-INT-J-ACCOUNT-INFO-SYS = "International Journal of Accounting
Information Systems"}
@String{j-INT-J-FOUND-COMP-SCI = "International Journal of Foundations of
Computer Science (IJFCS)"}
@String{j-INT-J-PLAST = "International Journal of Plasticity"}
@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
Education in Science and Technology"}
@String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and
Mathematical Sciences"}
@String{j-INT-J-MOD-PHYS-C = "International Journal of Modern Physics C
[Physics and Computers]"}
@String{j-INT-J-NUMBER-THEORY = "International Journal of Number Theory"}
@String{j-INT-J-PROD-ECON = "International Journal of Production
Economics"}
@String{j-INT-J-PURE-APPL-MATH = "International Journal of Pure and Applied
Mathematics"}
@String{j-INT-J-RES-MARK = "International Journal of Research in
Marketing"}
@String{j-INT-J-SCI-ENG-RESEARCH = "International Journal of Scientific and
Engineering Research"}
@String{j-INT-J-STAT-PROBAB = "International Journal of Statistics
and Probability"}
@String{j-INT-J-SYST-SCI = "International Journal of Systems Science"}
@String{j-INT-J-THEOR-PHYS = "International Journal of Theoretical
Physics"}
@String{j-INTERNET-MATH = "Internet Mathematics"}
@String{j-IZV-AKAD-NAUK-SSSR-MAT = "Izvestiia Akademii Nauk. USSR Seriia
Matematicheskaia (Moscow)"}
@String{j-J-ACCOUNT-EDUC = "Journal of Accounting Education"}
@String{j-J-ACCOUNTANCY = "Journal of Accountancy"}
@String{j-J-ACM = "Journal of the ACM"}
@String{j-J-AM-SOC-INF-SCI = "Journal of the American Society for
Information Science"}
@String{j-J-AM-SOC-INF-SCI-TECHNOL = "Journal of the American Society for
Information Science and Technology"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-ECONOMETRICS = "Journal of Applied Econometrics"}
@String{j-J-APPL-PROBAB = "Journal of Applied Probability"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-ASSET-MANAGE = "Journal of Asset Management"}
@String{j-J-ASSOC-INF-SCI-TECHNOL = "Journal of the Association for Information
Science and Technology"}
@String{j-J-ASTROPHYS-ASTRON = "Journal of Astrophysics and Astronomy"}
@String{j-J-BUS-ECON-STAT = "Journal of Business \& Economic Statistics"}
@String{j-J-CLIN-PATHOL = "Journal of Clinical Pathology"}
@String{j-J-CLIN-PSYCHOL = "Journal of Clinical Psychology"}
@String{j-J-COLLOID-INTERFACE-SCI = "Journal of Colloid and Interface Science"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-CONFL-RESOLUT = "Journal of Conflict Resolution"}
@String{j-J-DIFFER-EQU = "Journal of Differential Equations"}
@String{j-J-DIFFERENCE-EQU-APPL = "Journal of Difference Equations and
Applications"}
@String{j-J-DOC = "Journal of Documentation"}
@String{j-J-DYN-DIFFER-EQU = "Journal of Dynamics and Differential Equations"}
@String{j-J-ECON-DYN-CONTROL = "Journal of Economic Dynamics and Control"}
@String{j-J-EMPIR-FINANCE = "Journal of Empirical Finance"}
@String{j-J-EXP-PSYCH-GEN = "Journal of Experimental Psychology:
General"}
@String{j-J-FORENSIC-ACCOUNT = "Journal of Forensic Accounting"}
@String{j-J-GAMBL-STUD = "Journal of Gambling Studies"}
@String{j-J-GEN-PSYCH = "The Journal of General Psychology"}
@String{j-J-HUM-RESOUR = "Journal of Human Resources"}
@String{j-J-HYDROL = "Journal of Hydrology"}
@String{j-J-INFO-ORG-SCI = "Journal of Informational and Organizational
Sciences"}
@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
Cybernetics: EIK"}
@String{j-J-INFO-SCI-PRINCIPLES-PRACTICE = "Journal of Information Science,
Principles and Practice"}
@String{j-J-INFORMETRICS = "Journal of Informetrics"}
@String{j-J-INT-ECON = "Journal of International Economics"}
@String{j-J-INT-FINANC-MANAG-ACCOUNT = "Journal of International Financial
Management and Accounting"}
@String{j-J-JPN-INT-ECON = "Journal of the {Japanese} and International
Economies"}
@String{j-J-MAR-SYST = "Journal of Marine Systems"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-MATH-ARTS = "Journal of Mathematics and the Arts"}
@String{j-J-MATH-IMAG-VIS = "Journal of Mathematical Imaging and Vision:
JMIV"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MATH-SOC-JPN = "Journal of the {Mathematical Society of
Japan}"}
@String{j-J-MOL-BIOL = "Journal of Molecular Biology"}
@String{j-J-NETW-COMPUT-APPL = "Journal of Network and Computer
Applications"}
@String{j-J-NUMBER-THEORY = "Journal of Number Theory"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and
General)"}
@String{j-J-PHYS-SOC-JAP = "Journal of the Physical Society of Japan"}
@String{j-J-PROD-BRAND-MANAG = "Journal of Product \& Brand Management"}
@String{j-J-QUANT-CRIMINOL = "Journal of Quantitative Criminology"}
@String{j-J-QUANT-LINGUISTICS = "Journal of Quantitative Linguistics"}
@String{j-J-R-STAT-SOC = "Journal of the Royal Statistical Society"}
@String{j-J-R-STAT-SOC-SER-A-GENERAL = "Journal of the Royal Statistical
Society. Series A (General)"}
@String{j-J-R-STAT-SOC-SER-A-STAT-SOC = "Journal of the Royal
Statistical Society. Series A
(Statistics in Society)"}
@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
Society. Series D (The Statistician)"}
@String{j-J-REG-SCI = "Journal of Regional Science"}
@String{j-J-RISK-UNCERT = "Journal of Risk and Uncertainty"}
@String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and
Simulation"}
@String{j-J-STAT-MECH-THEORY-EXP = "Journal of Statistical Mechanics: Theory
and Experiment"}
@String{j-J-STAT-PHYS = "Journal of Statistical Physics"}
@String{j-J-SYST-SOFTW = "The Journal of systems and software"}
@String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"}
@String{j-J-THEOR-BIOL = "Journal of Theoretical Biology"}
@String{j-J-THEOR-PROBAB = "Journal of Theoretical Probability"}
@String{j-J-URBAN-ECON = "Journal of Urban Economics"}
@String{j-J-WASH-ACAD-SCI = "Journal of the Washington Academy of
Sciences"}
@String{j-JOCCH = "Journal on Computing and Cultural
Heritage (JOCCH)"}
@String{j-KNOWL-INFO-SYS = "Knowledge and Information Systems"}
@String{j-LANG-SCI = "Language Sciences"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LIBR-TRENDS = "Library Trends"}
@String{j-MAT-ZAMETKI = "Matematicheskie Zametki"}
@String{j-MATH-ANN = "Mathematische Annalen"}
@String{j-MATH-COMP-MODELLING = "Mathematical and Computer Modelling"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-GAZ = "The Mathematical Gazette"}
@String{j-MATH-GEOL = "Mathematical Geology"}
@String{j-MATH-GEOSCI = "Mathematical Geosciences"}
@String{j-MATH-INTEL = "The Mathematical Intelligencer"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-NACHR = "Mathematische Nachrichten"}
@String{j-MATH-NOTES-ACAD-SCI-USSR = "Mathematical Notes of the {Academy of
Sciences of the USSR = Matematicheskie
Zametki}"}
@String{j-MATH-SOC-SCI = "Mathematical Social Sciences"}
@String{j-MATH-USSR-IZV = "Mathematics of the {USSR} --- Izvestiya"}
@String{j-METAB-CLIN-EXP = "Metabolism, Clinical and Experimental"}
@String{j-METRIKA = "Metrika"}
@String{j-MICROELECT-RELIABILITY = "Microelectronics and Reliability"}
@String{j-MOD-PHYS-LETT-A = "Modern Physics Letters A (MPLA)"}
@String{j-MONAT-MATH = "Monatshefte f{\"u}r Mathematik"}
@String{j-NAMS = "Notices of the American Mathematical Society"}
@String{j-NATURE = "Nature"}
@String{j-NEW-J-PHYS = "New Journal of Physics"}
@String{j-NEW-SCIENTIST = "New Scientist"}
@String{j-NUCL-MED = "Journal of Nuclear Medicine"}
@String{j-NUCLEAR-INSTR-METH-PHYS-RES-A = "Nuclear instruments and methods in
physics research. Section A, Accelerators,
spectrometers, detectors and associated
equipment"}
@String{j-NY-TIMES = "New York Times"}
@String{j-OPER-SYS-REV = "Operating Systems Review"}
@String{j-PAP-REG-SCI = "Papers in Regional Science"}
@String{j-PATTERN-RECOGN-LETT = "Pattern Recognition Letters"}
@String{j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI = "Philosophical transactions
of the Royal Society of London Series B,
Biological sciences"}
@String{j-PHYS-LET-A = "Physics Letters A"}
@String{j-PHYS-REV = "Physical Review"}
@String{j-PHYS-REV-A = "Physical Review A (Atomic, Molecular, and
Optical Physics)"}
@String{j-PHYS-REV-C = "Physical Review C (Nuclear Physics)"}
@String{j-PHYS-REV-E = "Physical Review E (Statistical physics,
plasmas, fluids, and related
interdisciplinary topics)"}
@String{j-PHYS-REV-LET = "Physical Review Letters"}
@String{j-PHYSICA-A = "Physica A: Statistical Mechanics and its
Applications"}
@String{j-PHYSICA-B-PLUS-C = "Physica. B + C; B: Physics of condensed
matter. C: Atomic, molecular and plasma
physics; optics"}
@String{j-PHYSICA-D = "Physica. D, Nonlinear phenomena"}
@String{j-PLOS-MED = "PLoS Medicine"}
@String{j-PLOS-ONE = "PLoS One"}
@String{j-POLIT-ANAL = "Political Analysis"}
@String{j-PROB-ENG-INFO-SCI = "Probability in the Engineering and
Informational Sciences"}
@String{j-PROC-VLDB-ENDOWMENT = "Proceedings of the VLDB Endowment"}
@String{j-PROBAB-SURV = "Probability Surveys"}
@String{j-PROBAB-THEORY-RELAT-FIELDS = "Probability Theory and Related Fields"}
@String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical
Society"}
@String{j-PROC-AMER-PHIL-SOC = "Proceedings of the American Philosophical
Society"}
@String{j-PROC-INST-STATIST-MATH = "Proceedings of the Institute of
Statistical Mathematics"}
@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
Sciences of the United States of America"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI = "Proceedings of the Royal
Society A: Mathematical, Physical, \&
Engineering Sciences"}
@String{j-PROC-R-SOC-LOND-SER-B-BIO-SCI = "Proceedings of the Royal Society of
London. Series B. Biological sciences"}
@String{j-PROG-THEOR-PHYS = "Progress of Theoretical Physics"}
@String{j-PSYCHOL-REP = "Psychological Reports"}
@String{j-Q-J-ECON = "The Quarterly Journal of Economics"}
@String{j-QUAL-QUANT = "Quality \& Quantity"}
@String{j-RAND-STRUCT = "Random Structures and Algorithms"}
@String{j-REG-SCI-URBAN-ECON = "Regional Science and Urban Economics"}
@String{j-RELIABLE-COMPUTING = "Reliable Computing = Nadezhnye
vychisleniia"}
@String{j-RESONANCE = "Resonance"}
@String{j-REV-ECON-STAT = "Review of Economics and Statistics"}
@String{j-REV-INT-ECON = "Review of International Economics"}
@String{j-REV-MOD-PHYS = "Reviews of Modern Physics"}
@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}
@String{j-RUSS-J-MATH-PHYS = "Russian Journal of Mathematical Physics"}
@String{j-SANKHYA-B = "Sankhy{\=a} (Indian Journal of Statistics),
Series B. Methodological"}
@String{j-SCI-AMER = "Scientific American"}
@String{j-SCI-COMPUT = "Scientific Computing"}
@String{j-SCI-REP = "Scientific Reports"}
@String{j-SCIENCE = "Science"}
@String{j-SCIENTOMETRICS = "Scientometrics"}
@String{j-SCRIPTA-MATH = "Scripta Mathematica"}
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@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1--4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2369148",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
author-dates = "March 12, 1835--July 11, 1909",
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''. The article
contains no references to earlier work.",
remark-2 = "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
the earliest citations of Newcomb's work that I have
yet found in connection with Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Simon_Newcomb",
}
@Book{Pareto:1896:CEP,
author = "Vilfredo Pareto",
title = "Cours d'{\'e}conomie politique profess{\'e} a
l'universit{\'e} de {Lausanne}. (French) [{Course} on
political economy given at the {University of
Lausanne}]",
publisher = "F. Rouge",
address = "Lausanne, Switzerland",
pages = "????",
year = "1896--1897",
LCCN = "HB173 .P22",
bibdate = "Wed Nov 16 08:41:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "French",
remark = "Two volumes issued in successive years. The Italian
economist and mathematician, Vilfredo Federico (born in
Paris, France, and initially named Wilfried Fritz)
Pareto (15 July 1848--19 August 1923), introduced the
80--20 rule in economics (80\% of the wealth is owned
by 20\% of the people, which was true at the time in
Italy, and found to be similar in other countries). He
developed the Pareto distribution, in which a random
variable $X$ has the property that the probability that
it is greater than some number $x$ is given by $ {\rm
Pr}(X > x) = (x_m / x)^\alpha $ for $ x > x_m $, and $
{\rm Pr}(X > x) = 1 $ otherwise. The positive value $
x_m $ is a cutoff, and as $ \alpha \to \infty $, the
Pareto distribution approaches a Dirac delta function,
$ \delta (x - x_m) $. When this models the distribution
of wealth, the exponent $ \alpha $ is called the {\em
Pareto index}.",
}
@Article{Doolittle:1910:SNF,
author = "C. L. Doolittle",
title = "{Simon Newcomb, F.R.S., LL.D., D.C.L.}",
journal = j-PROC-AMER-PHIL-SOC,
volume = "49",
number = "197",
pages = "iii--xviii",
month = oct # "\slash " # dec,
year = "1910",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Sat Aug 24 19:37:51 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/procamerphilsoc1900.bib",
URL = "https://www.jstor.org/stable/984092",
acknowledgement = ack-nhfb,
ajournal = "Proc. Amer. Philos. Soc.",
fjournal = "Proceedings of the American Philosophical Society",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "This obituary does not mention Newcomb's short paper
on the leading-digit phenomenon now known as Benford's
Law, but it does give an overview of Newcomb's humble
origins, education, life, and scientific influence.",
}
@Book{Poincare:1912:CPL,
author = "H. Poincar{\'e}",
title = "Calcul des Probabilit{\'e}s: Le{\c{c}}ons
profess{\'e}es pendant le deuxi{\`e} me semestre
1893--1894. ({French}) [{Calculation} of Probabilities:
Lectures from the second semester 1893--1894]",
publisher = "Gauthier-Villars",
address = "Paris, France",
pages = "ii + 274",
year = "1912",
LCCN = "QA273 .P75",
bibdate = "Mon Nov 14 10:08:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
author-dates = "1854--1912",
language = "French",
remark = "See pp. 313--320.",
}
@Article{Auerbach:1913:GBG,
author = "Felix Auerbach",
title = "{Das Gesetz der Bev{\"o}lkerungskonzentration}.
({German}) [{The} law of population concentration]",
journal = "{Petermann's Geographische Mitteilungen}",
volume = "59",
number = "1",
pages = "74--76",
month = "????",
year = "1913",
CODEN = "PGGMA3",
ISSN = "0031-6229",
ISSN-L = "0031-6229",
bibdate = "Thu Nov 24 10:49:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper is reported in \cite{Newman:2005:PLP} to be
the first discovery of {\em Zipf's Law\/} in connection
with city populations (see \cite{Zipf:1932:SSP}). See
also \cite{Estoup:1916:GSM}.",
URL = "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
acknowledgement = ack-nhfb,
ajournal = "Petermanns Geogr. Mitteilung",
ajournal-2 = "Petermanns Geogr. Mitt.",
language = "German",
}
@Article{Stamp:1914:NIP,
author = "J. C. Stamp",
title = "A New Illustration of {Pareto}'s Law",
journal = j-J-R-STAT-SOC,
volume = "77",
number = "2",
pages = "200--204",
month = jan,
year = "1914",
DOI = "https://doi.org/10.2307/2339802",
ISSN = "0952-8385",
ISSN-L = "0952-8385",
bibdate = "Sat Jan 24 11:18:04 MST 2015",
bibsource = "http://www.jstor.org/stable/i315805;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1910.bib",
URL = "http://www.jstor.org/stable/2339802",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
}
@Article{Weyl:1915:GZM,
author = "Hermann Weyl",
title = "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}.
({German}) [{On} the uniform distribution of numbers
mod. one]",
journal = j-MATH-ANN,
volume = "77",
number = "3",
pages = "313--352",
month = "????",
year = "1915",
CODEN = "MAANA3",
DOI = "https://doi.org/10.1007/BF01475864",
ISSN = "0025-5831 (print), 1432-1807 (electronic)",
ISSN-L = "0025-5831",
bibdate = "Sun Nov 13 10:54:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Ann.",
fjournal = "Mathematische Annalen",
journal-URL = "http://link.springer.com/journal/208",
language = "German",
xxyear = "1916",
}
@Book{Estoup:1916:GSM,
author = "J. B. Estoup",
title = "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
pour l'acquisition de la vitesse ({French})
[Stenographic ranges: method and exercises for
achieving speed]",
publisher = "Institut St{\'e}nographique de France",
address = "Paris, France",
edition = "Fourth",
pages = "151",
year = "1916",
LCCN = "????",
bibdate = "Thu Nov 24 14:24:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This on shorthand writing is the earliest known
publication of the power-law distribution of word
frequencies, generally credited to
\cite{Zipf:1932:SSP}.",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
language = "French",
}
@Article{Franel:1917:PTL,
author = "J. Franel",
title = "{{\`A}} propos des tables de logarithmes. ({French})
[{On} tables of logarithms]",
journal = "Festschrift Naturforschenden der Gesellschaft in
Z{\"u}rich Vierteljahrsschrift",
volume = "62",
number = "??",
pages = "286--295",
month = "????",
year = "1917",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 10:09:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Boring:1920:LNL,
author = "Edwin G. Boring",
title = "The Logic of the Normal Law of Error in Mental
Measurement",
journal = j-AMER-J-PSYCHOLOGY,
volume = "31",
number = "1",
pages = "1--33",
month = jan,
year = "1920",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Thu Dec 01 21:35:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1413989",
acknowledgement = ack-nhfb,
fjournal = "The American journal of psychology",
remark = "A citation search in Google Scholar on 1-Dec-2011
found this article as the only one citing Newcomb's
work \cite{Newcomb:1881:NFU} before it was brought to
wider view by Raimi's frequently-cited paper
\cite{Raimi:1976:FDP}. Boring's article has only brief
mention of Newcomb's work, and then solely in
connection with the believed randomness of digits of
transcendental numbers.",
}
@InCollection{Macaulay:1922:PLG,
author = "F. R. Macaulay",
editor = "W. C. Mitchell",
booktitle = "Income in the {United States}: Its Amount and
Distribution: 1909--1919",
title = "{Pareto}'s law and the general problem of mathematical
describing the frequency of distribution of income",
publisher = "National Bureau of Economic Research",
address = "New York, NY, USA",
pages = "??--??",
year = "1922",
LCCN = "????",
bibdate = "Fri Nov 25 09:06:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Yule:1925:MTE,
author = "G. Udny Yule",
title = "A Mathematical Theory of Evolution, Based on the
Conclusions of {Dr. J. C. Willis, F.R.S.}",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI,
volume = "213",
number = "??",
pages = "21--87",
day = "14",
month = may,
year = "1925",
CODEN = "PTRBAE",
DOI = "https://doi.org/10.1098/rstb.1925.0002",
ISSN = "0962-8436 (print), 1471-2970 (electronic)",
ISSN-L = "0962-8436",
bibdate = "Tue Nov 15 10:45:15 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rstb.royalsocietypublishing.org/content/213/402-410/21",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London Series B, Biological sciences",
}
@Article{Lotka:1926:FDS,
author = "Alfred J. Lotka",
title = "The Frequency Distribution of Scientific
Productivity",
journal = j-J-WASH-ACAD-SCI,
volume = "16",
number = "12",
pages = "317--323",
day = "19",
month = jun,
year = "1926",
CODEN = "JWASA3",
ISSN = "0043-0439",
ISSN-L = "0043-0439",
bibdate = "Thu Nov 24 14:36:11 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This is the earliest known publication on the
phenomenon known as Zipf's Law, here applied to
publication counts of chemists and physicists. Lotka's
Law (a term possibly first used in
\cite{Zipf:1949:HBP}) says that the number of authors
producing $n$ publications is about $ 1 / n^2 $ of the
number producing only one. This `law' seems to have
been misunderstood and misapplied in other fields; see
\cite{Potter:1981:LLR}.",
URL = "http://www.jstor.org/stable/24529203",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Washington Academy of Sciences",
journal-URL = "http://www.jstor.org/journal/jwashacadscie",
keywords = "Lotka's Law",
}
@Article{Yule:1927:RS,
author = "G. Udny Yule",
title = "On Reading a Scale",
journal = j-J-R-STAT-SOC,
volume = "90",
number = "3",
pages = "570--587",
month = "????",
year = "1927",
ISSN = "0952-8385",
ISSN-L = "0952-8385",
bibdate = "Wed Nov 23 12:29:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See related later work \cite{Preece:1981:DFD}.",
URL = "http://www.jstor.org/stable/2341205",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
remark = "This paper reports on human bias in the recording of
last digits in measurements, or from roundings, or from
later scale conversions.",
}
@Article{Condon:1928:SV,
author = "E. U. Condon",
title = "Statistics of vocabulary",
journal = j-SCIENCE,
volume = "67",
number = "1733",
pages = "300--??",
day = "16",
month = mar,
year = "1928",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.67.1733.300",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Fri Nov 25 09:04:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
}
@Article{Sun:1928:EFD,
author = "C. P. Sun",
title = "On the Examination of Final Digits by Experiments in
Artificial Sampling",
journal = j-BIOMETRIKA,
volume = "20A",
number = "1/2",
pages = "64--68",
month = jul,
year = "1928",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2331941",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 13:38:07 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315380;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/biometrika1920.bib",
URL = "http://www.jstor.org/stable/2331941",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
}
@Article{Zipf:1929:RFD,
author = "George Kingsley Zipf",
title = "Relative frequency as a determinant of phonetic
change",
journal = "Harvard Studies in Classical Philology",
volume = "40",
number = "??",
pages = "1--95",
month = "????",
year = "1929",
CODEN = "????",
ISSN = "0073-0688",
ISSN-L = "0073-0688",
bibdate = "Fri Nov 25 09:02:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/journals/00730688.html;
http://www.jstor.org/stable/310585",
acknowledgement = ack-nhfb,
}
@Book{Gibrat:1931:IE,
author = "Robert Gibrat",
title = "Les In{\'e}galit{\'e}s {\'e}conomiques",
publisher = "Librairie du Recueil Sirey",
address = "Paris, France",
pages = "286",
year = "1931",
LCCN = "HB251.GIB",
bibdate = "Mon Feb 18 14:43:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
library.ox.ac.uk:210/ADVANCE",
note = "Applications: aux in{\'e}galit{\'e}s des richesses,
{\`a} la concentration des entreprises, aux populations
des villes, aux statistiques des familles, etc. d'une
loi nouvelle. La loi de l'effet proportionnel.",
URL = "http://en.wikipedia.org/wiki/Gibrat%27s_law",
acknowledgement = ack-nhfb,
author-dates = "1904--1980",
remark-1 = "According to at least one library catalog (SWB), this
book may be the author's doctoral dissertation from
l'Universit{\'e} de Paris in 1931.",
remark-2 = "This book is cited as the origin of Gibrat's Law, or
Gibrat's rule of proportionate growth, that ``the size
of a firm and its growth rate are independent''.",
}
@Misc{Anonymous:1932:FL,
author = "Anonymous",
title = "Fishpole Lamp",
howpublished = "Web site",
day = "30",
month = apr,
year = "1932",
bibdate = "Sat Feb 23 14:52:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This Web site reports that General Electric researcher
Frank Benford invented the electric light pointer, the
forerunner of the modern laser pointer.",
URL = "http://scienceservice.si.edu/pages/012020.htm",
acknowledgement = ack-nhfb,
remark = "CD 2478048, E\&MP12.020, Electric Appliances \
Apparatus.",
}
@Book{Zipf:1932:SSP,
author = "George Kingsley Zipf",
title = "Selected studies of the principle of relative
frequency in language",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "51",
year = "1932",
LCCN = "P123 .Z5",
bibdate = "Wed Nov 16 09:03:46 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This book is the origin of {\em Zipf's Law}, but the
phenomenon was apparently first reported two decades
earlier in \cite{Auerbach:1913:GBG} for city
populations, in \cite{Estoup:1916:GSM} for word
frequencies, and in \cite{Lotka:1926:FDS} for
researcher publication counts.",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
subject = "Plautus, Titus Maccius; language and languages;
semantics; comparative linguistics; Chinese language;
phonology; Latin language; glossaries, vocabularies,
etc; dialects; China; Beijing",
}
@Article{Bradford:1934:SIS,
author = "Samuel C. Bradford",
title = "Sources of Information on Specific Subjects",
journal = "Engineering: An Illustrated Weekly Journal (London)",
volume = "137",
number = "??",
pages = "85--86",
day = "26",
month = jan,
year = "1934",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 25 11:47:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper (reprinted in \cite{Bradford:1985:SIS})
introduces an observation later known as Bradford's
Law: there are exponentially-diminishing returns of
extending a search for references in journals.",
URL = "http://en.wikipedia.org/wiki/Bradford%27s_law",
acknowledgement = ack-nhfb,
}
@Book{Zipf:1935:PBL,
author = "George Kingsley Zipf",
title = "The psycho-biology of language: an introduction to
dynamic philology",
publisher = pub-HOUGHTON-MIFFLIN,
address = pub-HOUGHTON-MIFFLIN:adr,
pages = "ix + 336",
year = "1935",
LCCN = "P105 .Z5",
bibdate = "Wed Nov 16 09:07:09 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
subject = "language and languages; semantics; comparative
linguistics",
}
@Article{Keyser:1936:VFD,
author = "C. J. Keyser",
title = "{Vilfredo Federico Damaso Pareto}. {Mathematician},
economist, sociologist",
journal = j-SCRIPTA-MATH,
volume = "4",
number = "??",
pages = "5--23",
month = "????",
year = "1936",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "62.0027.01",
ZBmath = "2525107",
}
@Book{Moon:1936:SBI,
author = "Parry Moon",
title = "The Scientific Basis of Illuminating Engineering",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xi + 608",
year = "1936",
LCCN = "TH7703 .M65",
bibdate = "Mon Nov 14 10:11:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "See pages 420ff.",
}
@Article{Bresciani-Turroni:1937:PL,
author = "C. Bresciani-Turroni",
title = "On {Pareto}'s Law",
journal = j-J-R-STAT-SOC,
volume = "100",
number = "3",
pages = "421--432",
month = "????",
year = "1937",
DOI = "https://doi.org/10.2307/2980528",
ISSN = "0952-8385",
ISSN-L = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349533;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980528",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
}
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See comments about Benford's biased rounding practices
\cite{Diaconis:1979:RP}.",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
ZMnumber = "JFM 64.0555.03; Zbl 0018.26502",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
author-dates = "1883--December 4, 1948",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Frank_Benford",
}
@Article{Bethe:1938:MSE,
author = "H. A. Bethe and M. E. Rose and L. P. Smith",
title = "The Multiple Scattering of Electrons",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "573--585",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Wed Nov 23 14:27:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper, which immediately follows Benford's
\cite{Benford:1938:LAN} in this journal issue, is
reported in \cite[p. 197]{Logan:1978:FDP} to have been
of considerable interest to scientists involved in
secret nuclear physics work in World War II. That is
how Benford's paper ``in a journal of rather limited
circulation and not usually read by mathematicians''
came to be noticed by physicists.",
URL = "http://www.jstor.org/stable/984803",
acknowledgement = ack-nhfb,
author-dates = "Hans Albrecht Bethe (1906--2005)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "Biography supplement in \cite{Lee:2007:HAB} has this
as Proc. Am. Philos. Soc., 89, 373--383 (1938), but
that seems to be wrong: check??",
}
@Article{Benford:1943:PAG,
author = "Frank Benford",
title = "The Probable Accuracy of the General Physical
Constants",
journal = j-PHYS-REV,
volume = "63",
number = "5--6",
pages = "212--212",
month = mar,
year = "1943",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.63.212",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Mon Nov 21 21:52:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.63.212",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See later work \cite{Logan:1978:FDP}, and severe
criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "3924",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Unpublished{Stigler:1945:DLD,
author = "George J. Stigler",
title = "The distribution of leading digits in statistical
tables",
year = "1945",
bibdate = "Sat Nov 12 16:07:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unpublished, but written about 1945--1946, and
presented in an 1975 address at Haskell Hall,
University of Chicago. Stigler's distribution is more
complex than that of Newcomb and Benford. Stigler has $
F_d = (d \ln (d) - (d + 1) \ln (d + 1) + (1 + (10 / 9)
\ln (10))) / 9 $, which gives leading-digit frequencies
of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764,
0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for
a comparison of the Benford and Stigler distributions,
and their relations to Zipf and Pareto distributions.
For derivations of Stigler's distribution, see
\cite{Logan:1978:FDP,Raimi:1985:FDP}.",
URL = "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/",
acknowledgement = ack-nhfb,
remark = "Stigler won the 1982 Sveriges Riksbank Prize in
Economic Sciences in Memory of Alfred Nobel (often
called the Nobel Prize in Economics, although that
field was not among the original ones funded by Nobel's
will).",
}
@Book{Furlan:1946:HSU,
author = "Luigi Vladimir Furlan",
title = "{Das Harmoniegesetz der Statistik: Eine Untersuchung
{\"u}ber die metrische Interdependenz der sozialen
Erscheinungen}. ({German}) [{The} {Law of Harmony} in
statistics: an investigation of the metrical
interdependence of social phenomena]",
volume = "2",
publisher = "Verlag f{\"u}r Recht und Gesellschaft A.-G.",
address = "Basel, Switzerland",
pages = "xii + 504",
year = "1946",
LCCN = "HA29 .F85",
bibdate = "Mon Nov 14 09:40:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "{Beihefte zum Assekuranzjahrbuch}",
acknowledgement = ack-nhfb,
author-dates = "1886--",
keywords = "Benford--Furlan Law",
language = "German",
}
@Article{Geiringer:1948:RVF,
author = "Hilda Geiringer",
title = "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
der Statistik: Eine Untersuchung {\"u}ber die metrische
Interdependenz der sozialen Erscheinungen}. ({German})
[{The} {Law of Harmony} in statistics: an investigation
of the metrical interdependence of social phenomena]",
journal = j-J-AM-STAT-ASSOC,
volume = "43",
number = "242",
pages = "325--328",
month = jun,
year = "1948",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Nov 14 09:42:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See \cite{Furlan:1946:HSU}.",
URL = "http://www.jstor.org/stable/2280379",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Hsu:1948:ESM,
author = "E. H. Hs{\"u}",
title = "An Experimental Study on ``Mental Numbers'' and a New
Application",
journal = j-J-GEN-PSYCH,
volume = "38",
number = "1",
pages = "57--67",
month = "????",
year = "1948",
CODEN = "JGPSAY",
DOI = "https://doi.org/10.1080/00221309.1948.9711768",
ISSN = "0022-1309 (print), 1940-0888 (electronic)",
ISSN-L = "0022-1309",
bibdate = "Sat Jan 07 09:29:53 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
acknowledgement = ack-nhfb,
fjournal = "The Journal of General Psychology",
keywords = "Benford's Law",
onlinedate = "06 Jul 2010",
}
@Book{Hardy:1949:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 396",
year = "1949",
LCCN = "QA295 .H29",
bibdate = "Wed Nov 16 08:14:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
}
@Book{Zipf:1949:HBP,
author = "George Kingsley Zipf",
title = "Human behaviour and the principle of least effort",
publisher = "Hafner Pub. Co.",
address = "New York, NY, USA",
pages = "xi + 573",
year = "1949",
LCCN = "H91 .Z5 1949a",
bibdate = "Tue Nov 15 09:35:14 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
remark = "Reprinted 1965.",
subject = "Human ecology",
}
@Article{Anonymous:1950:BRZ,
author = "Anonymous",
title = "Book review: {Zipf, George K., \booktitle{Human
behavior and the principle of least effort}. Cambridge,
(Mass.): Addison-Wesley, 1949, pp. 573}",
journal = j-J-CLIN-PSYCHOL,
volume = "6",
number = "3",
pages = "306--306",
year = "1950",
CODEN = "JCPYAO",
DOI = "https://doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO%3B2-7",
ISSN = "0021-9762 (print), 1097-4679 (electronic)",
ISSN-L = "0021-9762",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Clinical Psychology",
}
@Book{Feller:1950:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "????",
year = "1950",
LCCN = "QA273 .F37",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@Article{Macon:1950:DFD,
author = "N. Macon and L. Moser",
title = "On the distribution of first digits of powers",
journal = "Scripta Mathematica",
volume = "16",
number = "??",
pages = "290--291",
month = "????",
year = "1950",
CODEN = "????",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
bibdate = "Sat Nov 12 16:28:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica",
}
@Article{Tsuji:1952:UDN,
author = "M. Tsuji",
title = "On the uniform distribution of numbers $ \bmod 1 $",
journal = j-J-MATH-SOC-JPN,
volume = "4",
number = "3--4",
pages = "313--322",
month = "????",
year = "1952",
CODEN = "NISUBC",
DOI = "https://doi.org/10.2969/jmsj/00430313",
ISSN = "0025-5645",
ISSN-L = "0025-5645",
bibdate = "Sun Feb 17 06:33:32 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.jmsj/1261415780",
acknowledgement = ack-nhfb,
fjournal = "Journal of the {Mathematical Society of Japan}",
}
@InProceedings{Mandelbrot:1953:ITS,
author = "Beno{\^\i}t B. Mandelbrot",
editor = "Willis Jackson",
booktitle = "{Communication theory: papers read at a Symposium on
``Applications of Communication Theory'' held at the
Institution of Electrical Engineers, London, September
22nd--26th 1952}",
title = "An Informational Theory of the Statistical Structure
of Languages",
publisher = pub-BUTTERWORTHS,
address = pub-BUTTERWORTHS:adr,
bookpages = "xii + 532",
pages = "486--502",
year = "1953",
LCCN = "Q350 .S92 1952",
bibdate = "Wed Nov 16 09:37:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://lccn.loc.gov/53004215;
http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
acknowledgement = ack-nhfb,
remark = "The paper is incorrectly referenced as a book in
\cite{Baek:2011:ZLU}. Mandelbrot got his Master of
Science in Aeronautics at CalTech in 1948, and his
Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in
1952 in Paris, so perhaps this is a translation of his
thesis work.",
}
@Book{Blackwell:1954:TGS,
author = "David Blackwell and Meyer A. Girshick",
title = "Theory of Games and Statistical Decisions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 355",
year = "1954",
LCCN = "QA269 .B5",
bibdate = "Mon Nov 14 10:04:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catalog.hathitrust.org/Record/000577721",
acknowledgement = ack-nhfb,
author-dates = "David Blackwell (1919--2010)",
keywords = "Benford's Law",
remark = "Brief mention of Benford's Law on page 74, problem
2.7.2 (??).",
}
@Article{Simon:1955:CSD,
author = "Herbert A. Simon",
title = "On a Class of Skew Distribution Functions",
journal = j-BIOMETRIKA,
volume = "42",
number = "3/4",
pages = "425--440",
month = dec,
year = "1955",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2333389",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62.0X",
MRnumber = "0073085 (17,380e)",
MRreviewer = "H. A. David",
bibdate = "Sat Jun 21 14:32:48 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315425;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib",
URL = "http://www.jstor.org/stable/2333389",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
keywords = "distribution of income; distribution of species among
genera; distributions of city populations;
distributions of document word frequencies;
distributions of scientific publication counts; Zipf's
Law",
remark = "This work is an extension of Yule's work
\cite{Yule:1925:MTE}. See discussion
\cite{Mandelbrot:1959:NCS} and comments
\cite{Mitzenmacher:2003:BHG}.",
}
@Article{Devooght:1957:LZM,
author = "J. Devooght",
title = "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the
{Zipf--Mandelbrot} law]",
journal = "Acad. Roy. Belg. Bull. Cl. Sci. (5)",
volume = "43",
pages = "244--251",
year = "1957",
CODEN = "????",
ISSN = "0001-4141",
ISSN-L = "0001-4141",
MRclass = "94.0X",
MRnumber = "0088412 (19,516a)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
des Sciences. Koninklijke Belgische Academie.
Mededelingen van de Klasse der Wetenschappen. 5e
S{\'e}rie",
language = "French",
}
@Book{Feller:1957:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "461 (vol. 1), 626 (vol. 2)",
year = "1957",
LCCN = "QA273 .F3712",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "{Bulletin de l'Institut International de
Statistique}",
volume = "35",
number = "2",
pages = "57--76",
year = "1957",
CODEN = "BISQA3",
ISSN = "????",
MRclass = "62.00",
MRnumber = "0117807 (22 \#8581)",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Internat. Stat.",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
xxvolume = "34 (wrong!)",
}
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "{Atti dell XV e XVII Riunione, Societa Italiana di
Statistica}",
volume = "??",
number = "??",
pages = "205--228",
year = "1957",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Miller:1957:SEI,
author = "George A. Miller",
title = "Some Effects of Intermittent Silence",
journal = j-AMER-J-PSYCHOLOGY,
volume = "70",
number = "2",
pages = "311--314",
month = jun,
year = "1957",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Tue Nov 15 09:40:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1419346",
acknowledgement = ack-nhfb,
fjournal = "The American Journal of Psychology",
keywords = "Zipf's Law",
}
@Book{Zeller:1958:TLG,
author = "Karl Zeller",
title = "{Theorie der Limitierungsverfahren}. (German)
[{Theory} of limiting processes]",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "242",
year = "1958",
LCCN = "QA295 .Z4",
bibdate = "Wed Nov 16 06:43:43 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "{Ergebnisse der Mathematik und ihrer Grenzgebiete}",
acknowledgement = ack-nhfb,
language = "German",
subject = "series; convergence",
}
@Article{Mandelbrot:1959:NCS,
author = "Beno{\^\i}t Mandelbrot",
title = "A note on a class of skew distribution functions:
analysis and critique of a paper by {H. A. Simon}",
journal = j-INF-CONTROL,
volume = "2",
number = "??",
pages = "90--99",
month = apr,
year = "1959",
CODEN = "IFCNA4",
DOI = "https://doi.org/10.1016/S0019-9958(59)90098-1",
ISSN = "0019-9958 (print), 1878-2981 (electronic)",
ISSN-L = "0019-9958",
bibdate = "Wed Nov 16 09:45:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Simon:1955:CSD}.",
abstract = "This note is a discussion of H. A. Simon's model
(1955) concerning the class of frequency distributions
generally associated with the name of G. K. Zipf. The
main purpose is to show that Simon's model is
analytically circular in the case of the linguistic
laws of Estoup--Zipf and Willis--Yule. Insofar as the
economic law of Pareto is concerned, Simon has himself
noted that his model is a particular case of that of
Champernowne; this is correct, with some reservation. A
simplified version of Simon's model is included.",
acknowledgement = ack-nhfb,
fjournal = "Information and Control",
journal-URL = "http://www.sciencedirect.com/science/journal/00199958",
}
@Article{Mandelbrot:1960:PLL,
author = "Beno{\^\i}t Mandelbrot",
title = "The {Pareto--Levy} law and the distribution of
income",
journal = j-INT-ECON-REV,
volume = "1",
number = "??",
pages = "79--106",
month = "????",
year = "1960",
CODEN = "INERAE",
ISSN = "0020-6598 (print), 1468-2354 (electronic)",
ISSN-L = "0020-6598",
bibdate = "Wed Nov 23 11:07:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingenta.com/journals/browse/bpl/iere",
acknowledgement = ack-nhfb,
fjournal = "International Economic Review",
journal-URL = "http://www.jstor.org/journal/inteeconrevi",
}
@Article{Cigler:1961:NET,
author = "J. Cigler and G. Helmberg",
title = "{Neuere Entwicklungen der Theorie der
Gleichverteilung}. ({German}) [{Recent} developments in
the theory of uniform distribution]",
journal = j-DEUTSCH-MATH-V,
volume = "64",
number = "??",
pages = "1--50",
month = "????",
year = "1961",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 16:33:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Jber. Deutsch. Math.--Verein",
language = "German",
}
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851",
ISSN-L = "0003-4851",
bibdate = "Sat Sep 17 10:19:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2237922",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 411",
year = "1962",
LCCN = "QA297 .H28",
MRclass = "65.00",
MRnumber = "0137279",
MRreviewer = "G. E. Forsythe",
bibdate = "Mon Aug 6 07:24:38 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
series = "International Series in Pure and Applied Mathematics",
acknowledgement = ack-nhfb,
HDnumber = "51",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers;
random numbers",
tableofcontents = "1. The difference calculus \\
2. Roundoff noise \\
3. The summation calculus \\
4. Evaluation of infinite series \\
5. Finite difference equations \\
6. The finite Fourier series \\
7--9. Polynomial approximation introduction \\
10. A uniform method for finding formulas \\
11. On finding the error term of a formula \\
12. Formulas for definite integrals \\
13. Indefinite integrals \\
14. Introduction to differential equations \\
15. A general theory of predictor-corrector methods \\
16. Special methods of integrating ordinary
differential equations \\
17--18. Least squares theory and practice \\
19. Chebyshev polynomials \\
20. Rational functions \\
21--22. Periodic functions --- Fourier series \\
23. Nonperiodic functions --- the Fourier integral \\
24. Linear filters --- smoothing and differentiating
\\
25. Integrals and differential equations \\
26. Exponential approximation \\
27. Singularities \\
28. On finding zeros \\
29. Simultaneous linear algebraic equations \\
30. Inversion of matrices and eigenvalues \\
31. Some examples of the simulation of situations and
processes \\
32. Random numbers and Monte Carlo methods \\
$N+1$: The art of computing for scientists and
engineers",
}
@TechReport{Mandelbrot:1962:SNR,
author = "Beno{\^\i}t Mandelbrot",
title = "Statistics of natural resources and the law of
{Pareto}",
type = "Research Note",
number = "NC-146",
institution = "IBM",
address = "Yorktown Heights, NY, USA",
day = "29",
month = jun,
year = "1962",
bibdate = "Mon Sep 10 17:35:59 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Weaver:1963:LLT,
author = "Warren Weaver",
title = "{Lady Luck}: The Theory of Probability",
publisher = "Doubleday Anchor Series",
address = "New York, NY, USA",
pages = "392",
year = "1963",
LCCN = "QA273 .W4",
bibdate = "Mon Nov 14 09:54:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Benford's Law is discussed on pp. 270--277.",
acknowledgement = ack-nhfb,
author-dates = "Warren, Weaver (1894--1978)",
remark = "Reprinted in \cite{Weaver:1982:LLT}.",
}
@Article{Cigler:1964:MSU,
author = "J. Cigler",
title = "Methods of summability and uniform distribution $
\bmod 1 $",
journal = j-COMPOS-MATH,
volume = "16",
number = "??",
pages = "44--51",
year = "1964",
CODEN = "CMPMAF",
ISSN = "0010-437X (print), 1570-5846 (electronic)",
ISSN-L = "0010-437X",
bibdate = "Mon Nov 14 10:15:31 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Compositio Mathematica",
}
@Article{Good:1965:LE,
author = "I. J. Good",
title = "Letter to the Editor",
journal = j-AMER-STAT,
volume = "19",
number = "3",
pages = "43--43",
month = jun,
year = "1965",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 09:56:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2681423",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law",
remark = "Refers to \cite{Pinkham:1961:DFS}, and cites a review
of that article published by Good in Mathematical
Reviews (1962), page 214, which I have not yet been
able to locate.",
}
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
ISSN-L = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. They conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}
@Article{Konheim:1965:MDT,
author = "Alan G. Konheim",
title = "Mantissa Distributions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "143--144",
month = apr,
year = "1965",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2004111",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Zipf:1965:PBL,
author = "George Kingsley Zipf",
title = "The psycho-biology of language: an introduction to
dynamic philology",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xv + 336",
year = "1965",
LCCN = "P105 .Z5 1965",
bibdate = "Wed Nov 16 09:07:09 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1950",
remark = "Reprint of \cite{Zipf:1935:PBL}.",
subject = "language; philology; semantics; psycholinguistics;
comparative linguistics",
}
@Article{Ball:1966:BRB,
author = "R. J. Ball",
title = "Book Review: {{\booktitle{Random Processes and the
Growth of Firms: A Study of the Pareto Law}}, by Josef
Steindl}",
journal = j-J-R-STAT-SOC-SER-A-GENERAL,
volume = "129",
number = "4",
pages = "600--601",
month = "????",
year = "1966",
CODEN = "JSSAEF",
DOI = "https://doi.org/10.2307/2982275",
ISSN = "0035-9238",
ISSN-L = "0035-9238",
bibdate = "Sat Jan 24 11:18:12 MST 2015",
bibsource = "http://www.jstor.org/stable/i349635;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1960.bib",
URL = "http://www.jstor.org/stable/2982275",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series A
(General)",
journal-URL = "http://www.jstor.org/journals/00359238.html",
}
@Book{Feller:1966:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xviii + 626",
year = "1966",
ISSN = "0271-6232",
LCCN = "QA273 .F3727 1966",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
remark = "Benford's Law is discussed on p. 62.",
}
@Article{Flehinger:1966:PRI,
author = "B. J. (Betty J.) Flehinger",
title = "On the probability that a random integer has initial
digit {$A$}",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "10",
pages = "1056--1061",
month = dec,
year = "1966",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2314636",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Sat Nov 12 15:33:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2314636",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Petersen:1966:RMT,
author = "Gordon Marshall Petersen",
title = "Regular Matrix Transformations",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "viii + 142",
year = "1966",
LCCN = "QA263 .P415 1966",
bibdate = "Mon Nov 14 10:18:15 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Duncan:1967:AUD,
author = "R. L. Duncan",
title = "An Application of Uniform Distributions to the
{Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "5",
number = "2",
pages = "137--140",
month = apr,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:52 MDT 2011",
bibsource = "http://www.fq.math.ca/5-2.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Groos:1967:BCB,
author = "Ole V. Groos",
title = "Brief Communications: {Bradford's Law} and the
{Keenan--Atherton} data",
journal = j-AM-DOC,
volume = "18",
number = "1",
pages = "46--46",
month = jan,
year = "1967",
CODEN = "AMDOA7",
DOI = "https://doi.org/10.1002/asi.5090180108",
ISSN = "0096-946X (print), 1936-6108 (electronic)",
ISSN-L = "0096-946X",
bibdate = "Fri Sep 11 06:21:26 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amdoc.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Documentation",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643/",
onlinedate = "23 Apr 2007",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See \cite{Diaconis:1979:RP} for further work.",
URL = "http://muse.jhu.edu/journals/dem/;
http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
http://www.jstor.org/stable/2060324",
abstract = "When percentages are computed for counts in several
categories or for several positive measurements0 each
taken as a fraction of their sum, the rounded
percentages often fail to add to 100 percent. We
investigate how frequently this failure occurs and what
the distributions of sums of rounded percentages are
for (1) an empirical set of data, (2) the multinomial
distribution in small samples, (3) spacings between
points dropped on an interval --- the broken-stick
model; and (4) for simulation for several categories.
The several methods produce similar distributions.We
find that the probability that the sum of rounded
percentages adds to exactly 100 percent is certain for
two categories, about three-fourths for three
categories, about two-thirds for four categories, and
about [Formula: see text] for larger numbers of
categories, c, on the average when categories are not
improbable.",
acknowledgement = ack-nhfb,
fjournal = "Demography",
pubmedid = "21318695",
}
@Article{Adhikari:1968:DMS,
author = "A. K. Adhikari and B. P. Sarkar",
title = "Distribution of most significant digit in certain
functions whose arguments are random variables",
journal = j-SANKHYA-B,
volume = "30",
number = "??",
pages = "47--58",
month = "????",
year = "1968",
CODEN = "SANBBV",
ISSN = "0976-8386 (print), 0976-8394 (electronic)",
ISSN-L = "0976-8394",
bibdate = "Sat Nov 12 16:09:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Book{Feller:1968:IPT,
author = "William Feller",
title = "Introduction to Probability Theory and its
Applications",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xviii + 509",
year = "1968",
ISBN = "0-471-25708-7",
ISBN-13 = "978-0-471-25708-0",
LCCN = "QA273 .F3713",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a
discussion of flaws in the derivation of Benford's Law
in this book.",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
remark = "Pages 63--64 (of xxiv + 669) in 1971 printing have
only brief mention of two papers
\cite{Benford:1938:LAN,Pinkham:1961:DFS}.",
}
@Article{Shenton:1968:PDM,
author = "L. R. Shenton",
title = "Periodicity and Density of Modified {Fibonacci}
Sequences",
journal = j-FIB-QUART,
volume = "6",
number = "2",
pages = "109--116",
month = apr,
year = "1968",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:02 MDT 2011",
bibsource = "http://www.fq.math.ca/6-2.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/6-2/shenton.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Wilk:1968:PPM,
author = "M. B. Wilk and R. Gnanadesikan",
title = "Probability Plotting Methods for the Analysis of
Data",
journal = j-BIOMETRIKA,
volume = "55",
number = "1",
pages = "1--17",
month = mar,
year = "1968",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2334448",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 14:33:29 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315458;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
URL = "http://www.jstor.org/stable/2334448",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
keywords = "empirical cumulative distribution function (ECDF);
percent ($p$--$p$) plots; quantile ($q$--$q$) plots",
remark = "This article does not mention Benford's Law, but MJN
\cite{Nigrini:2012:BLA} lists this reference for
analysis of data.",
}
@Article{Adhikari:1969:SRD,
author = "A. K. Adhikari",
title = "Some results on the distribution of the most
significant digit",
journal = j-SANKHYA-B,
volume = "31",
number = "??",
pages = "413--420",
month = "????",
year = "1969",
CODEN = "SANBBV",
ISSN = "0976-8386 (print), 0976-8394 (electronic)",
ISSN-L = "0976-8394",
bibdate = "Sat Nov 12 16:12:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{Bumby:1969:FAM,
author = "R. Bumby and E. Ellentuck",
title = "Finitely additive measures and the first digit
problem",
journal = j-FUNDAM-MATH,
volume = "65",
number = "??",
pages = "33--42",
month = "????",
year = "1969",
CODEN = "????",
ISSN = "0016-2736 (print), 1730-6329 (electronic)",
ISSN-L = "0016-2736",
bibdate = "Sat Nov 12 16:19:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fundamenta mathematicae",
}
@Article{Duncan:1969:NID,
author = "R. L. Duncan",
title = "Note on the Initial Digit Problem",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "474--475",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Fairthorne:1969:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "25",
number = "4",
pages = "313--343",
month = dec,
year = "1969",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026481",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprinted in \cite{Fairthorne:2005:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Unpublished{Hafner:1969:CSR,
author = "Everett M. Hafner",
title = "Circular slide roulette",
year = "1969",
bibdate = "Mon Nov 14 10:00:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unpublished but dated 1969. Presented in 1975 in an
address at Hampshire College, Amherst, MA, USA",
acknowledgement = ack-nhfb,
}
@Article{Haight:1969:TPD,
author = "F. A. Haight",
title = "Two probability distributions connected with {Zipf}'s
rank-size conjecture",
journal = j-ZASTOS-MAT,
volume = "10",
pages = "225--228",
year = "1969",
CODEN = "ZAMTAK",
ISSN = "0044-1899",
ISSN-L = "0044-1899",
MRclass = "62.31",
MRnumber = "0246425 (39 \#7729)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Polska Akademia Nauk. Instytut Matematyczny.
Zastosowania Matematyki",
}
@Article{Holewijn:1969:UDS,
author = "Dr. P. J. Holewijn",
title = "On the uniform distribution of sequences of random
variables",
journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
volume = "14",
number = "2",
pages = "89--92",
month = "????",
year = "1969",
CODEN = "ZWVGAA",
DOI = "https://doi.org/10.1007/BF00537514",
ISSN = "0044-3719",
ISSN-L = "0044-3719",
bibdate = "Sat Apr 26 19:23:29 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
URL = "http://link.springer.com/article/10.1007/BF00537514",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
verwandte Gebiete",
journal-URL = "http://link.springer.com/journal/440",
}
@Book{Knuth:1969:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Article{Kuipers:1969:RPR,
author = "L. Kuipers",
title = "Remark on a Paper by {R. L. Duncan} Concerning the
Uniform Distribution Mod $1$ of the Sequence of the
Logarithms of the {Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "465--466",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Raimi:1969:DFS,
author = "R. A. Raimi",
title = "On the Distribution of First Significant Figures",
journal = j-AMER-MATH-MONTHLY,
volume = "76",
number = "4",
pages = "342--348",
month = apr,
year = "1969",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2316424",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:39:22 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Raimi:1969:PDF,
author = "R. Raimi",
title = "The peculiar distribution of first significant
digits",
journal = j-SCI-AMER,
volume = "221",
number = "6",
pages = "109--120",
month = dec,
year = "1969",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican1269-109",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat Nov 12 16:39:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@PhdThesis{Wong:1969:GDS,
author = "James Teng Wong",
title = "On the Generalization of the Distribution of the
Significant Digits Under Computation",
type = "{Ph.D.} thesis",
school = "Department of Mathematics, Oregon State University",
address = "Corvallis, OR, USA",
pages = "52",
year = "1969",
bibdate = "Fri Nov 25 15:41:42 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/302476508?accountid=14677",
acknowledgement = ack-nhfb,
}
@Article{Aigner:1970:EPL,
author = "Dennis J. Aigner and Arthur S. Goldberger",
title = "Estimation of {Pareto's Law} from Grouped
Observations",
journal = j-J-AM-STAT-ASSOC,
volume = "65",
number = "330",
pages = "712--723",
month = jun,
year = "1970",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:44 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314212;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2284582",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Blum:1970:SID,
author = "M. Blum",
title = "On the Sums of Independently Distributed {Pareto}
Variates",
journal = j-SIAM-J-APPL-MATH,
volume = "19",
number = "1",
pages = "191--198",
month = jul,
year = "1970",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@Article{Brown:1970:MOU,
author = "J. L. {Brown, Jr.} and R. L. Duncan",
title = "Modulo One Uniform Distribution of the Sequence of
Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "8",
number = "5",
pages = "482--486",
month = dec,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:31 MDT 2011",
bibsource = "http://www.fq.math.ca/8-5.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See remark \cite{Kuipers:1973:RPD}.",
URL = "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "8",
pages = "1609--1625",
month = oct,
year = "1970",
CODEN = "BSTJAN",
ISSN = "0005-8580",
ISSN-L = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is include.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Hill:1970:ZLP,
author = "Bruce M. Hill",
title = "{Zipf}'s law and prior distributions for the
composition of a population",
journal = j-J-AM-STAT-ASSOC,
volume = "65",
number = "331",
pages = "1220--1232",
month = sep,
year = "1970",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62.35",
MRnumber = "0279936 (43 \#5657)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.jstor.org/stable/2284288",
ZMnumber = "Zbl 0224.92011",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Orlov:1970:GZM,
author = "Ju. K. Orlov",
title = "A generalization of the {Zipf--Mandelbrot} law",
journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
volume = "57",
pages = "37--40",
year = "1970",
CODEN = "????",
ISSN = "????",
MRclass = "94.50",
MRnumber = "0274234 (42 \#9109)",
MRreviewer = "T. Nemetz",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sakharth. SSR Mech. Akad. Moambe",
}
@Article{Taguchi:1970:ZLC,
author = "Tokio Taguchi",
title = "On {Zipf}'s law. {A} characterization of distributions
in linguistics and demography",
journal = j-PROC-INST-STATIST-MATH,
volume = "17",
pages = "83--90",
year = "1970",
CODEN = "????",
ISSN = "0912-6112",
ISSN-L = "0912-6112",
bibdate = "Sat Nov 12 10:39:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0238.68026",
acknowledgement = ack-nhfb,
ajournal = "Proc. Inst. Statist. Math.",
classmath = "68Q45 (Formal languages)",
fjournal = "Proceedings of the Institute of Statistical
Mathematics",
language = "Japanese",
}
@Book{Zeller:1970:TLG,
author = "Karl Zeller and Wolfgang Beekmann",
title = "{Theorie der Limitierungsverfahren}. (German)
[{Theory} of limiting processes]",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xii + 314",
year = "1970",
LCCN = "QA295 .Z4 1970",
bibdate = "Wed Nov 16 06:43:43 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Ergebnisse der Mathematik und ihrer Grenzgebiete",
acknowledgement = ack-nhfb,
language = "German",
subject = "series; convergence",
}
@Article{Thorp:1971:PCD,
author = "E. Thorp and R. Whitley",
title = "{Poincar{\'e}}'s conjecture and the distribution of
digits in logarithm tables",
journal = j-COMPOS-MATH,
volume = "21",
number = "??",
pages = "233--250",
month = "????",
year = "1971",
CODEN = "CMPMAF",
ISSN = "0010-437X (print), 1570-5846 (electronic)",
ISSN-L = "0010-437X",
bibdate = "Sat Nov 12 16:36:41 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Comp. Math.",
fjournal = "Compositio Mathematica",
}
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = j-FIB-QUART,
volume = "9",
number = "1",
pages = "87--88",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:33 MDT 2011",
bibsource = "http://www.fq.math.ca/9-1.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Aigner:1972:CEP,
author = "Dennis J. Aigner and Arthur S. Goldberger",
title = "Corrigenda: Estimation of {Pareto's Law} from Grouped
Observations",
journal = j-J-AM-STAT-ASSOC,
volume = "67",
number = "337",
pages = "252--252",
month = mar,
year = "1972",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:45 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314217;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2284755",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Krevitt:1972:BCC,
author = "Beth Krevitt and Belver C. Griffith",
title = "Brief Communications: A comparison of several
{Zipf}-type distributions in their goodness of fit to
language data",
journal = j-J-AM-SOC-INF-SCI,
volume = "23",
number = "3",
pages = "220--221",
month = may,
year = "1972",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630230310",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:44 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Krevitt:1972:CSZ,
author = "Beth Krevitt and Belver C. Griffith",
title = "A comparison of several {Zipf}-type distributions in
their goodness of fit to language data",
journal = j-J-AM-SOC-INF-SCI,
volume = "23",
number = "3",
pages = "220--221",
year = "1972",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630230310",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Varian:1972:LEB,
author = "Hal R. Varian",
title = "Letter to the {Editor}: {Benford's Law}",
journal = j-AMER-STAT,
volume = "26",
number = "3",
pages = "65--66",
month = jun,
year = "1972",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
abstract = "Around 1938 the physicist Frank Benford observed a
rather strange fact: tables of logarithms in libraries
tend to be dirtier at the beginning than at the end.
This indicated to Benford that people had more occasion
to calculate with numbers beginning with 1 or 2 than
with 8 or 9.\par
Benford also found that the frequency of the digit $p$
being the first digit of a decimal number was very
closely approximated by $ \log (p + 1) - \log p $
[i.e., $ \log (1 + 1 / p) $ ]. This has become known as
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Vlachy:1972:VFS,
author = "Jan Vlach{\'y}",
title = "Variable Factors in Scientific Communities
(Observations on {Lotka's Law})",
journal = "Teorie a Metoda",
volume = "4",
number = "??",
pages = "91--120",
month = "????",
year = "1972",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 25 07:53:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
xxvolume = "6",
}
@Article{Whitney:1972:MNI,
author = "R. E. Whitney",
title = "Mathematical Notes: Initial Digits for the Sequence of
Primes",
journal = j-AMER-MATH-MONTHLY,
volume = "79",
number = "2",
pages = "150--152",
month = feb,
year = "1972",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2316536",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:38 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Wilkinson:1972:ABL,
author = "Elizabeth A. Wilkinson",
title = "The Ambiguity of {Bradford's Law}",
journal = j-J-DOC,
volume = "28",
number = "2",
pages = "122--130",
month = "????",
year = "1972",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026534",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:20:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@TechReport{Diaconis:1973:LMI,
author = "Persi Diaconis",
title = "Limits of measures of the integers with applications
to random number generators and the distribution of
leading digits",
type = "Memorandum",
number = "NS-211",
institution = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
day = "22",
month = mar,
year = "1973",
bibdate = "Sat Nov 12 16:23:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Kreifelts:1973:OBG,
author = "Thomas Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
Basis for a Floating-Point Arithmetic]",
journal = j-COMPUTING,
volume = "11",
number = "4",
pages = "353--363",
month = dec,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "See correction \cite{Kreifelts:1975:OBF}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West
Germany",
classification = "723; 921; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "base; computer programming; floating point arithmetic;
mathematical techniques; optimal choice; rounding
errors",
language = "German",
}
@Article{Kuipers:1973:RPD,
author = "L. Kuipers and Jau-shyong Shiue",
title = "Remark on a Paper by {Duncan} and {Brown} on the
Sequence of Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "11",
number = "3",
pages = "292--293",
month = oct,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:42 MDT 2011",
bibsource = "http://www.fq.math.ca/11-3.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See \cite{Brown:1970:MOU}.",
URL = "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Loynes:1973:SRP,
author = "R. M. Loynes",
title = "Some results in the probabilistic theory of asymptotic
uniform distribution modulo 1",
journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
volume = "26",
number = "1",
pages = "33--41",
month = "????",
year = "1973",
CODEN = "ZWVGAA",
DOI = "https://doi.org/10.1007/BF00533958",
ISSN = "0044-3719",
ISSN-L = "0044-3719",
bibdate = "Sat Apr 26 19:24:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
URL = "http://link.springer.com/article/10.1007/BF00533958",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
verwandte Gebiete",
journal-URL = "http://link.springer.com/journal/440",
}
@Article{Murphy:1973:BCL,
author = "Larry J. Murphy",
title = "Brief Communications: ``{Lotka's Law} in the
humanities?''",
journal = j-J-AM-SOC-INF-SCI,
volume = "24",
number = "6",
pages = "461--462",
month = nov,
year = "1973",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630240607",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:48 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Murphy:1973:LLH,
author = "Larry J. Murphy",
title = "{Lotka's Law} in the Humanities?",
journal = j-J-AM-SOC-INF-SCI,
volume = "24",
number = "6",
pages = "461--462",
month = nov # "\slash " # dec,
year = "1973",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630240607",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:09:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Petruszewycz:1973:LLE,
author = "M. Petruszewycz",
title = "{L'histoire} de la loi d'{Estoup--Zipf}: documents.
({French}) [{The} history of the {Estoup--Zipf} law]",
journal = "Math. Sci. Humaines",
volume = "??",
number = "44",
pages = "41--56",
year = "1973",
CODEN = "????",
ISSN = "0025-5815",
ISSN-L = "0025-5815",
MRclass = "92A25",
MRnumber = "0354071 (50 \#6553)",
MRreviewer = "J. S. Joel",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Centre de Math{\'e}matique Sociale. \'Ecole Pratique
des Hautes \'Etudes. Math{\'e}matiques et Sciences
Humaines",
language = "French",
}
@Article{Sarkar:1973:OSD,
author = "B. P. Sarkar",
title = "An observation on the significant digits of the
binomial coefficients and factorials",
journal = j-SANKHYA-B,
volume = "35",
number = "??",
pages = "363--364",
month = "????",
year = "1973",
CODEN = "SANBBV",
ISSN = "0976-8386 (print), 0976-8394 (electronic)",
ISSN-L = "0976-8394",
bibdate = "Sat Nov 12 16:29:39 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{Schatte:1973:VMG,
author = "Peter Schatte",
title = "{Zur Verteilung der Mantisse in der
Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
({German}) [Distribution of the mantissa in the
floating-point representation of a random variable]",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "??",
pages = "553--565",
month = "????",
year = "1973",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "490--494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Banks:1974:AMN,
author = "William P. Banks and David K. Hill",
title = "The apparent magnitude of number scaled by random
production",
journal = j-J-EXP-PSYCH-GEN,
volume = "102",
number = "2",
pages = "353--376",
month = feb,
year = "1974",
CODEN = "JPGEDD",
DOI = "https://doi.org/10.1037/h0035850",
ISSN = "0096-3445 (print), 1939-2222 (electronic)",
ISSN-L = "0096-3445",
bibdate = "Fri Feb 15 06:32:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://psycnet.apa.org/journals/xge/102/2/353/;
http://psycnet.apa.org/psycinfo/1974-24305-001",
acknowledgement = ack-nhfb,
fjournal = "Journal of Experimental Psychology: General",
}
@PhdThesis{Diaconis:1974:WSA,
author = "Persi Diaconis",
title = "Weak and Strong Averages in probability and the theory
numbers",
type = "{Ph.D.} thesis",
school = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
pages = "xvii + 117",
year = "1974",
bibdate = "Mon Nov 14 10:26:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Duran:1974:ACS,
author = "J. Peter Duran",
title = "Almost convergence, summability and ergodicity",
journal = j-CAN-J-MATH,
volume = "26",
number = "??",
pages = "372--387",
month = "????",
year = "1974",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1974-039-6",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:45 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v26/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
remark = "In relation to Benford's Law, see theorem 6.2.",
}
@Article{Hill:1974:RFF,
author = "Bruce M. Hill",
title = "The rank-frequency form of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "1017--1026",
month = dec,
year = "1974",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15",
MRnumber = "0426242 (54 \#14188)",
MRreviewer = "S. M. Samuels",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0301.60011",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
USA",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
}
@Book{Kuipers:1974:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 390",
year = "1974",
ISBN = "0-471-51045-9",
ISBN-13 = "978-0-471-51045-1",
LCCN = "QA292 .K84",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "``A Wiley-Interscience publication.''.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@Article{Schorr:1974:LLL,
author = "Alan E. Schorr",
title = "{Lotka's Law} and Library Science",
journal = "RQ",
volume = "14",
number = "1",
pages = "32--33",
month = "Fall",
year = "1974",
CODEN = "????",
ISSN = "0033-7072",
ISSN-L = "0033-7072",
bibdate = "Fri Nov 25 08:12:46 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "RQ",
fjournal = "Reference Quarterly",
}
@Unpublished{Singmaster:1974:RSB,
author = "D. Singmaster",
title = "Recurrent sequences and {Benford}'s law",
year = "1974",
bibdate = "Sat Nov 12 16:25:29 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Preprint submitted to Fibonacci Quarterly in 1974, but
never published there.",
acknowledgement = ack-nhfb,
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Prentice-Hall Series in Automatic Computation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Compiling (Electronic computers); Computation by
computer systems --- Floating point representation;
Floating-point arithmetic; IBM 360 (Computer) ---
Programming",
remark = "From p. 116: ``There is general agreement that the
mantissas of floating-point numbers are not uniformly
distributed. [See Hamming (1962)
[\cite{Hamming:1962:NMS}], Pinkham (1961)
[Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
Instead, it is customary to assume that they are
distributed logarithmically, that is, that the
probability density function is
$$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
\leq m \leq 1. $$
This assumption is based on the following observations:
First, this distribution reproduces itself under
multiplication, but a uniform distribution does not.
[See Hamming (1962) [\cite{Hamming:1962:NMS}] and
Exercise 20.] A second justification is based on the
fact that many of the numbers that arise in computation
represent measurable quantities such as lengths,
forces, etc., and it is reasonable to believe that the
distribution of the mantissas of such quantities is
independent of the units in which they are measured.
Pinkham (1961) shows that this leads to the conclusion
that the distribution of mantissas must be
logarithmic.''",
reviewer = "F. J. Murray",
tableofcontents = "Preface / ix \\
1. Floating-Point Number Systems / 1 \\
1.1 Fixed-Point Calculation / 1 \\
1.2 Floating-Decimal Representation of Numbers / 4 \\
1.3 Floating-Decimal Arithmetic / 6 \\
1.4 Floating-Point Number Systems / 9 \\
1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
1.6 Laws of Algebra / 14 \\
1.7 Inequalities in FP(r,p, c) / 21 \\
1.8 FP(r, p, clq) / 22 \\
1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
1.10 Division / 33 \\
Exercises / 35 \\
2. Floating-Point Overflow and Underflow / 39 \\
2.1 Bounds for Exponents / 39 \\
2.2 $\Omega$-Zero Fixup / 41 \\
2.3 Interrupt / 44 \\
2.4 Messages and Tests / 46 \\
2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
2.6 Example / 50 \\
2.7 Counting Mode / 57 \\
2.8 Gradual Underflow / 59 \\
2.9 Imprecise Interrupt / 61 \\
2.10 Changing the Treatment of Spill / 62 \\
2.11 Virtual Overflow and Underflow / 64 \\
2.12 Division by Zero and Indeterminant Forms / 66 \\
Exercises / 67 \\
3. Error Analysis / 71 \\
3.1 Significant Digits / 71 \\
3.2 Relative Error / 73 \\
3.3 Relative Error in FP(r,p, clq) / 75 \\
3.4 Approximate Laws of Algebra / 80 \\
3.5 Propagation of Rounding Error / 87 \\
3.6 X**N / 92 \\
3.7 Condition / 98 \\
3.8 Error Analysis of a Program / 103 \\
3.9 Backward Error Analysis / 105 \\
3.10 Examples / 107 \\
3.11 Changing the Problem / 109 \\
3.12 Statistical Error Analysis / 113 \\
Exercises / 117 \\
4. Example / 123 \\
4.1 Quadrature / 123 \\
4.2 Power Series / 130 \\
4.3 Exact Sums and Differences in FP(r, p, clq) / 137
\\
4.4 Dismantling Floating-Point Numbers / 143 \\
Exercises / 146 \\
5. Double-Precision Calculation / 154 \\
5.1 Programs Using Double-Precision Arithmetic / 155
\\
5.2 Implicit Typing of Names / 162 \\
5.3 Routines to Perform Double-Precision Arithmetic /
163 \\
5.4 Double-Precision Multiplication / 165 \\
5.5 Double-Precision Addition and Subtraction / 168 \\
5.6 Double-Precision Division / 171 \\
5.7 Writing Double-Precision Programs Without Language
Support / 178 \\
5.8 Uses of Double-Precision / 180 \\
5.9 Higher-Precision Arithmetic / 185 \\
Exercises / 186 \\
6. Rounding / 189 \\
6.1 General Considerations / 189 \\
6.2 Uses of Rounding / 191 \\
6.3 Implementation of Rounding / 192 \\
6.4 Bias Removal / 194 \\
6.5 Other ``Rounding'' Procedures / 197 \\
Exercises / 198 \\
7. Automatic Analysis of Error / 201 \\
7.1 Introduction / 201 \\
7.2 Significance Arithmetic / 202 \\
7.3 Noisy Mode / 205 \\
7.4 Interval Arithmetic / 207 \\
7.5 Rerunning the Program in Higher-Precision / 213 \\
Exercises / 222 \\
8. Radix Conversion / 224 \\
8.1 Equivalent Number of Digits / 224 \\
8.2 Properties of Conversion Transformations / 228 \\
8.3 Conversion Techniques / 232 \\
Exercises / 238 \\
9/ Carefully Written Programs / 240 \\
9.1 Introduction / 240 \\
9.2 Average Problem / 240 \\
9.3 Quadratic Equation / 246 \\
Exercises / 252 \\
10. Checking and Testing / 255 \\
10.1 Range Checking / 255 \\
10.2 Mathematical Checks / 256 \\
10.3 Testing / 259 \\
Exercises / 261 \\
11. Language Features for Floating-Point Computation /
263 \\
11.1 Introduction / 263 \\
11.2 Predictability, Controllability, Observability /
264 \\
11.3 Ease of Programming / 265 \\
11.4 Machine Independence / 267 \\
Exercises / 269 \\
12. Floating-Point Hardware / 271 \\
12.1 Choice of Radix / 271 \\
12.2 The Representation of Floating-Point Numbers / 273
\\
12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
12.4 Unnormalized Numbers and Unnormalized Arithmetic /
278 \\
Exercises / 282 \\
13. Complex Numbers / 285 \\
13.1 Programs Using Complex Numbers / 285 \\
13.2 Relative Error / 286 \\
13.3 Complex Arithmetic / 287 \\
Exercises / 297 \\
Bibliography / 301 \\
Glossary of Symbols / 309 \\
Index / 311",
}
@Article{Tsao:1974:DSD,
author = "Nai Kuan Tsao",
title = "On the Distributions of Significant Digits and
Roundoff Errors",
journal = j-CACM,
volume = "17",
number = "5",
pages = "269--271",
month = may,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "49 6595",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Mon Jan 22 07:26:38 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Generalized logarithmic law is derived for the
distribution of the first $t$ significant digits of a
random digital integer. This result is then used to
determine the distribution of the roundoff errors in
floating-point operations, which is a mixture of
uniform and reciprocal distributions.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "921",
corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "Benford's Law; digital arithmetic; digital integer;
distributions; error analysis; floating point
operations; Law of Anomalous Numbers; logarithmic law;
mathematical techniques; mean value; random;
reciprocal; roundoff errors; significant digits;
uniform distribution; variance; Zipf's Law",
oldlabel = "Tsao74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}
@Article{Voos:1974:BCL,
author = "Henry Voos",
title = "Brief Communications: {Lotka} and information
science",
journal = j-J-AM-SOC-INF-SCI,
volume = "25",
number = "4",
pages = "270--272",
month = jul,
year = "1974",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630250410",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:50 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Voos:1974:LIS,
author = "Henry Voos",
title = "{Lotka} and Information Science",
journal = j-J-AM-SOC-INF-SCI,
volume = "25",
number = "4",
pages = "270--272",
month = jul # "\slash " # aug,
year = "1974",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:14:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
keywords = "Lotka's Law",
}
@Article{Yavuz:1974:ZLE,
author = "Davras Yavuz",
title = "{Zipf}'s law and entropy",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "20",
number = "5",
pages = "650--650",
year = "1974",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.1974.1055269",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Sat Nov 12 10:43:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0295.94048",
acknowledgement = ack-nhfb,
classmath = "94A15 (General topics of information theory)",
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@InProceedings{Bennett:1975:SDI,
author = "John M. Bennett",
booktitle = "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
title = "Storage design for information retrieval: {Scarrott}'s
conjecture and {Zipf}'s law",
publisher = "????",
address = "????",
pages = "233--237",
year = "1975",
bibdate = "Sat Nov 12 10:49:15 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0322.68068",
acknowledgement = ack-nhfb,
classmath = "68P20 (Information storage and retrieval) 68N01
(General)",
}
@Book{Hardy:1975:ITN,
author = "Godfrey H. Hardy and Edward M. Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
edition = "Fourth",
pages = "421",
year = "1975",
ISBN = "0-19-853310-1",
ISBN-13 = "978-0-19-853310-8",
LCCN = "????",
bibdate = "Fri Jun 24 12:32:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1975:SFZ,
author = "Bruce M. Hill and Michael Woodroofe",
title = "Stronger forms of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "70",
number = "349",
pages = "212--219",
month = mar,
year = "1975",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15 (62D05)",
MRnumber = "0440763 (55 \#13633)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0326.92014",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Kemperman:1975:BDM,
author = "J. H. B. Kemperman",
title = "Bounds on the discrepancy modulo $1$ of a real random
variable",
journal = j-BULL-INST-MATH-STAT,
volume = "4",
number = "1",
pages = "138--138",
month = "????",
year = "1975",
CODEN = "SMBCVA",
ISSN = "0146-3942",
ISSN-L = "0146-3942",
bibdate = "Sat Nov 12 16:26:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Abstract no. 75t-47.",
acknowledgement = ack-nhfb,
fjournal = "Bulletin --- Institute of Mathematical Statistics",
keywords = "Benford's Law",
}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
(Berichtigung)} ({German}) {Optimal Basis Choice for a
Floating-Point Arithmetic (Correction)}",
journal = j-COMPUTING,
volume = "14",
number = "3",
pages = "313--314",
month = sep,
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kreifelts:1973:OBG}.",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Partridge:1975:DDW,
author = "D. Partridge",
title = "A dynamic database which automatically removes
unwanted generalisation for the efficient analysis of
language features that exhibit a disparate frequency
distribution",
journal = j-COMP-J,
volume = "18",
number = "1",
pages = "43--48",
month = feb,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif",
abstract = "A self-organising database was developed as part of a
general language analysis system. The periodic,
automatic reorganisation of the database was aimed at
increasing the efficiency of analysis of a language in
which the constituent features exhibit a Zipfian type
rank-frequency relationship. Such a distribution means
that only a small number of features account for a
large proportion of the information, while a large
number of possible features are seldom encountered and
thus seldom accessed within the database. The mechanism
described aims at reconciling two conflicting
procedures: condensation by generalisation of language
features to minimise the total size of the database,
and the particularisation of the few commonly occurring
features to minimise the average analysis time. Results
are presented for the application of this mechanism to
the analysis of batches of FORTRAN programs that
constituted part of the `normal' workload for computers
within five different environments.",
acknowledgement = ack-nhfb,
classcodes = "C6120 (File organisation); C7820 (Humanities
computing)",
classification = "723",
corpsource = "Univ. Nairobi, Kenya",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; data bases; data processing; disparate
frequency distribution; dynamic database; file
organisation; language; language translation and
linguistics; self organising; unwanted generalisation",
treatment = "P Practical",
}
@Article{Pope:1975:BLP,
author = "Andrew Pope",
title = "{Bradford's Law} and the periodical literature of
information science",
journal = j-J-AM-SOC-INF-SCI,
volume = "26",
number = "4",
pages = "207--213",
month = jul,
year = "1975",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630260403",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:54 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Schorr:1975:BCL,
author = "Alan Edward Schorr",
title = "Brief Communications: {Lotka's Law} and {Map
Librarianship}",
journal = j-J-AM-SOC-INF-SCI,
volume = "26",
number = "3",
pages = "189--190",
month = may,
year = "1975",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630260308",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:53 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Schorr:1975:LLH,
author = "Alan E. Schorr",
title = "{Lotka's Law} and the History of Legal Medicine",
journal = "Research in Librarianship",
volume = "30",
number = "??",
pages = "205--209",
month = sep,
year = "1975",
CODEN = "????",
ISSN = "0034-5245",
ISSN-L = "0034-5245",
bibdate = "Fri Nov 25 08:17:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Res. Librarianship",
}
@Article{Schorr:1975:LLM,
author = "Alan E. Schorr",
title = "{Lotka's Law} and Map Librarianship",
journal = j-J-AM-SOC-INF-SCI,
volume = "26",
number = "3",
pages = "189--190",
month = may # "\slash " # jun,
year = "1975",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:11:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Webb:1975:DFD,
author = "William Webb",
title = "Distribution of the First Digits of {Fibonacci}
Numbers",
journal = j-FIB-QUART,
volume = "13",
number = "4",
pages = "334--336",
month = dec,
year = "1975",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:03 MDT 2011",
bibsource = "http://www.fq.math.ca/13-4.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Woodroofe:1975:ZL,
author = "Michael Woodroofe and Bruce Hill",
title = "On {Zipf}'s law",
journal = j-J-APPL-PROBAB,
volume = "12",
number = "3",
pages = "425--434",
month = sep,
year = "1975",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "62E20 (62P10)",
MRnumber = "0440764 (55 \#13634)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212857",
ZMnumber = "Zbl 0343.60012",
abstract = "A Zipf's law is a probability distribution on the
positive integers which decays algebraically. Such laws
describe (approximately) a large class of phenomena. We
formulate a model for such phenomena and, in terms of
our model, give necessary and sufficient conditions for
a Zipf's law to hold.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
keywords = "classical occupancy problem; laws of large numbers:
weak convergence; regularly varying functions",
}
@Article{Worthen:1975:ABL,
author = "Dennis B. Worthen",
title = "The Application of {Bradford's Law} to Monographs",
journal = j-J-DOC,
volume = "31",
number = "1",
pages = "19--25",
month = "????",
year = "1975",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026590",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:18:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{Allison:1976:LLP,
author = "Paul D. Allison and Derek de Solla Price and Belver C.
Griffith and Michael J. Moravcsik and John A. Stewart",
title = "{Lotka's Law}: a Problem in Its Interpretation and
Application",
journal = j-SOC-STUD-SCI,
volume = "6",
number = "2",
pages = "269--276",
day = "1",
month = may,
year = "1976",
CODEN = "SSSCDH",
DOI = "https://doi.org/10.1177/030631277600600205",
ISSN = "0306-3127 (print), 1460-3659 (electronic)",
ISSN-L = "0306-3127",
bibdate = "Mon Dec 3 09:12:29 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631277600600205",
acknowledgement = ack-nhfb,
fjournal = "Social Studies of Science",
journal-URL = "http://sss.sagepub.com/content/by/year",
keywords = "Lotka's Law of scientific authorship for the relative
contributions of the most prolific authors",
}
@Article{Billera:1976:PSC,
author = "Louis J. Billera and Robert E. Bixby",
title = "{Pareto} Surfaces of Complexity $1$",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "1",
pages = "81--89",
month = jan,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
keywords = "1-commodity representation; attainable sets;
complexity 1; game theory; graph theory; Pareto
surfaces; set theory",
treatment = "T Theoretical or Mathematical",
}
@Article{Brambilla:1976:DDA,
author = "Francisco Brambilla",
title = "La distribuzione delle aziende secondo le dimensioni.
{Verifica} empirica della legge logonormale e di quella
di {Zipf} e nuovi modelli interpretativi. ({Italian})
[{The} distribution of firms by size. {Empirical} test
of the log-normal law and {Zipf}'s law and new models
of interpretation]",
journal = "Giornale degli Economisti e Annali de Economia (Nuova
Serie)",
volume = "35",
number = "3--4",
pages = "131--153, 235",
month = mar # "\slash " # apr,
year = "1976",
CODEN = "????",
ISSN = "0017-0097",
ISSN-L = "0017-0097",
MRclass = "90A15",
MRnumber = "0452510 (56 \#10789)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/23242834",
acknowledgement = ack-nhfb,
ajournal = "Giorn. Econom. Ann. Econom. (N.S.)",
fjournal = "Giornale degli Economisti e Annali de Economia",
language = "Italian",
}
@Article{Cohen:1976:EFD,
author = "Daniel I. A. Cohen",
title = "An explanation of the first digit phenomenon",
journal = j-J-COMB-THEORY-A,
volume = "20",
number = "3",
pages = "367--370",
month = may,
year = "1976",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Davis:1976:SRI,
author = "Basil Davis",
title = "Some Remarks on Initial Digits",
journal = j-FIB-QUART,
volume = "14",
number = "1",
pages = "13--14",
month = feb,
year = "1976",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:05 MDT 2011",
bibsource = "http://www.fq.math.ca/14-1.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = "Convergence Estimates for the Distribution of Trailing
Digits",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "287--297",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321948",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An analysis is made of the distribution of trailing
digits (tail end digits) of positive real
floating-point numbers represented in arbitrary base $
\beta $ and randomly chosen from a logarithmic
distribution. The analysis shows that the $n$ th digit
for $ n \geq 2 $ is actually approximately uniformly
distributed. The approximation depends upon both $n$
and the base beta. It becomes better as $n$ increases,
and it is exact in the limit as $ n \rightarrow \infty
$. A table of this distribution is presented for
various $ \beta $ and $n$, along with a table of the
maximum digit by digit deviation $ \Delta $ of the
logarithmic distribution from the uniform distribution.
Various asymptotic results for $ \Delta $ are
included.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "Benford's Law; computer arithmetic; computer
programming; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Haspers:1976:YFB,
author = "Jan H. Haspers",
title = "The yield formula and {Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "27",
number = "5",
pages = "281--287",
month = sep,
year = "1976",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630270503",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:57 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Hubert:1976:NIB,
author = "John J. Hubert",
title = "On the {Naranan} interpretation of {Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "27",
number = "5",
pages = "339--341",
month = sep,
year = "1976",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630270510",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:57 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Orlov:1976:CBP,
author = "Ju. K. Orlov",
title = "The connection between the {Pareto} distribution and
the generalized {Zipf--Mandelbrot} law",
journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
volume = "83",
number = "1",
pages = "57--60",
year = "1976",
CODEN = "????",
ISSN = "????",
MRclass = "90A15",
MRnumber = "0434355 (55 \#7321)",
MRreviewer = "S. Krcevinac",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sakharth. SSR Mech. Akad. Moambe",
}
@Article{Raimi:1976:FDP,
author = "Ralph A. Raimi",
title = "The first digit problem",
journal = j-AMER-MATH-MONTHLY,
volume = "83",
number = "7",
pages = "521--538",
month = aug # "\slash " # sep,
year = "1976",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2319349",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Sat Nov 12 15:49:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2319349",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
remark = "This article surveys the literature up to 1976,
reports defects in several earlier mathematical
`explanations' of Benford's Law, and gives a 52-entry
bibliography of prior work. All of those entries are
incorporated in this bibliography. It criticizes parts
of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the
author reiterates that view in \cite{Raimi:1985:FDP}).
See also later work \cite{Logan:1978:FDP}. On page 529,
Raimi writes ``If the first digits of all the tables in
the universe obey some fixed distribution law,
Stigler's or Benford's or some other, that law must
surely be independent of the system of units chosen,
since God is not known to favor either the metric
system or the English system. In other words, a
universal first digit law, if it exists, must be
scale-invariant.''",
remark-2 = "This is so far the second earliest reference that I
have found to \cite{Newcomb:1881:NFU}; the earliest is
\cite{Boring:1920:LNL}, which has only brief mention of
the question of digit frequencies. Raimi comments on p.
522: ``This assertion, whatever it may mean, will be
called Benford's Law because it has been thought by
many writers to have originated with the General
Electric Company physicist Frank Benford [2]. Certainly
Benford popularized the problem, and he may well have
been unaware that the polymathic Simon Newcomb,
primarily an astronomer but also sometime editor of The
American Journal of Mathematics, had also formulated
the same law 57 years earlier [1]. There is ample
precedent for naming laws and theorems for persons
other than their discoverers, else half of analysis
would be named after Euler. Besides, even Newcomb
implied that the observation giving rise to the Benford
law was an old one in his day. One would hate to change
the name of the law now only to find later that another
change was called for.''",
}
@Article{Rouault:1976:PAE,
author = "Alain Rouault",
title = "Propri{\'e}t{\'e}s asymptotiques d'un
{$n$}-{\'e}chantillon d'une variable al{\'e}atoire
d{\'e}nombrable connues sous le nom de lois de {Zipf}.
({French}) [Asymptotic properties of an $n$-sample of a
denumerable random variable known under the name of
{Zipf}'s law]",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "283",
number = "6",
pages = "Aiv, A379--A380",
year = "1976",
CODEN = "CHASAP",
ISSN = "0151-0509",
ISSN-L = "0151-0509",
MRclass = "62E20",
MRnumber = "0423644 (54 \#11619)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
language = "French",
}
@Article{Rouault:1976:SML,
author = "Alain Rouault",
title = "Sources markoviennes et lois de {Zipf}. ({French})
[{Markovian} source and {Zipf} laws]",
journal = j-C-R-ACAD-SCI-PARIS-SER-AB,
volume = "283",
number = "10",
pages = "Aiii, A789--A790",
year = "1976",
CODEN = "CHASAP",
ISSN = "0151-0509",
ISSN-L = "0151-0509",
MRclass = "62E20",
MRnumber = "0423645 (54 \#11620)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
language = "French",
}
@Article{Vlachy:1976:TFL,
author = "Jan Vlach{\'y}",
title = "Time Factor in {Lotka's Law}",
journal = "Probleme de Informare si Documentare",
volume = "10",
number = "2",
pages = "44--87",
month = "????",
year = "1976",
CODEN = "PIDCA6",
ISSN = "0032-924X",
ISSN-L = "0032-924X",
bibdate = "Fri Nov 25 07:56:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Prob. inf. \& doc.",
}
@Article{Brookes:1977:TBL,
author = "Bertram C. Brookes",
title = "Theory of the {Bradford Law}",
journal = j-J-DOC,
volume = "33",
number = "3",
pages = "180--209",
month = "????",
year = "1977",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026641",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:16:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{Clark:1977:ESL,
author = "Douglas W. Clark and C. Cordell Green",
title = "An Empirical Study of List Structure in {Lisp}",
journal = j-CACM,
volume = "20",
number = "2",
pages = "78--87",
month = feb,
year = "1977",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:31:28 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Static measurements of the list structure of five
large Lisp programs are reported and analyzed. These
measurements reveal substantial regularity, or
predictability, among pointers to atoms and especially
among pointers to lists. Pointers to atoms are found to
obey, roughly, Zipf's law, which governs word
frequencies in natural languages; pointers to lists
usually point to a location physically nearby in
memory. The use of such regularities in the
space-efficient representation of list structure is
discussed.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques); C6140D (High level
languages)",
classification = "723",
comment = "Great paper; evidence pro CDR-coding, con fancy CONS",
corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "computer programming languages; data processing ---
Data Structures; empirical study; LISP; list structure;
measurements; regularity",
oldlabel = "ClarkG77",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77",
}
@Article{Coile:1977:LFD,
author = "Russell C. Coile",
title = "{Lotka}'s Frequency Distribution of Scientific
Productivity",
journal = j-J-AM-SOC-INF-SCI,
volume = "28",
number = "6",
pages = "366--370",
month = nov,
year = "1977",
CODEN = "AISJB6",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:08:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
keywords = "Lotka's Law",
}
@Article{Diaconis:1977:DLD,
author = "Persi Diaconis",
title = "The distribution of leading digits and uniform
distribution $ \bmod 1 $",
journal = j-ANN-PROBAB,
volume = "5",
number = "1",
pages = "72--81",
month = feb,
year = "1977",
CODEN = "APBYAE",
DOI = "https://doi.org/10.1214/aop/1176995891",
ISSN = "0091-1798 (print), 2168-894X (electronic)",
ISSN-L = "0091-1798",
bibdate = "Sun Apr 20 10:44:17 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.aop/1176995891",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aop",
keywords = "Benford's Law",
}
@Article{Goudsmit:1977:PEP,
author = "Samuel Goudsmit",
title = "Pitfalls in Elementary Probability",
journal = j-PROC-AMER-PHIL-SOC,
volume = "121",
number = "2",
pages = "188--189",
day = "29",
month = apr,
year = "1977",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Fri Mar 22 08:50:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Based on a lecture presented November 11, 1976.",
URL = "http://www.jstor.org/stable/986527",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; biased coin flips; biased dice throws;
roulette wheels",
}
@Article{Hubert:1977:LEL,
author = "John J. Hubert",
title = "Letters to the {Editor}: {Lotka's Law} in the
humanities",
journal = j-J-AM-SOC-INF-SCI,
volume = "28",
number = "1",
pages = "66--66",
month = jan,
year = "1977",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630280115",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Krisciunas:1977:LEL,
author = "Kevin Krisciunas",
title = "Letters to the {Editor}: {Lotka's Law} --- year by
year",
journal = j-J-AM-SOC-INF-SCI,
volume = "28",
number = "1",
pages = "65--66",
month = jan,
year = "1977",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630280114",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:02:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Kubovy:1977:RAA,
author = "M. Kubovy",
title = "Response Availability and the Apparent Spontaneity of
Numerical Choices",
journal = "Journal of Experimental Psychology: Human Performance
and Performance",
volume = "3",
number = "2",
pages = "359--364",
month = may,
year = "1977",
DOI = "https://doi.org/10.1037/0096-1523.3.2.359",
ISSN = "0096-1523 (print), 1939-1277 (electronic)",
ISSN-L = "0096-1523",
bibdate = "Sat Sep 10 12:51:40 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://psycnet.apa.org/index.cfm?fa=search.displayrecord&uid=1977-30946-001",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Ylvisaker:1977:TR,
author = "Donald Ylvisaker",
title = "Test Resistance",
journal = j-J-AM-STAT-ASSOC,
volume = "72",
number = "359",
pages = "551--556",
month = sep,
year = "1977",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:48 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314242;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2286216",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Brady:1978:MBL,
author = "W. G. Brady",
title = "More on {Benford}'s Law",
journal = j-FIB-QUART,
volume = "16",
number = "1",
pages = "51--52",
month = feb,
year = "1978",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:24 MDT 2011",
bibsource = "http://www.fq.math.ca/16-1.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Brookes:1978:FRD,
author = "Bertram C. Brookes and Jos{\'e} M. Griffiths",
title = "Frequency-rank distributions",
journal = j-J-AM-SOC-INF-SCI,
volume = "29",
number = "1",
pages = "5--13",
month = jan,
year = "1978",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630290104",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 10:40:13 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@PhdThesis{Chen:1978:ZL,
author = "Wen-Chen Chen",
title = "On {Zipf}'s law",
type = "Thesis ({Ph.D.})",
school = "University of Michigan",
address = "Ann Arbor, MI, USA",
pages = "114",
year = "1978",
MRclass = "Thesis",
MRnumber = "2627928",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
acknowledgement = ack-nhfb,
remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.
Author given name appears as Wen-Cheng in MathSciNet
database.",
}
@Article{Drott:1978:EEB,
author = "M. Carl Drott and Belver C. Griffith",
title = "An empirical examination of {Bradford's Law} and the
scattering of scientific literature",
journal = j-J-AM-SOC-INF-SCI,
volume = "29",
number = "5",
pages = "238--246",
month = sep,
year = "1978",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630290506",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:02 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Elshoff:1978:SSC,
author = "James L. Elshoff",
title = "A study of the structural composition of {PL/I}
programs",
journal = j-SIGPLAN,
volume = "13",
number = "6",
pages = "29--37",
month = jun,
year = "1978",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/987515.987518",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed Jun 18 16:08:52 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Some research on a theory of the structural
composition of an algorithm has recently been reported.
The theory embodies models of operator and operand
distributions that have been proposed by Bayer, Zipf,
and Zweben. This paper reports a study in which the
three models of operator distributions are compared
with the measured distributions found in 34 PL/I
programs. Two of three models, one by Zipf and one by
Zweben, are shown to correlate highly with the measured
distributions. Two variations of the Zipf model are
then formulated and tested with good results. Also, the
relationship between the method of counting operators
and the models is investigated.",
acknowledgement = ack-nhfb,
classification = "C4240 (Programming and algorithm theory); C6140D
(High level languages)",
corpsource = "Computer Sci. Dept., General Motors Res. Labs.,
Warren, MI, USA",
fjournal = "ACM SIG{\-}PLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "counting operators; operator distributions; PL/1; PL/1
programs; programming theory; structural composition",
treatment = "T Theoretical or Mathematical",
}
@Book{Heaps:1978:IRC,
author = "Harold Stanley Heaps",
title = "Information retrieval, computational and theoretical
aspects",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 344",
year = "1978",
ISBN = "0-12-335750-0",
ISBN-13 = "978-0-12-335750-2",
LCCN = "Z699 .H38",
bibdate = "Sat Nov 12 11:36:39 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Library and information science",
acknowledgement = ack-nhfb,
remark = "Heaps's Law is given on pp. 206--208.",
subject = "Information storage and retrieval systems",
}
@Article{Hubert:1978:BCR,
author = "John J. Hubert",
title = "Brief Communications: A relationship between two forms
of {Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "29",
number = "3",
pages = "159--161",
month = may,
year = "1978",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630290311",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:01 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "23 Mar 2007",
}
@Article{Logan:1978:FDP,
author = "Jonothan L. Logan and Samuel A. Goudsmit",
title = "The First Digit Phenomenon",
journal = j-PROC-AMER-PHIL-SOC,
volume = "122",
number = "4",
pages = "193--197",
day = "18",
month = aug,
year = "1978",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains derivations of both Stigler's Law
and Benford's Law, and receives strong criticism in
\cite{Raimi:1985:FDP}. This paper contains an important
historical note that is recorded in entry
\cite{Benford:1938:LAN}.",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
http://www.jstor.org/stable/986530",
abstract = "Forty years ago an article appeared in these
Proceedings, which has since then attracted much
attention of mathematicians and some physicists. It was
written by Frank Benford, a physicist from the General
Electric Company at Schenectady. He had examined a
large number of numerical tables, the kind that are
printed in almanacs, and in scientific and technical
handbooks. He noticed a most unusual and unexpected
property of many of these tables. Consider, for
example, the numbers representing the populations of
states or all the countries in the world, or their
areas, their budgets, their numbers of hospital beds,
etc. One would expect that on the average just as many
of these entries would begin with the digit $1$ as with
$2$ or $3$ or $4$, and so on. But Benford noticed that
small values of the first digits occur far more
often.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@Article{Praunlich:1978:BDN,
author = "Peter Praunlich and Michael Kroll",
title = "{Bradford}'s distribution: a new formulation",
journal = j-J-AM-SOC-INF-SCI,
volume = "29",
number = "2",
pages = "51--55",
month = mar,
year = "1978",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630290203",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:01 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Rouault:1978:LZS,
author = "Alain Rouault",
title = "Lois de {Zipf} et sources markoviennes. ({French})
[{Zipf}'s law and {Markovian} sources]",
journal = "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)",
volume = "14",
number = "2",
pages = "169--188",
year = "1978",
CODEN = "AHPBAR",
ISSN = "0020-2347",
ISSN-L = "0020-2347",
MRclass = "62E99 (60J20 62P99)",
MRnumber = "507732 (80c:62026a)",
MRreviewer = "Bruce M. Hill",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de l'Institut Henri Poincar{\'e}. Section B.
Calcul des Probabilit{\'e}s et Statistique. Nouvelle
S{\'e}rie",
language = "French",
}
@Article{Samson:1978:STU,
author = "W. B. Samson and R. H. Davis",
title = "Search Times Using Hash Tables for Records with
Non-Unique Keys",
journal = j-COMP-J,
volume = "21",
number = "3",
pages = "210--214",
month = aug,
year = "1978",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif",
abstract = "Recent research in hash coding has concentrated on
unique keys, or uniform distributions of keys. This
paper is intended to clarify the effect of non-unique
keys with various distributions on search times in the
hash table thus enabling recommendations to be made to
those who must deal with hash tables of this type. It
is found that extreme rank-order frequency distribution
of keys, such as the Zipf distribution, result in much
higher access times than more uniform distributions,
but it is possible to reduce these to some extent by
loading records with common keys on to the hash table
first.",
acknowledgement = ack-nhfb,
classcodes = "C6120 (File organisation); C6130 (Data handling
techniques)",
classification = "723",
corpsource = "Dept. of Math. and Computer Studies, Dundee Coll. of
Technol., Dundee, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
journalabr = "Comput J",
keywords = "common keys; compiler symbol; computer programming;
data handling; data processing --- Data Structures;
direct access files; distribution; extreme; file
organisation; hash tables; higher access times; non
unique keys; overflow method; rank order frequency
distribution of keys; records; search times;
simulation; tables; uniform distributions; Zipf",
treatment = "T Theoretical or Mathematical",
}
@Article{Brookes:1979:LEB,
author = "B. C. Brookes",
title = "Letters to the {Editor}: The {Bradford Law}: a new
calculus for the social sciences?",
journal = j-J-AM-SOC-INF-SCI,
volume = "30",
number = "4",
pages = "233--234",
month = jul,
year = "1979",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630300412",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:05 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Diaconis:1979:RP,
author = "Persi Diaconis and David Freedman",
title = "On Rounding Percentages",
journal = j-J-AM-STAT-ASSOC,
volume = "74",
number = "366",
pages = "359--364",
month = jun,
year = "1979",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Nov 23 11:24:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "The authors extend prior work on correctness of sums
of rounded percentages \cite{Mosteller:1967:DSR}, and
criticize biased rounding practices in
\cite{Benford:1938:LAN}.",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Benford's Law",
remark = "When percentage-column entries are rounded, their sum
may differ from 100\%. The authors use a prior proof
\cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
values, the probability of a correct sum is $ \sqrt {6
/ (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
rounding may produce large changes in computed
chi-squared values, and they conclude their article
with this recommendation: ``it is important to
calculate with many-digit accuracy when computing $
\chi^2 $ for large sample sizes.''",
}
@Article{Marulli:1979:BCB,
author = "Luciana Marulli and Michael E. D. Koenig",
title = "Brief Communications: {Bradford} distribution of data
elements",
journal = j-J-AM-SOC-INF-SCI,
volume = "30",
number = "2",
pages = "107--108",
month = mar,
year = "1979",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630300209",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:04 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Mohanty:1979:MMQ,
author = "Siba N. Mohanty",
title = "Models and Measurements for Quality Assessment of
Software",
journal = j-COMP-SURV,
volume = "11",
number = "3",
pages = "251--275",
month = sep,
year = "1979",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356778.356783",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:25:12 MDT 2008",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
http://www.acm.org/pubs/contents/journals/surveys/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
annote = "Several software quality assessment methods which span
the software life cycle are discussed. The quality of a
system design can be estimated by measuring the system
entropy function or the system work function. The
quality improvement due to reconfiguration can be
determined by calculating system entropy loading
measures. Software science and Zipf's law are shown to
be useful for estimating program length and
implementation time.",
country = "USA",
date = "11/10/79",
descriptors = "Software; design; software engineering; reliability;
measurement; model; fundamentals in statistics;
performance evaluation",
enum = "2189",
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
references = "65",
}
@Article{Radhakrishnan:1979:LLC,
author = "T. Radhakrishnan and R. Kernizan",
title = "{Lotka's Law} and Computer Science Literature",
journal = j-J-AM-SOC-INF-SCI,
volume = "30",
number = "1",
pages = "51--54",
month = jan,
year = "1979",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630300109",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 07:45:09 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "6 September 2007",
remark = "This paper analyzes publication statistics from
Communications of the Association for Computing
Machinery (CACM) and in the Journal of the ACM
(JACM).",
}
@Article{Vlachy:1979:FDS,
author = "Jan Vlach{\'y}",
title = "Frequency Distribution of Scientific Performance: a
Bibliography of {Lotka's Law} and Related Phenomena",
journal = j-SCIENTOMETRICS,
volume = "1",
number = "1",
pages = "107--130",
month = sep,
year = "1979",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02016844",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Fri Nov 25 07:59:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF02016844;
http://www.springerlink.com/content/0138-9130/",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
xxjournal = "Scientometrics, Bibliography Section",
}
@Article{Brookes:1980:FISa,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part I}.
{Philosophical} aspects",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "3--4",
pages = "125--133",
month = jun,
year = "1980",
CODEN = "JISCDI",
DOI = "https://doi.org/10.1177/016555158000200302",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/3-4/125.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Brookes:1980:FISb,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part II}.
{Quantitative} aspects: classes of things and the
challenge of human individuality",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "5",
pages = "209--221",
month = oct,
year = "1980",
CODEN = "JISCDI",
DOI = "https://doi.org/10.1177/016555158000200502",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 11:01:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/5/209.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Brookes:1980:FISc,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part III}.
{Quantitative} aspects: Objective maps and subjective
landscapes",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "2",
number = "6",
pages = "269--275",
month = dec,
year = "1980",
CODEN = "JISCDI",
DOI = "https://doi.org/10.1177/016555158000200602",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/2/6/269.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Chen:1980:WFZ,
author = "Wen Chen Chen",
title = "On the weak form of {Zipf}'s law",
journal = j-J-APPL-PROBAB,
volume = "17",
number = "3",
pages = "611--622",
year = "1980",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "62E10 (62F10)",
MRnumber = "580021 (81m:62021)",
MRreviewer = "Patrick L. Brockett",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212955",
ZMnumber = "Zbl 0435.60017",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
}
@Article{Dunn:1980:SFW,
author = "Stanley Dunn",
title = "Surveyor's Forum: {Working} on Interpretations",
journal = j-COMP-SURV,
volume = "12",
number = "2",
pages = "255--255",
month = jun,
year = "1980",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356810.356817",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Leimkuhler:1980:EFB,
author = "Ferdinand F. Leimkuhler",
title = "An Exact Formulation of {Bradford's Law}",
journal = j-J-DOC,
volume = "36",
number = "4",
pages = "285--292",
month = "????",
year = "1980",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026699",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:14:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An exact, discrete formulation of Bradford's law
describing the distribution of articles in journals is
derived by showing that Bradford's law is a special
case of the Zipf--Mandelbrot `rank frequency' law. A
relatively simple method is presented for fitting the
model to empirical data and estimating the number of
journals and articles in a subject collection. This
method is demonstrated with an example application.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{McKee:1980:POR,
author = "Arnold F. McKee",
title = "The {Pareto} Optimum: Reconcilable with Social
Thought?",
journal = "International Journal of Social Economics",
volume = "7",
number = "7",
pages = "366--375",
month = "????",
year = "1980",
CODEN = "ISLEBC",
DOI = "https://doi.org/10.1108/eb013878",
ISSN = "0306-8293 (print), 1758-6712 (electronic)",
ISSN-L = "0306-8293",
bibdate = "Fri Nov 25 07:01:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Mohanty:1980:SFW,
author = "Siba Mohanty",
title = "Surveyor's Forum: {Working} on Interpretations",
journal = j-COMP-SURV,
volume = "12",
number = "2",
pages = "256--256",
month = jun,
year = "1980",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356810.356818",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Asai:1981:GFB,
author = "Isao Asai",
title = "A general formulation of {Bradford}'s distribution:
the graph-oriented approach",
journal = j-J-AM-SOC-INF-SCI,
volume = "32",
number = "2",
pages = "113--119",
month = mar,
year = "1981",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630320206",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:10 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Brookes:1981:FIS,
author = "Bertram C. Brookes",
title = "The foundations of information science. {Part IV}.
{Information} science: the changing paradigm",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "3",
number = "1",
pages = "3--12",
month = feb,
year = "1981",
CODEN = "JISCDI",
DOI = "https://doi.org/10.1177/016555158100300102",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Mon Feb 25 10:36:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jis.sagepub.com/content/3/1/3",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Book{Fleiss:1981:SMR,
author = "Joseph L. Fleiss",
title = "Statistical Methods for Rates and Proportions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xviii + 321",
year = "1981",
ISBN = "0-471-06428-9",
ISBN-13 = "978-0-471-06428-2",
LCCN = "QA279 .F58 1981",
bibdate = "Fri Mar 22 08:46:57 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in probability and mathematical
statistics",
URL = "http://www.loc.gov/catdir/description/wiley032/80026382.html;
http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html;
http://www.loc.gov/catdir/toc/onix02/80026382.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Analysis of variance; Sampling (Statistics);
Biometry",
}
@Article{Kennard:1981:MDF,
author = "Robert W. Kennard and John E. Reith",
title = "{M32}. {On} the distribution of first digits",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "10",
number = "1",
pages = "97--98",
year = "1981",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1080/03610918108812195",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
bibdate = "Sat Jan 30 06:32:15 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
keywords = "Benford's Law",
onlinedate = "27 Jun 2007",
}
@Article{Morse:1981:IEB,
author = "Philip M. Morse",
title = "Implications of the exact {Bradford} distribution",
journal = j-J-AM-SOC-INF-SCI,
volume = "32",
number = "1",
pages = "43--50",
month = jan,
year = "1981",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630320106",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:10 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "22 Mar 2007",
}
@Article{Pavlov:1981:DFF,
author = "A. I. Pavlov",
title = "On the distribution of fractions and {F. Benford}'s
law",
journal = j-IZV-AKAD-NAUK-SSSR-MAT,
volume = "45",
number = "4",
pages = "760--774, 927",
year = "1981",
CODEN = "IZAMAT",
ISSN = "0373-2436",
ISSN-L = "0373-2436",
MRclass = "10K10",
MRnumber = "631437 (83m:10093)",
MRreviewer = "Michael Keane",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
(Moscow)",
xxtitle = "On the distribution mod one and {Benford}'s law",
}
@Article{Peters:1981:EFB,
author = "James V. Peters",
title = "An Equivalent Form of {Benford's Law}",
journal = j-FIB-QUART,
volume = "19",
number = "1",
pages = "74--76",
month = feb,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "60C05 (10K10 60-01)",
MRnumber = "606117 (82k:60024)",
MRreviewer = "L. E. Clarke",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/19-1.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Peters:1981:SCC,
author = "James V. Peters",
title = "Short Communications: a combinatoric proof of
{Benford}'s law",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "23",
number = "1",
pages = "122--123",
year = "1981",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/BF02188018",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
MRclass = "Contributed Item",
MRnumber = "1553878",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/BF02188018",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
}
@Article{Potter:1981:LLR,
author = "William Gray Potter",
title = "{Lotka's Law} revisited",
journal = j-LIBR-TRENDS,
volume = "31",
number = "2",
pages = "21--39",
month = "Summer",
year = "1981",
CODEN = "LIBTA3",
ISSN = "0024-2594 (print), 1559-0682 (electronic)",
ISSN-L = "0024-2594",
bibdate = "Thu Nov 24 14:41:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842",
acknowledgement = ack-nhfb,
fjournal = "Library Trends",
}
@Article{Preece:1981:DFD,
author = "D. A. Preece",
title = "Distributions of Final Digits in Data",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "30",
number = "1",
pages = "31--60",
month = mar,
year = "1981",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Wed Nov 23 12:19:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2987702",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
remark = "This paper extends previous work \cite{Yule:1927:RS}
on human bias in the recording of last digits in
measurements, or from roundings, or from later scale
conversions, and how such bias can be detected.",
}
@Article{Schatte:1981:RVL,
author = "Peter Schatte",
title = "On random variables with logarithmic mantissa
distribution relative to several bases",
journal = j-ELEK-INFO-KYBER,
volume = "17",
number = "??",
pages = "293--295",
month = "????",
year = "1981",
CODEN = "EIVKAX",
ISSN = "0013-5712",
ISSN-L = "0013-5712",
bibdate = "Sat Nov 12 15:53:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elektronische Informationsverarbeitung und Kybernetik
(EIK)",
}
@Article{Washington:1981:BLF,
author = "Lawrence C. Washington",
title = "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
journal = j-FIB-QUART,
volume = "19",
number = "2",
pages = "175--177",
month = apr,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "10A30 (10A35)",
MRnumber = "614056 (82f:10009)",
MRreviewer = "S. P. Mohanty",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/19-2.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Fedorowicz:1982:TFZ,
author = "Jane Fedorowicz",
title = "The Theoretical Foundation of {Zipf's Law} and Its
Application to the Bibliographic Database Environment",
journal = j-J-AM-SOC-INF-SCI,
volume = "33",
number = "5",
pages = "285--293",
year = "1982",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630330507",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Fedorowicz:1982:ZMA,
author = "Jane Fedorowicz",
title = "A {Zipfian} Model of an Automatic Bibliographic
System: An Application to {MEDLINE}",
journal = j-J-AM-SOC-INF-SCI,
volume = "33",
number = "4",
pages = "223--232",
month = jul,
year = "1982",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630330406",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:14 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "6 Sep 2007",
}
@Article{Lefort:1982:LOA,
author = "B. Lefort",
title = "{L}'Emploi des Outils au Cours de Taches d'Entretien
et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of
Tools in Maintenance Tasks and the {Zipf--Mandelbrot
Law}]",
journal = j-TRAV-HUM,
volume = "45",
number = "2",
pages = "307--316",
month = "????",
year = "1982",
CODEN = "TRHUAH",
ISSN = "0041-1868 (print), 2104-3663 (electronic)",
ISSN-L = "0041-1868",
bibdate = "Mon Sep 10 07:17:32 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/40657805",
acknowledgement = ack-nhfb,
fjournal = "Le Travail Humain",
language = "French",
}
@Article{MacRoberts:1982:REL,
author = "Michael H. MacRoberts and Barbara R. MacRoberts",
title = "A Re-evaluation of {Lotka}'s {Law of Scientific
Productivity}",
journal = j-SOC-STUD-SCI,
volume = "12",
number = "3",
pages = "443--450",
day = "1",
month = aug,
year = "1982",
CODEN = "SSSCDH",
DOI = "https://doi.org/10.1177/030631282012003005",
ISSN = "0306-3127 (print), 1460-3659 (electronic)",
ISSN-L = "0306-3127",
bibdate = "Mon Dec 3 09:12:38 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631282012003005",
acknowledgement = ack-nhfb,
fjournal = "Social Studies of Science",
journal-URL = "http://sss.sagepub.com/content/by/year",
keywords = "Lotka's Law of scientific authorship for the relative
contributions of the most prolific authors",
}
@Article{Pavlov:1982:DFP,
author = "A. I. Pavlov",
title = "On the Distribution of Fractional Parts and {Benford's
Law}",
journal = j-MATH-USSR-IZV,
volume = "19",
number = "1",
pages = "65--77",
month = "????",
year = "1982",
CODEN = "MUSIAE",
DOI = "https://doi.org/10.1070/IM1982v019n01ABEH001411",
ISSN = "0025-5726 (print), 2169-5075 (electronic)",
ISSN-L = "0025-5726",
bibdate = "Sun Nov 13 10:46:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://stacks.iop.org/0025-5726/19/i=1/a=A05",
abstract = "This article investigates the distribution of the
first digits (from the left) in the $q$-nary expansions
of numerical sequences and functions ($q$ an integer $
\geq 2 $ )",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of the {USSR} --- Izvestiya",
journal-URL = "http://iopscience.iop.org/0025-5726",
}
@PhdThesis{Perline:1982:EVM,
author = "Richard K. Perline",
title = "An extreme value model of weakly harmonic
({Pareto--Zipf} type) laws",
type = "Thesis ({Ph.D.})",
school = "Department of Behavioral Sciences, The University of
Chicago",
address = "Chicago, IL, USA",
pages = "129",
month = dec,
year = "1982",
MRnumber = "2611828",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/251796701",
acknowledgement = ack-nhfb,
remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.",
}
@Article{Regazzini:1982:BFL,
author = "Eugenio Regazzini",
title = "The {Benford--Furlan} law as a statistical law",
journal = j-STATISTICA-BOLOGNA,
volume = "42",
number = "3",
pages = "351--370",
year = "1982",
CODEN = "STATDJ",
ISSN = "0390-590X (print), 1973-2201 (electronic)",
ISSN-L = "0390-590X",
MRclass = "62E99 (10K05 62A15)",
MRnumber = "695467 (84h:62032)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistica (Bologna)",
}
@Article{Turner:1982:DLS,
author = "Peter R. Turner",
title = "The distribution of leading significant digits",
journal = j-IMA-J-NUMER-ANAL,
volume = "2",
number = "4",
pages = "407--412",
month = oct,
year = "1982",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/2.4.407",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G99 (60E05)",
MRnumber = "84f:65038",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Book{Weaver:1982:LLT,
author = "Warren Weaver",
title = "{Lady Luck}: the theory of probability",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "392",
year = "1982",
ISBN = "0-486-24342-7",
ISBN-13 = "978-0-486-24342-9",
LCCN = "QA273 .W4 1982",
bibdate = "Mon Nov 14 11:35:17 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover031/82007396.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1978",
remark = "Reprint of \cite{Weaver:1963:LLT}.",
subject = "Probabilities",
}
@Article{White:1982:FSS,
author = "Warren H. White",
title = "On the form of steady-state solutions to the
coagulation equations",
journal = j-J-COLLOID-INTERFACE-SCI,
volume = "87",
number = "1",
pages = "204--208",
month = may,
year = "1982",
CODEN = "JCISA5",
DOI = "https://doi.org/10.1016/0021-9797(82)90382-4",
ISSN = "0021-9797 (print), 1095-7103 (electronic)",
ISSN-L = "0021-9797",
bibdate = "Thu Feb 28 10:46:13 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021979782903824",
acknowledgement = ack-nhfb,
fjournal = "Journal of Colloid and Interface Science",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Iyengar:1983:SPL,
author = "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R.
Uppuluri",
title = "String patterns of leading digits",
journal = j-APPL-MATH-COMP,
volume = "12",
number = "4",
pages = "321--337",
month = jul,
year = "1983",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(83)90045-0",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Feb 16 18:02:26 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
URL = "http://www.sciencedirect.com/science/article/pii/0096300383900450",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Montroll:1983:NOD,
author = "Elliott W. Montroll and Michael F. Shlesinger",
title = "On $ 1 / f $ noise and other distributions with long
tails",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "79",
number = "10",
pages = "3380--3383",
day = "15",
month = may,
year = "1983",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.79.10.3380",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Thu Feb 28 11:03:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.pnas.org/content/79/10/3380.abstract",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Orlov:1983:SSZ,
author = "Yu. K. Orlov and R. Ya. Chitashvili",
title = "The statistical significance of {Zipf}'s
distribution",
journal = "Soobshch. Akad. Nauk Gruzin. SSR",
volume = "109",
number = "3",
pages = "505--508",
year = "1983",
CODEN = "????",
ISSN = "0132-1447",
ISSN-L = "0132-1447",
MRclass = "62E99 (62P99)",
MRnumber = "723296",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}
@Article{Schatte:1983:AUD,
author = "Peter Schatte",
title = "On the asymptotic uniform distribution of sums reduced
$ \bmod 1 $",
journal = j-MATH-NACHR,
volume = "115",
number = "1",
pages = "257--281",
month = "????",
year = "1983",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19841150121",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Feb 16 19:12:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}
@Article{Schatte:1983:SUD,
author = "Peter Schatte",
title = "On {$ H_\infty $}-summability and the uniform
distribution of sequences",
journal = j-MATH-NACHR,
volume = "113",
number = "1",
pages = "237--243",
month = "????",
year = "1983",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19831130122",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Feb 16 19:13:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}
@Article{Whittaker:1983:SID,
author = "James V. Whittaker",
title = "On Scale-Invariant Distributions",
journal = j-SIAM-J-APPL-MATH,
volume = "43",
number = "2",
pages = "257--267",
month = apr,
year = "1983",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "60E05 (10K10 62E10)",
MRnumber = "84h:60035",
MRreviewer = "K. C. Chanda",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
affiliation = "Univ of British Columbia, Dep of Mathematics,
Vancouver, BC, Can",
classification = "922",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
journalabr = "SIAM J Appl Math",
keywords = "probability",
}
@Article{Bennett:1984:ZLS,
author = "J. M. Bennett",
title = "{Zipf's Law}, Structured Programming and Creativity",
journal = j-AUSTRALIAN-COMP-J,
volume = "16",
number = "4",
pages = "122--129",
year = "1984",
CODEN = "ACMJB2",
ISSN = "0004-8917",
ISSN-L = "0004-8917",
bibdate = "Fri Mar 9 17:59:26 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "As software projects increase in size, the effort
required to implement them increases at a greater rate.
The use of higher level languages and adherence to
various rules of ``good programming practice'' appear
to help only marginally in reducing the impact of this
non-linear effect, and progress can only be made by
calling on techniques for managing complexity which
have emerged in other fields. Hierarchical structures
are discussed with particular reference to software as
is the effect which appears to be common to a wide
range of human activities, and which is known as Zipf's
law. The effects of variation in individual programming
skills, the roles of creativity, invention and
innovation and lessons to be learned from case studies
of past failure are also examined.",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "creativity; innovation; invention; large software
projects; project failures; structured programming;
Zipf's law",
}
@Article{Boroda:1984:ZML,
author = "M. G. Boroda and A. A. Polikarpov",
title = "The {Zipf--Mandelbrot} law and units of different
levels of text organization",
journal = "Tartu Riikl. {\"U}l. Toimetised",
volume = "??",
number = "689",
pages = "35--60",
year = "1984",
CODEN = "????",
ISSN = "????",
MRclass = "92A25",
MRnumber = "781731 (86c:92030)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Brookes:1984:RTE,
author = "Bertram C. Brookes",
title = "Ranking techniques and the empirical log law",
journal = j-INFO-PROC-MAN,
volume = "20",
number = "1--2",
pages = "37--46",
month = "????",
year = "1984",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/0306-4573(84)90038-4",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Mon Feb 25 10:38:32 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0306457384900384",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
keywords = "Anomalous Law of Numbers; Benford's Law",
}
@Article{Bunt:1984:MPL,
author = "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
Majumdar",
title = "A measure of program locality and its application",
journal = j-SIGMETRICS,
volume = "12",
number = "3",
pages = "28--40",
month = aug,
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.1145/1031382.809311",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Thu Jun 26 11:00:50 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Although the phenomenon of locality has long been
recognized as the single most important characteristic
of program behaviour, relatively little work has been
done in attempting to measure it. Recent work has led
to the development of an intrinsic measure of program
locality based on the Bradford--Zipf distribution.
Potential applications for such a measure are many, and
include the evaluation of program restructuring methods
(manual and automatic), the prediction of system
performance, the validation of program behaviour
models, and the enhanced understanding of the phenomena
that characterize program behaviour. A consideration of
each of these areas is given in connection with the
proposed measure, both to increase confidence in the
validity of the measure and to illustrate a methodology
for dealing with such problems.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
}
@Article{Cohen:1984:PNF,
author = "D. I. A. Cohen and T. M. Katz",
title = "Prime numbers and the first digit phenomenon",
journal = j-J-NUMBER-THEORY,
volume = "18",
number = "3",
pages = "261--268",
month = jun,
year = "1984",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/0022-314X(84)90061-1",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Fri Nov 25 13:58:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
}
@Article{Fedorowicz:1984:DEU,
author = "Jane Fedorowicz",
title = "Database evaluation using multiple regression
techniques",
journal = j-SIGMOD,
volume = "14",
number = "2",
pages = "70--76",
year = "1984",
CODEN = "SRECD8",
ISBN = "0-89791-128-8",
ISBN-13 = "978-0-89791-128-3",
ISSN = "0163-5808 (print), 1943-5835 (electronic)",
ISSN-L = "0163-5808",
bibdate = "Mon Dec 9 07:58:51 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A model of the inverted file of an automated
bibliographic system is constructed using the Zipf
distribution of word frequency. By ascertaining the
parameters of the Zipfian model of the inverted file
system, one can estimate the minimum data storage
requirements of the database. In addition, given a few
additional system parameters, access time for a
specified query can be estimated. The estimation
procedures are accomplished using logarithmic
transformations and multiple regression techniques.
This paper introduces the Zipfian models, their
regression formulation, and their results and
interpretation for application to database
evaluation.",
acknowledgement = ack-nhfb,
affiliation = "Northwestern Univ, Kellogg Graduate Sch of Management,
Evanston, IL, USA",
affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
Management, Evanston, IL, USA",
classification = "723; 901; 922",
conference = "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
Interest Group on Management of Data).",
fjournal = "SIGMOD Record (ACM Special Interest Group on
Management of Data)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689",
keywords = "access time model; bibliographic techniques; database
systems; evaluation; information storage systems;
mathematical models; multiple regression techniques;
Zipfian model",
meetingaddress = "Boston, MA, USA",
sponsor = "ACM, Special Interest Group on Management of Data, New
York, NY, USA",
}
@Article{Friedberg:1984:DFD,
author = "Stephen H. Friedberg",
title = "The Distribution of First Digits",
journal = j-COLLEGE-MATH-J,
volume = "15",
number = "2",
pages = "120--125",
month = mar,
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.1080/00494925.1984.11972760",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:49:53 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
URL = "http://www.jstor.org/stable/2686516;
http://www.tandfonline.com/doi/abs/10.1080/00494925.1984.11972760",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
keywords = "Benford's Law",
onlinedate = "30 Jan 2018",
}
@Article{Fuchs:1984:PDP,
author = "A. Fuchs and G. Letta",
title = "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}.
({French}) [{On} the problem of the first decimal
digit]",
journal = "{Bollettino della Unione Matem{\`a}tica Italiana.
Serie VI. B}",
volume = "3",
pages = "451--461",
year = "1984",
ISSN = "0392-4041",
ISSN-L = "0392-4041",
bibdate = "Wed Aug 12 10:09:50 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0557.60011",
acknowledgement = ack-nhfb,
ajournal = "Boll. Unione Mat. Ital., VI. Ser., B",
keywords = "analytical density; asymptotic density; first-digit
problem",
language = "French",
ZMclass = "60B99 (Probability theory on general structures)",
ZMreviewer = "R. Scozzafava",
}
@Article{Karmeshu:1984:RBL,
author = "Karmeshu and N. C. Lind and V. Cano",
title = "Rationales for {Bradford's Law}",
journal = j-SCIENTOMETRICS,
volume = "6",
number = "4",
pages = "233--241",
month = jul,
year = "1984",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02279358",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:02:53 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
URL = "http://link.springer.com/article/10.1007/BF02279358",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Kohyama:1984:TIC,
author = "Tamotsu Kohyama and Y{\=o}ji Aizawa",
title = "Theory of the intermittent chaos. {$ 1 / f $} spectrum
and the {Pareto--Zipf} law",
journal = j-PROG-THEOR-PHYS,
volume = "71",
number = "5",
pages = "917--929",
year = "1984",
CODEN = "PTPKAV",
DOI = "https://doi.org/10.1143/PTP.71.917",
ISSN = "0033-068X (print), 1347-4081 (electronic)",
ISSN-L = "0033-068X",
MRclass = "58F13 (76F99)",
MRnumber = "756214 (86a:58063)",
MRreviewer = "Joseph Ford",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
journal-URL = "http://ptp.oxfordjournals.org/content/by/year",
}
@Article{Maia:1984:UBL,
author = "M. J. F. Maia and M. D. Maia",
title = "On the Unity of {Bradford's Law}",
journal = j-J-DOC,
volume = "40",
number = "3",
pages = "206--216",
month = "????",
year = "1984",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026765",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:11:46 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{McLaughlin:1984:DFI,
author = "William I. McLaughlin and Sylvia A. Lundy",
title = "Digit Functions of Integer Sequences",
journal = j-FIB-QUART,
volume = "22",
number = "2",
pages = "105--115",
month = may,
year = "1984",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:30 MDT 2011",
bibsource = "http://www.fq.math.ca/22-2.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Nagasaka:1984:BL,
author = "Kenji Nagasaka",
title = "On {Benford}'s law",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "36",
number = "1",
pages = "337--352",
month = "????",
year = "1984",
CODEN = "AISXAD",
DOI = "https://doi.org/10.1007/BF02481974",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
MRclass = "60F99 (11K06 11K36 62E99)",
MRnumber = "758506 (86a:60052)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Jan 31 18:19:56 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF02481974",
acknowledgement = ack-nhfb,
ajournal = "Ann. Inst. Statist. Math.",
fjournal = "Annals of the Institute of Statistical Mathematics
(Tokyo)",
journal-URL = "http://link.springer.com/journal/10463",
}
@Article{Schatte:1984:AUD,
author = "Peter Schatte",
title = "On the asymptotic uniform distribution of sums reduced
$ \bmod 1 $",
journal = j-MATH-NACHR,
volume = "115",
number = "1",
pages = "275--281",
month = "????",
year = "1984",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19841150121",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sat Nov 12 15:54:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}
@Article{Turner:1984:FRD,
author = "Peter R. Turner",
title = "Further revelations on l.s.d",
journal = j-IMA-J-NUMER-ANAL,
volume = "4",
number = "2",
pages = "225--231",
month = apr,
year = "1984",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/4.2.225",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G10 (11K99)",
MRnumber = "85m:65039",
MRreviewer = "Calvin T. Long",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
abstract = "In a recent paper the author showed that the
distribution of leading significant digits, l.s.d.,
resulting from successive multiplications is
logarithmic. In this paper these results are extended
by establishing, still without any assumptions of
invariance to scaling, that this distribution remains
invariant under all further arithmetic operations ---
both multiplicative and additive. The fact that 30\% of
decimal numbers have l.s.d. 1 persists.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "l. s. d. (leading significant digits)",
}
@Article{Yuan:1984:LOC,
author = "Y. Yuan",
title = "On the least {$Q$}-order of convergence of variable
metric algorithms",
journal = j-IMA-J-NUMER-ANAL,
volume = "4",
number = "2",
pages = "233--239",
month = apr,
year = "1984",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65K05",
MRnumber = "85h:65133",
MRreviewer = "A. I. \c Schiop",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Barlow:1985:RED,
author = "J. L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "325--347",
month = dec,
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65045",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ, Computer Science Dep,
University Park, PA, USA",
affiliationaddress = "USA",
classification = "723",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory; floating
point arithmetic; logarithmic arithmetic; roundoff
error distributions",
}
@Article{Bradford:1985:SIS,
author = "Samuel C. Bradford",
title = "Sources of Information on Specific Subjects",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "10",
number = "4",
pages = "173--180",
month = oct,
year = "1985",
CODEN = "JISCDI",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Fri Nov 25 11:49:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Bradford:1934:SIS}, the source of
Bradford's Law.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
journal-URL = "http://jis.sagepub.com/",
}
@Article{Egghe:1985:CLL,
author = "L. Egghe",
title = "Consequences of {Lotka's Law} for the {Law of
Bradford}",
journal = j-J-DOC,
volume = "41",
number = "3",
pages = "173--189",
month = "????",
year = "1985",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026780",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:23:22 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
keywords = "Bradford's Law",
}
@Article{Faber:1985:AML,
author = "Vance Faber and Andrew B. {White, Jr.} and G. Milton
Wing",
title = "Analysis of a model that leads to the {Pareto} law of
wealth distribution",
journal = j-J-MATH-ANAL-APPL,
volume = "112",
number = "2",
pages = "579--594",
year = "1985",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(85)90264-1",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90A14",
MRnumber = "813621 (87b:90027)",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
}
@Article{Lagarias:1985:PG,
author = "Jeffrey C. Lagarias",
title = "The $ 3 x + 1 $ Problem and Its Generalizations",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "1",
pages = "3--23",
month = jan,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K55 (11K31)",
MRnumber = "86i:11043",
MRreviewer = "A. D. Pollington",
bibdate = "Mon Jun 28 12:37:47 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
keywords = "Benford's Law",
}
@Article{Pao:1985:LLT,
author = "Miranda Lee Pao",
title = "{Lotka}'s law: a testing procedure",
journal = j-INFO-PROC-MAN,
volume = "21",
number = "4",
pages = "305--320",
month = "????",
year = "1985",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/0306-4573(85)90055-X",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Fri Nov 25 08:41:41 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
}
@Article{Raimi:1985:FDP,
author = "Ralph A. Raimi",
title = "The First Digit Phenomenon Again",
journal = j-PROC-AMER-PHIL-SOC,
volume = "129",
number = "2",
pages = "211--219",
month = jun,
year = "1985",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Sat Nov 12 16:56:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains strong criticism of a derivation
of Benford's Law \cite{Logan:1978:FDP}.",
URL = "http://www.jstor.org/stable/986989",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "This paper contains mathematical derivations of both
Stigler's Law and Benford's Law. Raimi comments on p.
217: ``the Benford law itself as a conclusion to be
derived is by no means as firm as Kepler's planetary
curves. Indeed, it has been pointed out by Diaconis and
Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
statistical analysis of Benford's announced data gives
a high probability to the conjecture that he did a bit
of rounding-off here and there, always in the direction
of his law. The license that a physicist often takes on
the path from his hypotheses to verified, observable,
and repeatable conclusion is not justified here.''.",
}
@Article{Tichy:1985:UDD,
author = "Robert F. Tichy",
title = "Uniform distribution and diophantine inequalities",
journal = j-MONAT-MATH,
volume = "99",
number = "2",
pages = "147--152",
month = jun,
year = "1985",
CODEN = "MNMTA2",
DOI = "https://doi.org/10.1007/BF01304194",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
bibdate = "Sun Feb 17 06:26:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF01304194",
ZMnumber = "0538.10039",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
keywords = "diophantine inequalities; discrepancy; Uniformly
distributed sequences",
ZMclass = "11K06 (General theory of distribution modulo 1); 11D75
(Diophantine inequalities)",
}
@Article{Tuldava:1985:FST,
author = "Yu. A. Tuldava",
title = "The frequency structure of a text and {Zipf}'s law",
journal = "Tartu Riikl. {\"U}l. Toimetised",
volume = "??",
number = "711",
pages = "93--116",
year = "1985",
CODEN = "????",
ISSN = "????",
MRclass = "92A25 (94A15)",
MRnumber = "836129 (87c:92063)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Uppuluri:1985:DFD,
author = "V. R. R. Uppuluri and S. A. Patil",
title = "The distribution of the first $j$ digits of beta
related random variables",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "14",
number = "2",
pages = "467--472",
year = "1985",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1080/03610918508812450",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
bibdate = "Sat Jan 30 06:32:23 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
keywords = "Benford's Law",
}
@Article{Chen:1986:RBL,
author = "Ye-Sho Chen and Ferdinand F. Leimkuhler",
title = "A relationship between {Lotka's Law}, {Bradford's
Law}, and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "5",
pages = "307--314",
year = "1986",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Chen:1986:RRB,
author = "Ye-Sho Chen and Ferdinand F. Leimkuhler",
title = "Research: A relationship between {Lotka's Law},
{Bradford's Law}, and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "5",
pages = "307--314",
month = sep,
year = "1986",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:27 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Jan 1999",
}
@Article{Egghe:1986:RDB,
author = "L. Egghe",
title = "Research: The dual of {Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "4",
pages = "246--255",
month = jul,
year = "1986",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198607)37:4<246::AID-ASI10>3.0.CO%3B2-D",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:27 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Jan 1999",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, underflow, and severe loss of significance
in floating-point addition and subtraction",
journal = j-IMA-J-NUMER-ANAL,
volume = "6",
number = "2",
pages = "241--251",
month = apr,
year = "1986",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05",
MRnumber = "89h:65065",
bibdate = "Sat Dec 23 14:52:49 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper it is shown that, under the assumption
of the logarithmic distribution of numbers,
floating-point addition and subtraction can result in
overflow or underflow with alarming frequency --- a
frequency that increases rapidly with machine speed
unless the range of the exponent is also increased. If
numbers are assumed to be distributed in accordance
with Sweeney's (1965) experiments, then severe loss of
significance occurs with large probability in floating
point subtraction. These results have implications for
computer design and lead to the suggestion of a long
word format which will reduce the risks to acceptable
levels.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Green:1986:BRP,
author = "M. W. Green",
title = "Book Reviews: {{\em Pareto Distributions}}, by {B. C.
Arnold}",
journal = j-APPL-STAT,
volume = "35",
number = "2",
pages = "215--215",
year = "1986",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:24:36 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Hoare:1986:DFS,
author = "G. T. Q. Hoare and E. Wright",
title = "The distribution of first significant digits",
journal = j-MATH-GAZ,
volume = "70",
number = "451",
pages = "34--37",
month = mar,
year = "1986",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Sat Feb 16 17:57:52 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3615826",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Katz:1986:FDP,
author = "Talbot M. Katz and Daniel I. A. Cohen",
title = "The First Digit Property for Exponential Sequences is
Independent of the Underlying Distribution",
journal = j-FIB-QUART,
volume = "24",
number = "1",
pages = "2--7",
month = feb,
year = "1986",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:45 MDT 2011",
bibsource = "http://www.fq.math.ca/24-1.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Lemons:1986:NTD,
author = "Don S. Lemons",
title = "On the number of things and the distribution of first
digits",
journal = j-AMER-J-PHYSICS,
volume = "54",
number = "9",
pages = "816--817",
month = sep,
year = "1986",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.14453",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Wed Nov 23 12:03:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ajp.aapt.org/",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
keywords = "Benford's Law",
remark = "Lemons gives a derivation of Benford's Law that does
not assume scale invariance, unlike other widely-cited
derivations
\cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}
@Book{Lines:1986:NYT,
author = "Malcolm E. Lines",
title = "A number for your thoughts: facts and speculations
about numbers from {Euclid} to the latest computers",
publisher = pub-ADAM-HILGER,
address = pub-ADAM-HILGER:adr,
pages = "vi + 214",
year = "1986",
ISBN = "0-85274-495-1 (paperback)",
ISBN-13 = "978-0-85274-495-6 (paperback)",
LCCN = "QA241 .L617 1986",
bibdate = "Wed Nov 23 11:34:02 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
URL = "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
acknowledgement = ack-nhfb,
remark = "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
of Benford''.",
subject = "number theory",
}
@Article{MacRoberts:1986:QMC,
author = "Michael H. MacRoberts and Barbara R. MacRoberts",
title = "Quantitative Measures of Communication in Science: a
Study of the Formal Level",
journal = j-SOC-STUD-SCI,
volume = "16",
number = "1",
pages = "151--172",
day = "1",
month = feb,
year = "1986",
CODEN = "SSSCDH",
DOI = "https://doi.org/10.1177/030631286016001008",
ISSN = "0306-3127 (print), 1460-3659 (electronic)",
ISSN-L = "0306-3127",
bibdate = "Mon Dec 3 09:12:44 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
note = "See \cite{Stigler:1987:PMF} and reply
\cite{MacRoberts:1987:MFU}.",
URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631286016001008",
acknowledgement = ack-nhfb,
fjournal = "Social Studies of Science",
journal-URL = "http://sss.sagepub.com/content/by/year",
}
@Article{Pao:1986:EEL,
author = "Miranda Lee Pao",
title = "An empirical examination of {Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "1",
pages = "26--33",
month = jan,
year = "1986",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/asi.4630370105",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:25 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "24 May 2007",
}
@Article{Pao:1986:REE,
author = "Miranda Lee Pao",
title = "Research: An empirical examination of {Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "37",
number = "1",
pages = "26--33",
month = jan,
year = "1986",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198601)37:1<26::AID-ASI4>3.0.CO%3B2-Z",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:25 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Jan 1999",
}
@Article{Patil:1986:DFD,
author = "S. A. Patil and V. R. R. Uppuluri",
title = "The Distribution of First $j$ Digits",
journal = j-COLLEGE-MATH-J,
volume = "17",
number = "3",
pages = "240--243",
month = may,
year = "1986",
CODEN = "????",
DOI = "https://doi.org/10.1080/07468342.1986.11972963",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:50:20 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
URL = "http://www.jstor.org/stable/2686982;
http://www.tandfonline.com/doi/abs/10.1080/07468342.1986.11972963",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
keywords = "Benford's Law",
onlinedate = "30 Jan 2018",
}
@Article{Pontigo:1986:QAB,
author = "J. Pontigo and F. W. Lancaster",
title = "Qualitative aspects of the {Bradford} distribution",
journal = j-SCIENTOMETRICS,
volume = "9",
number = "1--2",
pages = "59--70",
month = jan,
year = "1986",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02016608",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:02:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
URL = "http://link.springer.com/article/10.1007/BF02016608",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Schatte:1986:ALD,
author = "Peter Schatte",
title = "On the asymptotic logarithmic distribution of the
floating-point mantissas of sums",
journal = j-MATH-NACHR,
volume = "127",
number = "1",
pages = "7--20",
month = "????",
year = "1986",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19861270102",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Sun Feb 17 06:04:23 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}
@Article{Tichy:1986:GZU,
author = "Robert F. Tichy",
title = "{Gleichverteilung und zahlentheoretische Ungleichungen
II}. ({German}) [{Uniform} distribution and
number-theoretic inequalities {II}]",
journal = "Anzeiger der {\"O}sterreichischen Akademie der
Wissenschaften. Mathematisch-Naturwissenschaftliche
Klasse",
volume = "122(1985)",
number = "??",
pages = "95--99",
month = "????",
year = "1986",
CODEN = "OSAWA8",
DOI = "????",
ISSN = "0065-535X",
ISSN-L = "0065-535X",
bibdate = "Sun Feb 17 06:24:23 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
classmath = "11K06 (General theory of distribution modulo 1); 11J25
(Diophantine inequalities)",
keywords = "diophantine inequalities; discrepancy; H infinity;
logarithmic mean; summation method; uniform
distribution",
language = "German",
xxnote = "Despite repeated searches, I have not found this
journal online, not even from links at the Austrian
Academy of Sciences, \path=http://www.oeaw.ac.at=.",
}
@Article{Bak:1987:SOC,
author = "Per Bak and Chao Tang and Kurt Wiesenfeld",
title = "Self-organized criticality: An explanation of the $ 1
/ f $ noise",
journal = j-PHYS-REV-LET,
volume = "59",
number = "4",
pages = "381--384",
month = jul,
year = "1987",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.59.381",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 10:54:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.59.381",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Chen:1987:AZL,
author = "Ye-Sho Chen and Ferdinand F. Leimkuhler",
title = "Analysis of {Zipf}'s law: An index approach",
journal = j-INFO-PROC-MAN,
volume = "23",
number = "3",
pages = "171--182",
day = "1",
month = apr,
year = "1987",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/0306-4573(87)90002-1",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0306457387900021",
ZMnumber = "0614.62150",
abstract = "A rigorous analysis of Zipf's law is made using an
index for the sequence of observed values of the
variables in a Zipf-type relationship. Three important
properties relating rank, count, and frequency are
identified. Using this approach, the shape of Zipf-type
curves can be described in terms of three distinct
regions and two parameters of the Mandelbrot--Zipf law.
This result has considerable practical significance,
since it provides rigorous foundations for the
application of Zipf's law.",
acknowledgement = ack-nhfb,
classmath = "62P99 (Appl. of statistics)",
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
keywords = "index approach; Mandelbrot-Zipf law; Zipf's law",
}
@Article{Chen:1987:BLI,
author = "Ye-Sho Chen and F. F. Leimkuhler",
title = "{Bradford's Law}: An index approach",
journal = j-SCIENTOMETRICS,
volume = "11",
number = "3--4",
pages = "183--198",
month = mar,
year = "1987",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02016591",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:03:03 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
URL = "http://link.springer.com/article/10.1007/BF02016591",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Fedorowicz:1987:DPE,
author = "Jane Fedorowicz",
title = "Database Performance Evaluation in an Indexed File
Environment",
journal = j-TODS,
volume = "12",
number = "1",
pages = "85--110",
month = mar,
year = "1987",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Compendex database; Database/Graefe.bib;
Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
abstract = "The use of database systems for managerial decision
making often incorporates information-retrieval
capabilities with numeric report generation. Of great
concern to the user of such a system is the response
time associated with issuing a query to the database.
This study presents a procedure for estimating response
time for one of the most frequently encountered
physical storage mechanisms, the indexed file. The
model provides a fairly high degree of accuracy, but is
simple enough so that the cost of applying the model is
not exorbitant. The model incorporates the knowledge
that the distribution of access key occurrences is
known to follow Zipf's law. It first estimates the
access time required to complete the query, which
includes the time needed for all input and output
transactions, and CPU time used in performing the
search. The effects of multiple users on an
individual's response time are then assessed using a
simple regression estimation technique. The two-step
procedure allows for the separation of access time from
multiuser influences.",
acknowledgement = ack-nhfb,
affiliation = "Boston Univ, Boston, MA, USA",
affiliationaddress = "Boston Univ, Boston, MA, USA",
annote = "a procedure for estimating response time; distribution
of access key occurrences follow Zipf's law. Early
version with Kellogg, J. L. Model provides a fairly
high degree of accuracy but is simple. The effects of
multiple users are assessed using simple regression
estimation.",
classification = "723; 912; 922",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Design; Performance",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "data processing --- File organization; database
performance; database systems; indexed file
environment; MANAGEMENT --- Information Systems;
multiple users, design; Performance; performance;
response time; statistical methods --- regression
analysis; Zipf's law",
subject = "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems
Management, File organization. {\bf H.2.2}: Information
Systems, DATABASE MANAGEMENT, Physical Design, Access
methods. {\bf H.3.2}: Information Systems, INFORMATION
STORAGE AND RETRIEVAL, Information Storage, File
organization. {\bf H.3.3}: Information Systems,
INFORMATION STORAGE AND RETRIEVAL, Information Search
and Retrieval, Retrieval models.",
}
@Article{Hosking:1987:PQE,
author = "J. R. M. Hosking and J. R. Wallis",
title = "Parameter and Quantile Estimation for the Generalized
{Pareto} Distribution",
journal = j-TECHNOMETRICS,
volume = "29",
number = "3",
pages = "339--349",
month = "????",
year = "1987",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Fri Nov 25 16:39:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
}
@Article{Kunoff:1987:FDP,
author = "Sharon Kunoff",
title = "{$ N! $} has the First Digit Property",
journal = j-FIB-QUART,
volume = "25",
number = "4",
pages = "365--367",
month = nov,
year = "1987",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:01:00 MDT 2011",
bibsource = "http://www.fq.math.ca/25-4.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{MacRoberts:1987:MFU,
author = "Michael H. MacRoberts and Barbara R. MacRoberts",
title = "Measurement in the Face of Universal Uncertainty: a
Reply to {Stigler}",
journal = j-SOC-STUD-SCI,
volume = "17",
number = "2",
pages = "334--336",
day = "1",
month = may,
year = "1987",
CODEN = "SSSCDH",
DOI = "https://doi.org/10.1177/030631287017002008",
ISSN = "0306-3127 (print), 1460-3659 (electronic)",
ISSN-L = "0306-3127",
bibdate = "Mon Dec 3 09:12:46 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
note = "See \cite{MacRoberts:1986:QMC}.",
URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002008",
acknowledgement = ack-nhfb,
fjournal = "Social Studies of Science",
journal-URL = "http://sss.sagepub.com/content/by/year",
}
@Article{Nagasaka:1987:BLL,
author = "Kenji Nagasaka and Jau-Shyong Shiue",
title = "{Benford}'s law for linear recurrence sequences",
journal = "Tsukuba J. Math.",
volume = "11",
number = "2",
pages = "341--351",
year = "1987",
CODEN = "????",
ISSN = "0387-4982",
ISSN-L = "0387-4982",
MRclass = "60E99 (11B37)",
MRnumber = "926460 (88m:60047)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tsukuba Journal of Mathematics",
}
@Article{Nicholls:1987:BCE,
author = "Paul Travis Nicholls",
title = "Brief Communications: Estimation of {Zipf}
parameters",
journal = j-J-AM-SOC-INF-SCI,
volume = "38",
number = "6",
pages = "443--445",
month = nov,
year = "1987",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:31 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "24 May 2007",
}
@Article{Nicholls:1987:EZP,
author = "Paul Travis Nicholls",
title = "Estimation of {Zipf} parameters",
journal = j-J-AM-SOC-INF-SCI,
volume = "38",
number = "6",
pages = "443--445",
year = "1987",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}
@Article{Sanders:1987:PPUa,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Consumer Marketing",
volume = "4",
number = "1",
pages = "47--50",
month = "????",
year = "1987",
CODEN = "????",
DOI = "https://doi.org/10.1108/eb008188",
ISSN = "0736-3761",
ISSN-L = "0736-3761",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sanders:1987:PPUb,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Services Marketing",
volume = "1",
number = "2",
pages = "37--40",
month = "????",
year = "1987",
CODEN = "????",
DOI = "https://doi.org/10.1108/eb024706",
ISSN = "0887-6045",
ISSN-L = "0887-6045",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1987:ABM,
author = "Peter Schatte",
title = "On the asymptotic behaviour of the mantissa
distribution of sums",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "23",
number = "??",
pages = "353--360",
month = "????",
year = "1987",
CODEN = "JICYE5",
ISSN = "0863-0593",
ISSN-L = "0863-0593",
bibdate = "Sat Nov 12 15:58:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Inform. Process. Cybern. EIK",
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
}
@Article{Schatte:1987:SEU,
author = "Peter Schatte",
title = "Some estimates of the {$ \mathcal {H}_\infty
$}-uniform distribution",
journal = j-MONAT-MATH,
volume = "103",
number = "3",
pages = "233--249",
month = sep,
year = "1987",
CODEN = "MNMTA2",
DOI = "https://doi.org/10.1007/BF01364342",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
bibdate = "Sat Nov 12 15:57:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF01364342",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@Article{Stigler:1987:PMF,
author = "Stephen M. Stigler",
title = "Precise Measurement in the Face of Error: a Comment on
{MacRoberts} and {MacRoberts}",
journal = j-SOC-STUD-SCI,
volume = "17",
number = "2",
pages = "332--334",
day = "1",
month = may,
year = "1987",
CODEN = "SSSCDH",
DOI = "https://doi.org/10.1177/030631287017002007",
ISSN = "0306-3127 (print), 1460-3659 (electronic)",
ISSN-L = "0306-3127",
bibdate = "Mon Dec 3 09:12:46 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
note = "See \cite{MacRoberts:1986:QMC} and reply
\cite{MacRoberts:1987:MFU}.",
URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002007",
acknowledgement = ack-nhfb,
fjournal = "Social Studies of Science",
journal-URL = "http://sss.sagepub.com/content/by/year",
}
@Article{Tague:1987:MVZ,
author = "Jean Tague and Paul Nicholls",
title = "The maximal value of a {Zipf} size variable: Sampling
properties and relationship to other parameters",
journal = j-INFO-PROC-MAN,
volume = "23",
number = "3",
pages = "155--170",
day = "7",
month = jun,
year = "1987",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/0306-4573(87)90001-X",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/030645738790001X",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
keywords = "Zipf's Law",
}
@Article{Tichy:1987:GS,
author = "Robert F. Tichy",
title = "{Gleichverteilung zum Summierungsverfahren {$ H_\infty
$}}. ({German}) [{Uniform} distribution to the {$
H_\infty $} summation method]",
journal = j-MATH-NACHR,
volume = "131",
number = "??",
pages = "119--125",
month = "????",
year = "1987",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19871310112",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Mon Feb 18 06:44:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0626.10044",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
keywords = "$H_\infty$-discrepancy; difference sequences; real
sequences; uniform distribution",
language = "German",
ZMclass = "11K06 (General theory of distribution modulo 1); 40J05
(Summability in abstract structures)",
ZMreviewer = "D. Leitmann",
}
@Article{Turner:1987:DDI,
author = "Peter R. Turner",
title = "The Distribution of l.s.d. and Its Implications for
Computer Design",
journal = j-MATH-GAZ,
volume = "71",
number = "455",
pages = "26--31",
month = mar,
year = "1987",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.2307/3616283",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Tue Oct 30 23:36:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "[l.s.d. = least significant digits]. The topic is
variously known as Benford's Law, the Law of Anomalous
Numbers, and Zipf's Law.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Belevitch:1988:PQD,
author = "Vitold Belevitch",
title = "{{\`A}} propos de la queue de la distribution de
{Zipf}. ({French}) [{On} the tail of the {Zipf}
distribution]",
journal = "Ann. Soc. Sci. Bruxelles S{\'e}r. I",
volume = "102",
number = "3",
pages = "73--85 (1989)",
year = "1988",
CODEN = "ASSBAH",
ISSN = "0037-959X",
ISSN-L = "0037-959X",
MRclass = "92A90",
MRnumber = "1016850 (90g:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de la Societ{\'e} Scientifique de Bruxelles.
S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
et Physiques",
language = "French",
}
@Article{Carslaw:1988:AIN,
author = "C. A. Carslaw",
title = "Anomalies in Income Numbers: Evidence of Goal-Oriented
Behavior",
journal = j-ACCOUNT-REV,
volume = "63",
number = "2",
pages = "321--327",
month = apr,
year = "1988",
CODEN = "ACRVAS",
ISSN = "0001-4826 (print), 1558-7967 (electronic)",
ISSN-L = "0001-4826",
bibdate = "Sat Sep 10 11:00:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/248109",
acknowledgement = ack-nhfb,
fjournal = "The Accounting Review",
journal-URL = "https://www.jstor.org/journal/accountingreview",
keywords = "Benford's Law; New Zealand firms; second-digit
frequency",
remark-1 = "This paper references neither Newcomb nor Benford, but
it uses their digit-frequency formula from
\cite{Feller:1966:IPT} to compare with data on revenues
of New Zealand companies.",
remark-2 = "According to \cite{Kossovsky:2015:BLT}, this may be
the first published serious use of Benford's Law for
fraud detection in accounting, although the possibility
had been mentioned 16 years earlier
\cite{Varian:1972:LEB}, and that earlier paper is not
cited in this 1988 paper.",
}
@Article{Hill:1988:RNG,
author = "Theodore Hill",
title = "Random number guessing and the first digit
phenomenon",
journal = j-PSYCHOL-REP,
volume = "62",
number = "3",
pages = "967--971",
month = jun,
year = "1988",
CODEN = "PYRTAZ",
DOI = "https://doi.org/10.2466/pr0.1988.62.3.967",
ISSN = "0033-2941 (print), 1558-691X (electronic)",
ISSN-L = "0033-2941",
bibdate = "Fri Feb 15 06:41:31 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967",
acknowledgement = ack-nhfb,
ajournal = "Psychol. rep.",
fjournal = "Psychological Reports",
}
@InCollection{Kanemitsu:1988:BLF,
author = "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
Rauzy and Jau-Shyong Shiue",
booktitle = "Probability theory and mathematical statistics
({Kyoto}, 1986)",
title = "On {Benford}'s law: the first digit problem",
volume = "1299",
publisher = pub-SV,
address = pub-SV:adr,
pages = "158--169",
year = "1988",
DOI = "https://doi.org/10.1007/BFb0078471",
MRclass = "11K06 (60E99)",
MRnumber = "935987 (89d:11059)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Math.",
acknowledgement = ack-nhfb,
}
@InCollection{Nicolis:1988:PBZ,
author = "John S. Nicolis",
booktitle = "Synergetics, order and chaos ({Madrid}, 1987)",
title = "On the parallel between {Zipf}'s law and {$ 1 / f $}
processes in chaotic systems possessing coexisting
attractors",
publisher = "World Sci. Publ.",
address = "Teaneck, NJ, USA",
pages = "723--734",
year = "1988",
MRclass = "58F13 (00A69)",
MRnumber = "1115922 (92g:58087)",
MRreviewer = "Dieter H. Mayer",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Prather:1988:CET,
author = "R. E. Prather",
title = "Comparison and Extension of Theories of {Zipf} and
{Halstead}",
journal = j-COMP-J,
volume = "31",
number = "3",
pages = "248--252",
month = jun,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
affiliation = "Trinity Univ, San Antonio, TX, USA",
affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
classcodes = "C6110B (Software engineering techniques)",
classification = "723",
corpsource = "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX,
USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "behavioural psychology; computer programming; computer
software; empirical law; Halstead metrics; Halstead's
hypothesis; length estimates; Measurements;
probabilistic hypothesis; process; programming;
software engineering; software metrication; software
science; Zipf metrics; Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Article{Sanders:1988:PPU,
author = "Robert Sanders",
title = "The {Pareto Principle}: Its Use and Abuse",
journal = "Journal of Business \& Industrial Marketing",
volume = "3",
number = "2",
pages = "37--40",
month = "????",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1108/eb006057",
ISSN = "0885-8624",
ISSN-L = "0885-8624",
bibdate = "Fri Nov 25 07:04:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1988:ASC,
author = "Peter Schatte",
title = "On the Almost Sure Convergence of Floating-Point
Mantissas and {Benford's Law}",
journal = j-MATH-NACHR,
volume = "135",
number = "1",
pages = "79--83",
month = "????",
year = "1988",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19881350108",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "60F15 (11K31)",
MRnumber = "944219 (89g:60114)",
MRreviewer = "S. A. Book",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
onlinedate = "12 Nov 2006",
reviewer = "S. A. Book",
}
@Article{Schatte:1988:LIL,
author = "Peter Schatte",
title = "On a law of the iterated logarithm for sums {$ \bmod 1
$} with application to {Benford}'s law",
journal = j-PROBAB-THEORY-RELAT-FIELDS,
volume = "77",
number = "2",
pages = "167--178",
month = feb,
year = "1988",
CODEN = "PTRFEU",
DOI = "https://doi.org/10.1007/BF00334035",
ISSN = "0178-8051 (print), 1432-2064 (electronic)",
ISSN-L = "0178-8051",
MRclass = "60F15 (11K31)",
MRnumber = "927235 (89b:60081)",
MRreviewer = "L. Kuipers",
bibdate = "Sun Apr 27 11:18:06 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/probab-theory-relat-fields.bib",
URL = "http://link.springer.com/article/10.1007/BF00334035",
acknowledgement = ack-nhfb,
fjournal = "Probability Theory and Related Fields",
journal-URL = "http://link.springer.com/journal/440",
}
@Article{Schatte:1988:MDC,
author = "Peter Schatte",
title = "On Mantissa Distribution in Computing and {Benford's
Law}",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "24",
number = "9",
pages = "443--455",
month = "????",
year = "1988",
CODEN = "JICYE5",
ISSN = "0863-0593",
ISSN-L = "0863-0593",
MRclass = "60E05 (11K06 11K31 65G99)",
MRnumber = "984516 (90g:60016)",
MRreviewer = "F. Schweiger",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/eik/eik24.html#Schatte88",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
dblp-key = "journals/eik/Schatte88",
dblp-mdate = "2020-03-06",
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Schatte:1988:UDC,
author = "Peter Schatte",
title = "On the uniform distribution of certain sequences and
{Benford}'s law",
journal = j-MATH-NACHR,
volume = "136",
number = "1",
pages = "271--273",
year = "1988",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.19881360119",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "11K06 (11K31)",
MRnumber = "952478 (89j:11075)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
onlinedate = "11 Nov 2006",
}
@Article{Tichy:1988:SRC,
author = "Robert F. Tichy",
title = "{Statistische Resultate {\"u}ber computergerechte
Darstellungen von Zahlen}. ({German}) [Statistical
results on computer-oriented representations of
numbers]",
journal = "Anzeiger der {\"O}sterreichischen Akademie der
Wissenschaften. Mathematisch-Naturwissenschaftliche
Klasse",
volume = "1987",
number = "??",
pages = "1--8",
month = "????",
year = "1988",
CODEN = "OSAWA8",
DOI = "????",
ISSN = "0065-535X",
ISSN-L = "0065-535X",
bibdate = "Mon Feb 18 06:45:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0625.10041",
acknowledgement = ack-nhfb,
ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
language = "German",
xxnote = "Despite repeated searches, I have not found this
journal online, not even from links at the Austrian
Academy of Sciences, \path=http://www.oeaw.ac.at=.",
ZMclass = "11K16 (Normal numbers, etc.); 11J71 (Distribution
modulo one); 11K38 (Irregularities of distribution)",
}
@Article{Arnold:1989:BEP,
author = "Barry C. Arnold and S. James Press",
title = "{Bayesian} estimation and prediction for {Pareto}
data",
journal = j-J-AM-STAT-ASSOC,
volume = "84",
number = "408",
pages = "1079--1084",
month = "????",
year = "1989",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62F15 (62F10)",
MRnumber = "92f:62034",
bibdate = "Mon May 5 12:36:01 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Chen:1989:ZLT,
author = "Ye-Sho Chen",
title = "{Zipf}'s laws in text modeling",
journal = "International Journal of General Systems. Methodology,
Applications, Education",
volume = "15",
number = "3",
pages = "233--252",
year = "1989",
CODEN = "IJGSAX",
DOI = "https://doi.org/10.1080/03081078908935048",
ISSN = "0308-1079, 1026-7492, 1563-5104",
ISSN-L = "0308-1079",
MRclass = "92A90",
MRnumber = "1015844",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Internat. J. Gen. Systems",
fjournal = "International Journal of General Systems. Methodology,
Applications, Education",
}
@Article{Family:1989:KDG,
author = "Fereydoon Family and Paul Meakin",
title = "Kinetics of droplet growth processes: Simulations,
theory, and experiments",
journal = j-PHYS-REV-A,
volume = "40",
number = "7",
pages = "3836--3854",
month = oct,
year = "1989",
CODEN = "PLRAAN",
DOI = "https://doi.org/10.1103/PhysRevA.40.3836",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Thu Feb 28 10:49:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevA.40.3836",
acknowledgement = ack-nhfb,
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
}
@InProceedings{Kitsuregawa:1989:EBS,
author = "Masaru Kitsuregawa and Masaya Nakayama and Mikio
Takagi",
title = "The Effect of Bucket Size Tuning in the Dynamic Hybrid
{GRACE} Hash Join Method",
crossref = "Apers:1989:VLD",
pages = "257--266",
month = aug,
year = "1989",
CODEN = "VLDBDP",
bibdate = "Sat Jan 25 17:38:12 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/hash.bib",
abstract = "In this paper, we show detailed analysis and
performance evaluation of the Dynamic Hybrid GRACE Hash
Join Method (DHGH Method) when the tuple distribution
in buckets is unbalanced. The conventional Hash Join
Methods specify the tuple distribution in buckets
statically. However it may differ from estimation since
join operations are applied with selection operations.
When the tuple distribution in buckets is unbalanced,
the processing cost of join operation becomes more
costly than the ideal case when you use Hybrid Hash
Join Method (HH Method). On the other hand, when you
use the DHGH Method, the destaging buckets are selected
dynamically, gives the same performance as the ideal
case even if the tuple distribution in buckets is
unbalanced such as Zipf-like distributions.",
acknowledgement = ack-nhfb,
affiliation = "Univ of Tokyo",
affiliationaddress = "Tokyo, Jpn",
classification = "723",
journalabr = "Very Large Data Bases Int Conf Very Large Data Bases",
keywords = "Computer Metatheory --- Programming Theory; Computer
Programming --- Algorithms; Database Systems; Query
Processing; Relational; Relational Algebra; VLDB",
}
@Article{Lang:1989:UAB,
author = "Sheau-Dong Lang and James R. Driscoll and Jiann H.
Jou",
title = "A Unified Analysis of Batched Searching of Sequential
and Tree-Structured Files",
journal = j-TODS,
volume = "14",
number = "4",
pages = "604--618",
month = dec,
year = "1989",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
MRclass = "68P10 (68P20)",
MRnumber = "1 073 204",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Database/Graefe.bib; Database/Wiederhold.bib;
http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
abstract = "A direct and unified approach is used to analyze the
efficiency of batched searching of sequential and
tree-structured files. The analysis is applicable to
arbitrary search distributions, and closed-form
expressions are obtained for the expected batched
searching cost and savings. In particular, we consider
a search distribution satisfying Zipf's law for
sequential files and four types of uniform (random)
search distribution for sequential and tree-structured
files. These results unify and extend earlier research
on batched searching and estimating block accesses for
database systems.",
acknowledgement = ack-nhfb,
affiliation = "Central Florida Univ., Orlando, FL, USA",
annote = "closed-form expressions for the number of accesses
needed given arbitrary search distributions.",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Algorithms; Design; Performance; Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "algorithms; design; performance; theory",
subject = "{\bf H.3.3}: Information Systems, INFORMATION STORAGE
AND RETRIEVAL, Information Search and Retrieval, Search
process. {\bf H.3.2}: Information Systems, INFORMATION
STORAGE AND RETRIEVAL, Information Storage, File
organization. {\bf H.2.2}: Information Systems,
DATABASE MANAGEMENT, Physical Design, Access methods.",
}
@Article{Nicholls:1989:RBM,
author = "Paul Travis Nicholls",
title = "Research: Bibliometric modeling processes and the
empirical validity of {Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "40",
number = "6",
pages = "379--385",
month = nov,
year = "1989",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(198911)40:6<379::AID-ASI1>3.0.CO%3B2-Q",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:37 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "27 May 2007",
}
@Article{Nicolis:1989:CDM,
author = "G. Nicolis and C. Nicolis and John S. Nicolis",
title = "Chaotic dynamics, {Markov} partitions, and {Zipf}'s
law",
journal = j-J-STAT-PHYS,
volume = "54",
number = "3--4",
pages = "915--924",
month = feb,
year = "1989",
CODEN = "JSTPSB",
DOI = "https://doi.org/10.1007/BF01019781",
ISSN = "0022-4715 (print), 1572-9613 (electronic)",
ISSN-L = "0022-4715",
MRclass = "58F13 (58F14 58F20)",
MRnumber = "988565 (90b:58184)",
MRreviewer = "Shi Hai Li",
bibdate = "Thu Aug 28 18:40:55 MDT 2014",
bibsource = "http://link.springer.com/journal/10955;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=54&issue=3;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
URL = "http://link.springer.com/article/10.1007/BF01019781",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Physics",
journal-URL = "http://link.springer.com/journal/10955",
}
@Article{Nicolis:1989:PBZ,
author = "John S. Nicolis and Ichiro Tsuda",
title = "On the parallel between {Zipf}'s law and {$ 1 / f $}
processes in chaotic systems possessing coexisting
attractors",
journal = j-PROG-THEOR-PHYS,
volume = "82",
number = "2",
pages = "254--274",
year = "1989",
CODEN = "PTPKAV",
ISSN = "0033-068X (print), 1347-4081 (electronic)",
ISSN-L = "0033-068X",
MRclass = "58F13 (92K20)",
MRnumber = "1023357 (91d:58165)",
MRreviewer = "Nima Geffen",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
journal-URL = "http://ptp.oxfordjournals.org/content/by/year",
}
@Article{Schatte:1989:MUD,
author = "Peter Schatte",
title = "On measures of uniformly distributed sequences and
{Benford}'s law",
journal = j-MONAT-MATH,
volume = "107",
number = "3",
pages = "245--256",
year = "1989",
CODEN = "MNMTA2",
DOI = "https://doi.org/10.1007/BF01300347",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
MRclass = "11K36 (60F99)",
MRnumber = "1008683 (90k:11097)",
MRreviewer = "Kazuo Goto",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@Article{Shanbhag:1989:BRBa,
author = "D. N. Shanbhag",
title = "Book Review: {{\booktitle{Pareto Distributions}}, by
B. C. Arnold}",
journal = j-J-R-STAT-SOC-SER-A-STAT-SOC,
volume = "152",
number = "2",
pages = "253--254",
month = "????",
year = "1989",
CODEN = "JSSAEF",
DOI = "https://doi.org/10.2307/2982920",
ISSN = "0964-1998 (print), 1467-985X (electronic)",
ISSN-L = "0964-1998",
bibdate = "Sat Jan 24 15:13:38 MST 2015",
bibsource = "http://www.jstor.org/stable/i349642;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1980.bib",
URL = "http://www.jstor.org/stable/2982920",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series A
(Statistics in Society)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-985X;
http://www.jstor.org/journals/09641998.html",
}
@Article{Shieh:1989:BZE,
author = "Yeung-Nan Shieh",
title = "The {Beckmann--Zipf} effect and plant location under
uniform pricing",
journal = j-ECONOM-LETT,
volume = "30",
number = "1",
pages = "89--92",
day = "1",
month = jan,
year = "1989",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/0165-1765(89)90162-6",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "90A12 (90B05)",
MRnumber = "1010312",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0165176589901626",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Thomas:1989:UPR,
author = "Jacob K. Thomas",
title = "Unusual patterns in reported earnings",
journal = j-ACCOUNT-REV,
volume = "59",
number = "4",
pages = "773--787",
month = oct,
year = "1989",
CODEN = "ACRVAS",
ISSN = "0001-4826 (print), 1558-7967 (electronic)",
ISSN-L = "0001-4826",
bibdate = "Fri Feb 15 06:49:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/247861",
acknowledgement = ack-nhfb,
fjournal = "The Accounting Review",
keywords = "Benford's Law; distribution of first digits;
distribution of second digits",
}
@Article{Xekalaki:1989:APY,
author = "E. Xekalaki and J. Panaretos",
title = "On the Association of the {Pareto} and the {Yule}
Distribution",
journal = j-THEORY-PROBAB-APPL,
volume = "33",
number = "1",
pages = "191--195",
month = "????",
year = "1989",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/1133028",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Tue Apr 1 10:40:04 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/33/1;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
onlinedate = "January 1989",
}
@Article{Egghe:1990:RAT,
author = "L. Egghe",
title = "Research: Applications of the theory of {Bradford}'s
{Law} to the calculation of {Leimkuhler's Law} and to
the completion of bibliographies",
journal = j-J-AM-SOC-INF-SCI,
volume = "41",
number = "7",
pages = "469--492",
month = oct,
year = "1990",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199010)41:7<469::AID-ASI1>3.0.CO%3B2-P",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:41 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Jan 1999",
}
@Article{Egghe:1990:RND,
author = "L. Egghe",
title = "Research: A note on different {Bradford} multipliers",
journal = j-J-AM-SOC-INF-SCI,
volume = "41",
number = "3",
pages = "204--209",
month = apr,
year = "1990",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199004)41:3<204::AID-ASI7>3.0.CO%3B2-8",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:39 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Jan 1999",
}
@Article{Katsikas:1990:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic dynamics of generating {Markov} partitions and
linguistic sequences mimicking {Zipf}'s law",
journal = "Nuovo Cimento D (1)",
volume = "12",
number = "2",
pages = "177--195",
year = "1990",
CODEN = "NCSDDN",
DOI = "https://doi.org/10.1007/BF02450454",
ISSN = "0392-6737 (print), 1826-9893 (electronic)",
ISSN-L = "0392-6737",
MRclass = "92A90 (58F13 92A08 94A15)",
MRnumber = "1049338 (90m:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
Serie 1",
}
@InCollection{Nagasaka:1990:BLL,
author = "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
Shiue",
booktitle = "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
title = "{Benford}'s law: the logarithmic law of first digit",
volume = "51",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "361--391",
year = "1990",
MRclass = "11K06",
MRnumber = "1058225 (92b:11048)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Colloq. Math. Soc. J{\'a}nos Bolyai",
acknowledgement = ack-nhfb,
}
@Article{Peritz:1990:BDB,
author = "Bluma C. Peritz",
title = "A {Bradford} distribution for bibliometrics",
journal = j-SCIENTOMETRICS,
volume = "18",
number = "5--6",
pages = "323--329",
month = may,
year = "1990",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02020148",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:03:16 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
URL = "http://link.springer.com/article/10.1007/BF02020148",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Schatte:1990:BLC,
author = "Peter Schatte",
title = "On {Benford}'s law for continued fractions",
journal = j-MATH-NACHR,
volume = "148",
pages = "137--144",
year = "1990",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
MRclass = "11K50 (11K06)",
MRnumber = "1127337 (92m:11077)",
MRreviewer = "Harald Niederreiter",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}
@Book{Szekely:1990:PKN,
author = "G{\'a}bor J. Sz{\'e}kely",
title = "{Paradoxa: klassische und neue {\"U}berraschungen aus
Wahrscheinlichkeitsrechnung und mathematischer
Statistik}. (German) [{Paradoxes}: traditional and new
surprises in probability and mathematical statistics]",
publisher = "Deutsch",
address = "Thun, Switzerland",
pages = "239",
year = "1990",
ISBN = "3-87144-850-8",
ISBN-13 = "978-3-87144-850-8",
LCCN = "????",
bibdate = "Thu Nov 17 19:26:05 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
note = "Translation by Ulrike Leitner from the Hungarian
original.",
URL = "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf;
http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{VandenBroeck:1990:LFB,
author = "C. {Van den Broeck} and R. Kawai",
title = "Learning in feedforward {Boolean} networks",
journal = j-PHYS-REV-A,
volume = "42",
number = "??",
pages = "6210--??",
day = "15",
month = nov,
year = "1990",
CODEN = "PLRAAN",
DOI = "https://doi.org/10.1103/PhysRevA.42.6210",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevA.42.6210",
acknowledgement = ack-nhfb,
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Yeh:1990:ODT,
author = "Hsiaw-Chan Yeh",
title = "One discrete time series model for fat-tailed integer
random variables: {Zipf} process",
journal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
volume = "18",
number = "1",
pages = "19--33",
year = "1990",
CODEN = "BIMSDG",
ISSN = "0304-9825",
ISSN-L = "0304-9825",
MRclass = "60J10 (62M10)",
MRnumber = "1072827 (91i:60175)",
MRreviewer = "Ed McKenzie",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Acad. Sinica",
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
}
@Article{Antonini:1991:NUD,
author = "Rita Giuliano Antonini",
title = "On the Notion of Uniform Distribution Mod $1$",
journal = j-FIB-QUART,
volume = "29",
number = "3",
pages = "230--234",
month = aug,
year = "1991",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:01:34 MDT 2011",
bibsource = "http://www.fq.math.ca/29-3.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/29-3/antonini.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
keywords = "Benford's Law",
}
@Article{Burke:1991:BLP,
author = "John Burke and Eric Kincanon",
title = "{Benford}'s law and physical constants: The
distribution of initial digits",
journal = j-AMER-J-PHYSICS,
volume = "59",
number = "10",
pages = "952--952",
month = oct,
year = "1991",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.16838",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Mon Nov 14 17:31:11 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Burrell:1991:BDG,
author = "Q. L. Burrell",
title = "The {Bradford} distribution and the {Gini} index",
journal = j-SCIENTOMETRICS,
volume = "21",
number = "2",
pages = "181--194",
month = jun,
year = "1991",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02017568",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:03:22 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
URL = "http://link.springer.com/article/10.1007/BF02017568",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Chen:1991:ZLN,
author = "Ye-Sho Chen",
title = "{Zipf}'s law in natural languages, programming
languages, and command languages: the {Simon--Yule}
approach",
journal = j-INT-J-SYST-SCI,
volume = "22",
number = "11",
pages = "2299--2312",
year = "1991",
CODEN = "IJSYA9",
DOI = "https://doi.org/10.1080/00207729108910791",
ISSN = "0020-7721 (print), 1464-5319 (electronic)",
ISSN-L = "0020-7721",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0793.68020",
abstract = "Zipf's law and issues in natural languages,
programming languages and command languages related to
it, are reviewed. We point out the need for a unified
theory to resolve the issues. Based on Herbert Simon's
creative process for scientific discovery, we evaluate
four leading theories of language generation. As a
result, the Simon--Yule model of text generation is
selected as a promising theory. The implications of the
theory related to the issues in natural languages,
programming languages and command languages are
discussed.",
acknowledgement = ack-nhfb,
classmath = "68N15 (Programming languages) 68T50 (Natural language
processing)",
fjournal = "International Journal of Systems Science",
keywords = "command languages; natural languages; programming
languages; Simon-Yule model; text generation; Zipf's
law",
}
@Book{Durrett:1991:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Wadsworth and Brooks\slash Cole Advanced Books and
Software",
address = "Pacific Grove, CA, USA",
pages = "ix + 453",
year = "1991",
ISBN = "0-534-13206-5",
ISBN-13 = "978-0-534-13206-4",
LCCN = "QA273 .D865 1991",
bibdate = "Mon Nov 21 10:06:18 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$49.95",
series = "The Wadsworth and Brooks\slash Cole statistics\slash
probability series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 300ff. Hill \cite[page
893]{Hill:1995:BII} reports that Durrett has a proof
that the $k$-th digit of powers of integers follows
Benford's Law.",
subject = "Probabilities",
}
@Book{Hardy:1991:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
edition = "Second",
pages = "xvi + 396",
year = "1991",
ISBN = "0-8284-0334-1",
ISBN-13 = "978-0-8284-0334-4",
LCCN = "QA295 .H29 1991",
bibdate = "Wed Nov 16 08:17:27 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
remark = "Unaltered reprint of \cite{Hardy:1949:DS}, despite
label of second edition.",
subject = "Divergent series",
}
@Article{Katsikas:1991:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic Dynamics of Generating {Markov} Partitions,
and Linguistic Sequences Mimicking {Zipf}'s Law",
journal = j-LECT-NOTES-COMP-SCI,
volume = "565",
pages = "335--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon May 13 08:51:55 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Schatte:1991:NBL,
author = "P. Schatte and K. Nagasaka",
title = "A note on {Benford}'s law for second order linear
recurrences with periodical coefficients",
journal = j-Z-ANAL-ANWEND,
volume = "10",
number = "2",
pages = "251--254",
year = "1991",
CODEN = "????",
ISSN = "0232-2064 (print), 1661-4534 (electronic)",
ISSN-L = "0232-2064",
MRclass = "11K31",
MRnumber = "1155374 (93b:11101)",
MRreviewer = "F. Schweiger",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}
@Article{Schatte:1991:ULI,
author = "P. Schatte",
title = "On a uniform law of the iterated logarithm for sums
mod {$1$} and {Benford}'s law",
journal = "Litovsk. Mat. Sb.",
volume = "31",
number = "1",
pages = "205--217",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1007/BF00972327",
ISSN = "0132-2818",
ISSN-L = "0132-2818",
MRclass = "60F15 (11K99)",
MRnumber = "1161363 (93g:60067)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR
Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys.
Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye
Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\
Matematicheski{\u\i} Sbornik",
xxnote = "Check pages: reprinted in two version of this
journal??",
}
@Book{Schroeder:1991:FCP,
author = "Manfred Schroeder",
title = "Fractals, Chaos, Power Laws",
publisher = pub-W-H-FREEMAN,
address = pub-W-H-FREEMAN:adr,
pages = "xviii + 429",
year = "1991",
ISBN = "0-671-74217-5, 0-7167-2136-8, 0-7167-2357-3",
ISBN-13 = "978-0-671-74217-1, 978-0-7167-2136-9,
978-0-7167-2357-8",
LCCN = "QD921 .S3 1990",
bibdate = "Wed Dec 15 10:41:35 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/shannon-claude-elwood.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
abstract = "Reveals the extraordinary dimensions of new
mathematical insights about the nature of physical
reality; explores the powerful applications of these
symmetry concepts in physics, chemistry, music, and the
visual arts. Includes such areas as deterministic chaos
and strange attractors, iterated mappings, nonlinear
dynamics, Cayley trees, cellular automata, random
fractals and related topics.",
acknowledgement = ack-nhfb,
shorttableofcontents = "Introduction \\
Similarity and dissimilarity \\
Self-similarity --- discrete, continuous, strict, and
otherwise \\
Power laws: endless sources of self-similarity \\
Noises: white, pink, brown, and black \\
Brownian motion, gambling losses, and intergalactic
voids: random fractals par excellence \\
Cantor sets: self-similarity and arithmetic dust \\
Fractals in higher dimensions and a digital sundial \\
Multifractals: intimately intertwined fractals \\
Some practical fractals and their measurement \\
Iteration, strange mappings, and a billion digits for
$\pi$ \\
A self-similar sequence, the logistic parabola, and
symbolic dynamics \\
A forbidden symmetry, Fibonacci's rabbits, and a new
state of matter \\
Periodic and quasiperiodic structures in space --- the
route to spatial chaos \\
Percolation: from forest fires to epidemics \\
Phase transitions and renormalization \\
Cellular automata",
tableofcontents = "Preface / xiii \\
1: Introduction / 1 \\
Einstein, Pythagoras, and Simple Similarity / 3 \\
A Self-Similar Array of Self-Preserving Queens / 4 \\
A Self-Similar Snowflake / 7 \\
A New Dimension for Fractals / 9 \\
A Self-Similar Tiling and a ``Non-Euclidean'' Paradox /
13 \\
At the Gates of Cantor's Paradise / 15 \\
The Sierpinski Gasket / 17 \\
Sir Pinski's Game and Deterministic Chaos / 20 \\
Three Bodies Cause Chaos / 25 \\
Strange Attractors, Their Basins, and a Chaos Game 2 /
7 \\
Percolating Random Fractals / 30 \\
Power Laws: from Alvarez to Zipf / 33 \\
Newton's Iteration and How to Abolish Two-Nation
Boundaries / 38 \\
Could Minkowski Hear the Shape of a Drum? / 40 \\
Discrete Self-Similarity: Creases and Center Folds / 45
\\
Golden and Silver Means and Hyperbolic Chaos / 49 \\
Winning at Fibonacci Nim / 53 \\
Self-Similar Sequences from Square Lattices / 55 \\
John Horton Conway's ``Death Bet'' / 57 \\
2: Similarity and Dissimilarity / 61 \\
More Than One Scale / 61 \\
To Scale or Not to Scale: A Bit of Biology and
Astrophysics / 63 \\
Similarity in Physics: Some Astounding Consequences /
66 \\
Similarity in Concert Halls, Microwaves, and
Hydrodynamics / 68 \\
Scaling in Psychology / 70 \\
Acousticians, Alchemy, and Concert Halls / 72 \\
Preference and Dissimilarity: Concert Halls Revisited /
74 \\
3: Self-Similarity --- Discrete, Continuous, Strict,
and Otherwise / 81 \\
The Logarithmic Spiral, Cutting Knives, and Wideband
Antennas / 89 \\
Some Simple Cases of Self-Similarity / 93 \\
Weierstrass Functions and a Musical Paradox / 96 \\
More Self-Similarity in Music: The Tempered Scales of
Bach / 99 \\
The Excellent Relations between the Primes 3, 5, and 7
/ 102 \\
4: Power Laws: Endless Sources of Self-Similarity / 103
\\
The Sizes of Cities and Meteorites / 103 \\
A Fifth Force of Attraction / 105 \\
Free of Natural Scales / 107 \\
Bach Composing on All Scales / 107 \\
Birkhoff's Aesthetic Theory / 109 \\
Heisenberg's Hyperbolic Uncertainty Principle / 112 \\
Fractional Exponents / 115 \\
The Peculiar Distribution of the First Digit / 116 \\
The Diameter Exponents of Trees, Rivers, Arteries, and
Lungs / 117 \\
5: Noises: White, Pink, Brown, and Black / 121 \\
Pink Noise / 122 \\
Self-Similar Trends on the Stock Market / 126 \\
Black Noises and Nile Floods / 129 \\
Warning: World Warming / 131 \\
Fractional Integration: A Modem Tool / 131 \\
Brownian Mountains / 133 \\
Radon Transform and Computer Tomography / 134 \\
Fresh and Tired Mountains / 135 \\
6: Brownian Motion, Gambling Losses, and Intergalactic
Voids: Random Fractals Par Excellence / 139 \\
The Brownian Beast Tamed / 140 \\
Brownian Motion as a Fractal / 141 \\
How Many Molecules? / 143 \\
The Spectrum of Brownian Motion / 144 \\
The Gambler's Ruin, Random Walks, and Information
Theory / 145 \\
Counterintuition Runs Rampant in Random Runs / 146 \\
More Food for Fair Thought / 147 \\
The St. Petersburg Paradox / 148 \\
Shannon's Outguessing Machine / 149 \\
The Classical Mechanics of Roulette and Shannon's
Channel Capacity / 150 \\
The Clustering of Poverty and Galaxies / 152 \\
Levy Flights through the Universe / 155 \\
Paradoxes from Probabilistic Power Laws / 155 \\
Invariant Distributions: Gauss, Cauchy, and Beyond /
157 \\
7: Cantor Sets: Self-Similarity and Arithmetic Dust /
161 \\
A Comer of Cantor's Paradise / 161 \\
Cantor Sets as Invariant Sets / 165 \\
Symbolic Dynamics and Deterministic Chaos / 166 \\
Devil's Staircases and a Pinball Machine / 167 \\
Mode Locking in Swings and Clocks / 171 \\
The Frustrated Manhattan Pedestrian / 172 \\
Arnold Tongues 17 / 4 \\
8: Fractals in Higher Dimensions and a Digital Sundial
/ 177 \\
Cartesian Products of Cantor Sets / 177 \\
A Leaky Gasket, Soft Sponges, and Swiss Cheeses / 178
\\
A Cantor-Set Sundial / 181 \\
Fat Fractals / 183 \\
9: Multifractals: Intimately Intertwined Fractals / 187
\\
The Distributions of People and Ore / 187 \\
Self-Affine Fractals without Holes / 190 \\
The Multifractal Spectrum: Turbulence and
Diffusion-Limited Aggregation / 193 \\
Viscous Fingering / 199 \\
Multifractals on Fractals / 200 \\
Fractal Dimensions from Generalized Entropies / 203 \\
The Relation between the Multifractal Spectrum
$f(\alpha)$ and the Mass Exponents $(q)$ / 205 \\
Strange Attractors as Multifractals / 206 \\
A Greedy Algorithm for Unfavorable Odds / 207 \\
10: Some Practical Fractals and Their Measurement / 211
\\
Dimensions from Box Counting / 213 \\
The Mass Dimension / 215 \\
The Correlation Dimension / 220 \\
Infinitely Many Dimensions / 220 \\
The Determination of Fractal Dimensions from Time
Series / 223 \\
Abstract Concrete / 224 \\
Fractal Interfaces Enforce Fractional Frequency
Exponents / 225 \\
The Fractal Dimensions of Fracture Surfaces / 230 \\
The Fractal Shapes of Clouds and Rain Areas / 231 \\
Cluster Agglomeration / 232 \\
Diffraction from Fractals / 233 \\
11: Iteration, Strange Mappings, and a Billion Digits
for Pi / 237 \\
Looking for Zeros and Encountering Chaos / 239 \\
The Strange Sets of Julia / 243 \\
A Multifractal Julia Set / 245 \\
The Beauty of Broken Linear Relationships / 249 \\
The Baker's Transformation and Digital Musical Chairs /
251 \\
Arnol'd's Cat Map / 253 \\
A Billion Digits for $\pi$ / 257 \\
Bushes and Flowers from Iterations / 259 \\
12: A Self-Similar Sequence, the Logistic Parabola, and
Symbolic Dynamics / 263 \\
Self-Similarity from the Integers / 264 \\
The Logistic Parabola and Period Doubling / 268 \\
Self-Similarity in the Logistic Parabola / 272 \\
The Scaling of the Growth Parameter / 274 \\
Self-Similar Symbolic Dynamics / 277 \\
Periodic Windows Embedded in Chaos / 279 \\
The Parenting of New Orbits / 282 \\
The Calculation of the Growth Parameters for Different
Orbits / 286 \\
Tangent Bifurcations, Intermittency, and I/f Noise /
289 \\
A Case of Complete Chaos / 291 \\
The Mandelbrot Set / 295 \\
The Julia Sets of the Complex Quadratic Map / 297 \\
13: A Forbidden Symmetry, Fibonacci's Rabbits, and a
New State of Matter / 301 \\
The Forbidden Fivefold Symmetry / 301 \\
Long-Range Order from Neighborly Interactions / 304 \\
Generation of the Rabbit Sequence from the Fibonacci
Number System / 307 \\
The Self-Similar Spectrum of the Rabbit Sequence / 308
\\
Self-Similarity in the Rabbit Sequence / 310 \\
A One-Dimensional Quasiperiodic Lattice / 310 \\
Self-Similarity from Projections / 311 \\
More Forbidden Symmetries / 315 \\
14: Periodic and Quasiperiodic Structures in Space ---
The route to Spatial Chaos / 319 \\
Periodicity and Quasiperiodicity in Space / 320 \\
The Devil's Staircase for Ising Spins / 321 \\
Quasiperiodic Spatial Distributions / 322 \\
Beatty Sequence Spins / 325 \\
The Scaling Laws for Quasiperiodic Spins / 329 \\
Self-Similar Winding Numbers / 330 \\
Circle Maps and Arnold Tongues / 331 \\
Mediants, Farey Sequences, and the Farey Tree / 334 \\
The Golden-Mean Route to Chaos / 340 \\
15: Percolation: From Forest Fires to Epidemics / 345
\\
Critical Conflagration on a Square Lattice / 346 \\
Universality / 350 \\
The Critical Density / 353 \\
The Fractal Perimeters of Percolation / 353 \\
Finite-Size Scaling / 354 \\
16: Phase Transitions and Renormalization / 357 \\
A First-Order Markov Process / 357 \\
Self-Similar and Non-Self-Similar Markov Processes /
358 \\
The Scaling of Markov Output's / 360 \\
Renormalization and Hierarchical Lattices / 362 \\
The Percolation Threshold of the Bethe Lattice / 363
\\
A Simple Renormalization / 367 \\
17: Cellular Automata / 371 \\
The Game of Life / 373 \\
Cellular Growth and Decay / 375 \\
Biological Pattern Formation / 382 \\
Self-Similarity from a Cellular Automaton / 383 \\
A Catalytic Converter as a Cellular Automaton / 386 \\
Pascal's Triangle Modulo $N$ / 387 \\
Bak's Self-Organized Critical Sandpiles / 389 \\
Appendix / 391 \\
References / 395 \\
Author Index / 411 \\
Subject Index / 417",
}
@Article{Trubnikov:1991:SDZ,
author = "B. A. Trubnikov and I. A. Rumynski{\u\i}",
title = "A simple derivation of the {Zipf--Krylov} law for
words and the possibility of its ``evolution''
interpretation",
journal = j-DOKL-AKAD-NAUK,
volume = "321",
number = "2",
pages = "270--275",
year = "1991",
CODEN = "DANKAS",
ISSN = "0002-3264",
ISSN-L = "0002-3264",
MRclass = "00A69 (92K20)",
MRnumber = "1153554",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
}
@Article{Basu:1992:RHD,
author = "Aparna Basu",
title = "Research: Hierarchical distributions and {Bradford's
Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "43",
number = "7",
pages = "494--500",
month = aug,
year = "1992",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<494::AID-ASI4>3.0.CO%3B2-F",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:51 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@TechReport{Busta:1992:TRN,
author = "B. Busta and R. Sundheim",
title = "Tax return numbers tend to obey {Benford}'s law",
type = "Working Paper",
number = "W93-106-94",
institution = "Center for Business Research, St. Cloud State
University",
address = "St. Cloud, MN, USA",
year = "1992",
bibdate = "Sat Feb 16 17:29:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Dehaene:1992:CLR,
author = "Stanislas Dehaene and Jacques Mehler",
title = "Cross-linguistic regularities in the frequency of
number words",
journal = j-COGNITION,
volume = "43",
number = "1",
pages = "1--29",
year = "1992",
CODEN = "CGTNAU",
DOI = "https://doi.org/10.1016/0010-0277(92)90030-L",
ISSN = "0010-0277 (print), 1873-7838 (electronic)",
ISSN-L = "0010-0277",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001002779290030L",
abstract = "We examine the frequency of numerals and ordinals in
seven different languages and/or cultures. Many
cross-cultural and cross-linguistic patterns are
identified. The most striking is a decrease of
frequency with numerical magnitude, with local
increases for reference numerals such as 10, 12, 15,
20, 50 or 100. Four explanations are considered for
this effect: sampling artifacts, notational
regularities, environmental biases and psychological
limitations on number representations. The
psychological explanation, which appeals to a
Fechnerian encoding of numerical magnitudes and to the
existence of numerical points of reference, accounts
for most of the data. Our finding also has practical
importance since it reveals the frequent confound of
two experimental variables: numerical magnitude and
numeral frequency.",
acknowledgement = ack-nhfb,
fjournal = "Cognition",
keywords = "Benford's Law",
}
@Article{Goto:1992:SEB,
author = "Kazuo Got{\^o}",
title = "Some examples of {Benford} sequences",
journal = "Math. J. Okayama Univ.",
volume = "34",
pages = "225--232 (1994)",
year = "1992",
CODEN = "MJOKAP",
ISSN = "0030-1566",
ISSN-L = "0030-1566",
MRclass = "11K36",
MRnumber = "1272624 (95c:11097)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Journal of Okayama University",
}
@Article{Gunther:1992:PCZ,
author = "R. G{\"u}nther and B. Schapiro and P. Wagner",
title = "Physical complexity and {Zipf}'s law",
journal = j-INT-J-THEOR-PHYS,
volume = "31",
number = "3",
pages = "525--543",
year = "1992",
CODEN = "IJTPBM",
DOI = "https://doi.org/10.1007/BF00740003",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
MRclass = "58F40",
MRnumber = "1154668 (92k:58252)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Theoretical Physics",
journal-URL = "http://link.springer.com/journal/10773",
}
@Article{Jech:1992:LDL,
author = "Thomas Jech",
title = "The logarithmic distribution of leading digits and
finitely additive measures",
journal = j-DISCRETE-MATH,
volume = "108",
number = "1--3",
pages = "53--57",
month = "????",
year = "1992",
CODEN = "DSMHA4",
ISSN = "0012-365X (print), 1872-681X (electronic)",
ISSN-L = "0012-365X",
bibdate = "Fri Nov 18 12:12:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete Mathematics",
}
@Article{Lagarias:1992:PTS,
author = "J. C. Lagarias and A. Weiss",
title = "The $ 3 x + 1 $ Problem: Two Stochastic Models",
journal = j-ANN-APPL-PROBAB,
volume = "2",
number = "1",
pages = "229--261",
month = feb,
year = "1992",
CODEN = "????",
ISSN = "1050-5164",
ISSN-L = "1050-5164",
bibdate = "Fri Jun 6 11:35:34 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annapplprobab.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.aoap/1177005779",
acknowledgement = ack-nhfb,
fjournal = "Annals of Applied Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aoap/;
http://www.jstor.org/journals/10505164.html",
}
@Article{Li:1992:RTE,
author = "W. Li",
title = "Random texts exhibit {Zipf}'s-law-like word frequency
distribution",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "38",
number = "6",
pages = "1842--1845",
month = "????",
year = "1992",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.165464",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Nov 18 12:32:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@Article{Longfellow:1992:LER,
author = "Charles A. {Longfellow, Jr.}",
title = "Letters to the {Editor}: Regarding {``Lotka's Law and
the Kolmogorov--Smirnov Test: An Error in
Calculation''}",
journal = j-J-AM-SOC-INF-SCI,
volume = "43",
number = "7",
pages = "518--518",
month = aug,
year = "1992",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<518::AID-ASI7>3.0.CO%3B2-#",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:51 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
note = "See \cite{Loughner:1992:BCL}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Loughner:1992:BCL,
author = "William Loughner",
title = "Brief Communications: {Lotka's Law} and the
{Kolmogorov--Smirnov} test: an error in calculation",
journal = j-J-AM-SOC-INF-SCI,
volume = "43",
number = "2",
pages = "149--150",
month = mar,
year = "1992",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199203)43:2<149::AID-ASI4>3.0.CO%3B2-Y",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
note = "See comment \cite{Longfellow:1992:LER}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@PhdThesis{Nigrini:1992:DIE,
author = "Mark John Nigrini",
title = "The detection of income tax evasion through an
analysis of digital distributions",
type = "{Ph.D.} Dissertation",
school = "Department of Accounting\slash Business Law,
University of Cincinnati",
address = "Cincinnati, OH, USA",
pages = "xvi + 309",
day = "28",
month = aug,
year = "1992",
bibdate = "Sat Nov 12 15:47:41 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/304052348",
acknowledgement = ack-nhfb,
advisor = "Wallace R. Wood",
remark = "There are more than 230 mentions of Frank Benford, and
8 of Simon Newcomb, but no mention of Pareto or Zipf.",
}
@Article{Rousseau:1992:RBR,
author = "Ronald Rousseau",
title = "Research: Breakdown of the robustness property of
{Lotka's Law}: the case of adjusted counts for
multiauthorship attribution",
journal = j-J-AM-SOC-INF-SCI,
volume = "43",
number = "10",
pages = "645--647",
month = dec,
year = "1992",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199212)43:10<645::AID-ASI1>3.0.CO%3B2-X",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:48 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Sanders:1992:PPU,
author = "Robert Sanders",
title = "The {Pareto Principle}: its Use and Abuse",
journal = j-J-PROD-BRAND-MANAG,
volume = "1",
number = "2",
pages = "37--40",
month = "????",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1108/10610429210036762",
ISSN = "1061-0421",
ISSN-L = "1061-0421",
bibdate = "Fri Nov 25 06:50:32 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Product \& Brand Management",
keywords = "80/20 rule",
}
@Article{Too:1992:UDM,
author = "Yeu-Hua Too",
title = "On the uniform distribution modulo one of some
log-like sequences",
journal = "Proceedings of the Japan Academy, Series A.
Mathematical Sciences",
volume = "68",
number = "9",
pages = "269--272",
month = "????",
year = "1992",
DOI = "https://doi.org/10.3792/pjaa.68.269",
ISSN = "0021-4280",
ISSN-L = "0021-4280",
bibdate = "Mon Feb 18 06:55:06 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.pja/1195511634",
acknowledgement = ack-nhfb,
}
@Article{Trachtenberg:1992:WFR,
author = "M. Trachtenberg",
title = "Why failure rates observe {Zipf}'s law in operational
software",
journal = j-IEEE-TRANS-RELIAB,
volume = "41",
number = "3",
pages = "386--389",
year = "1992",
CODEN = "IEERAJ",
DOI = "https://doi.org/10.1109/24.159803",
ISSN = "0018-9529 (print), 1558-1721 (electronic)",
ISSN-L = "0018-9529",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0825.68222",
acknowledgement = ack-nhfb,
classmath = "68M15 (Reliability and testing of computer systems)
68N01 (General)",
fjournal = "IEEE Transactions on Reliability",
}
@Article{Anonymous:1993:WFR,
author = "Anonymous",
title = "Why failure rates observe {Zipf}'s law in operational
software: {M. Trachtenberg. IEEE Transactions on
Reliability, {\bf 41}(3), 386 (1992)}",
journal = j-MICROELECT-RELIABILITY,
volume = "33",
number = "13",
pages = "2062--2062",
month = oct,
year = "1993",
CODEN = "MCRLAS",
DOI = "https://doi.org/10.1016/0026-2714(93)90406-O",
ISSN = "0026-2714 (print), 1872-941X (electronic)",
ISSN-L = "0026-2714",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002627149390406O",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics and Reliability",
keywords = "Zipf's Law",
}
@Article{Buck:1993:IBF,
author = "B. Buck and A. C. Merchant and S. M. Perez",
title = "An illustration of {Benford}'s first digit law using
alpha decay half lives",
journal = j-EUR-J-PHYS,
volume = "14",
number = "2",
pages = "59--63",
month = "????",
year = "1993",
CODEN = "EJPHD4",
DOI = "https://doi.org/10.1088/0143-0807/14/2/003",
ISSN = "0143-0807 (print), 1361-6404 (electronic)",
ISSN-L = "0143-0807",
bibdate = "Mon Nov 14 17:32:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Physics",
journal-URL = "http://iopscience.iop.org/0143-0807/",
}
@Article{Christian:1993:NES,
author = "C. W. Christian and S. Gupta",
title = "New Evidence on ``Secondary Evasion''",
journal = "Journal of the {American Taxation Association}",
volume = "15",
number = "??",
pages = "72--93",
month = "????",
year = "1993",
ISSN = "0198-9073 (print), 1558-8017 (electronic)",
ISSN-L = "0198-9073",
bibdate = "Thu Oct 13 06:50:53 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Amer. Tax. Assoc.",
fjournal = "Journal of the {American Taxation Association}",
journal-URL = "http://aaajournals.org/loi/atax",
remark = "No journal issues online before 1999.",
}
@Article{Deakin:1993:ADB,
author = "Michael A. B. Deakin",
title = "Another derivation of {Benford}'s law",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "20",
number = "5",
pages = "162--163",
year = "1993",
CODEN = "????",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
MRclass = "11K36",
MRnumber = "1268513 (95j:11072)",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Mathematical Society Gazette",
journal-URL = "http://www.austms.org.au/gazette",
}
@Article{Nigrini:1993:CBL,
author = "Mark Nigrini",
title = "Can {Benford's Law} be used in Forensic Accounting?",
journal = "The Balance Sheet",
volume = "??",
number = "??",
pages = "7--8",
month = jun,
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 21 22:03:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Oluic-Vukovic:1993:LEW,
author = "Vesna Olui{\'c}-Vukovi{\'c}",
title = "Letters to the {Editor}: Why has {Bradford's Law} been
an elusive phenomenon so far?",
journal = j-J-AM-SOC-INF-SCI,
volume = "44",
number = "3",
pages = "182--183",
month = apr,
year = "1993",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199304)44:3<182::AID-ASI9>3.0.CO%3B2-S",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:54 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@TechReport{Stewart:1993:LAN,
author = "Ian Stewart",
title = "The law of anomalous numbers",
type = "Working paper",
institution = "Mathematics Institute, University of Warwick",
address = "Warwick, UK",
year = "1993",
bibdate = "Fri Mar 22 09:15:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Published in Spektrum der Wissenschaft (April 1994)",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@TechReport{Sundheim:1993:FNT,
author = "R. Sundheim and B. Busta",
title = "{Fibonacci} numbers tend to obey {Benford's Law}: an
extension of {Wlodarski} and {Sentance}",
type = "Working Paper",
institution = "St. Cloud State University",
address = "St. Cloud, MN, USA",
month = "????",
year = "1993",
bibdate = "Mon Feb 18 06:37:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sury:1993:FPD,
author = "B. Sury",
title = "Fractional parts of $ \log p $ and a digit function",
journal = j-EXPO-MATH,
volume = "11",
number = "4",
pages = "381--384",
month = "????",
year = "1993",
DOI = "????",
ISSN = "0723-0869 (print), 1878-0792 (electronic)",
ISSN-L = "0723-0869",
bibdate = "Mon Feb 18 06:39:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
ZMnumber = "0787.11003",
acknowledgement = ack-nhfb,
ajournal = "Expo. Math.",
fjournal = "Expositiones Mathematicae",
journal-URL = "http://www.sciencedirect.com/science/journal/07230869",
keywords = "decimal expansion; sum of digits",
ZMclass = "11A63 (Radix representation; digital problems)",
ZMreviewer = "G. Larcher (Salzburg)",
}
@Article{Wolf:1993:PHJ,
author = "Joel L. Wolf and Philip S. Yu and John Turek and
Daniel M. Dias",
title = "A parallel hash join algorithm for managing data
skew",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "4",
number = "12",
pages = "1355--1371",
month = dec,
year = "1993",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/71.250117",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Apr 11 15:20:39 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM T. J. Watson Research Cent",
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P
(Parallel programming and algorithm theory); C4250
(Database theory); C6160D (Relational DBMS)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Algorithms; combinatorial; Combinatorial mathematics;
Combinatorial optimization; Complex queries; complex
queries; Computational complexity; Data handling; Data
skew; data skew; database theory; hash; Hash joins;
hashing; heuristic optimization; hierarchical; join
column; joins; load balancing; Load balancing;
optimization; parallel algorithms; parallel hash join
algorithm; Parallel processing systems; Program
processors; Query languages; query processing;
Relational database systems; relational databases;
resource allocation; scheduling; Zipf-like
distribution",
treatment = "T Theoretical or Mathematical",
}
@Article{Wolf:1993:PSM,
author = "Joel L. Wolf and Daniel M. Dias and Philip S. Yu",
title = "Parallel sort merge join algorithm for managing data
skew",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "4",
number = "1",
pages = "70--86",
month = jan,
year = "1993",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/71.205654",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Apr 11 15:20:39 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM",
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "723.1; 723.3; 921.5; C4240P (Parallel programming
and algorithm theory); C4250 (Database theory); C6130
(Data handling techniques); C6160B (Distributed DBMS);
C6160D (Relational DBMS)",
corpsource = "IBM T. J. Watson Res. Center. Yorktown Heights, NY,
USA",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Algorithms; Computer systems programming; Data skew;
data skew management; distributed databases; Divide and
conquer approach; divide-and-conquer; join phases; load
balancing; merging; multiple processors;
Multiprocessing programs; Optimization; parallel;
Parallel algorithms; parallel algorithms; Parallel sort
merge join algorithm; parallelizable optimization
algorithm; phase; Query processing; relational algebra;
Relational database systems; relational databases;
scheduling; Scheduling; sort merge join algorithm; sort
phase; sorting; Sorting; transfer phase; Zipf-like
distribution",
treatment = "T Theoretical or Mathematical",
}
@Book{Arthur:1994:IRP,
author = "W. Brian Arthur",
title = "Increasing returns and path dependence in the
economy",
publisher = pub-U-MICHIGAN,
address = pub-U-MICHIGAN:adr,
pages = "xx + 201",
year = "1994",
ISBN = "0-472-09496-3, 0-472-06496-7 (paperback)",
ISBN-13 = "978-0-472-09496-7, 978-0-472-06496-0 (paperback)",
LCCN = "HD69.S5 A77 1994",
bibdate = "Wed Feb 27 07:08:40 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by Kenneth J. Arrow.",
series = "Economics, cognition, and society",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Economies of scale; Mathematical models; Economic
development; Economics, Mathematical",
}
@Article{Basu:1994:LEE,
author = "Aparna Basu",
title = "Letters to the {Editor}: The elusive phenomenon of
{Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "45",
number = "1",
pages = "59--60",
month = jan,
year = "1994",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199401)45:1<59::AID-ASI8>3.0.CO%3B2-F",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:03:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Bookstein:1994:TMD,
author = "A. Bookstein",
title = "Towards a multi-disciplinary {Bradford Law}",
journal = j-SCIENTOMETRICS,
volume = "30",
number = "1",
pages = "353--361",
month = may,
year = "1994",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02017233",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Thu Sep 3 07:35:17 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
URL = "http://link.springer.com/article/10.1007/BF02017233",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Boyle:1994:AFS,
author = "Jeff Boyle",
title = "An application of {Fourier} series to the most
significant digit problem",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "9",
pages = "879--886",
month = nov,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "60F99",
MRnumber = "1 300 493",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Egghe:1994:RSF,
author = "L. Egghe",
title = "Research: Special features of the author--publication
relationship and a new explanation of {Lotka's Law}
based on convolution theory",
journal = j-J-AM-SOC-INF-SCI,
volume = "45",
number = "6",
pages = "422--427",
month = jul,
year = "1994",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199407)45:6<422::AID-ASI8>3.0.CO%3B2-C",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:01 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Fuchs:1994:PDP,
author = "Aim{\'e} Fuchs and Giorgio Letta",
title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
les nombres premiers. ({French}) [The problem for the
first decimal digit of prime numbers]",
journal = "Rendiconti della Accademia Nazionale delle Scienze
detta dei XL. Serie V. Memorie di Matem{\`a}tica",
volume = "18",
number = "1",
pages = "81--87",
month = "????",
year = "1994",
bibdate = "Sat Feb 16 17:40:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
ZMnumber = "0838.11004",
acknowledgement = ack-nhfb,
ajournal = "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.",
keywords = "asymptotic densities; logarithmic density; primes;
relative densities",
language = "French",
xxjournal = "Rend. Acad. Naz. Sci. Detta",
xxvolume = "XL",
ZMclass = "11B05 (Topology etc. of sets of numbers); 11K16
(Normal numbers, etc.)",
ZMreviewer = "I. Z. Ruzsa (Budapest)",
}
@Article{Ley:1994:TPB,
author = "Eduadro Ley and Hal R. Varian",
title = "Are there psychological barriers in the {Dow--Jones}
index?",
journal = j-APPL-FINANC-ECON,
volume = "4",
number = "3",
pages = "217--224",
month = "????",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1080/758526902",
ISSN = "0960-3107 (print), 1466-4305 (electronic)",
ISSN-L = "0960-3107",
bibdate = "Sat Feb 16 18:29:52 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/758526902",
acknowledgement = ack-nhfb,
fjournal = "Applied Financial Economics",
}
@Article{Mantegna:1994:LFN,
author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
and S. Havlin and C. K. Peng and M. Simons and H. E.
Stanley",
title = "Linguistic Features of Noncoding {DNA} Sequences",
journal = j-PHYS-REV-LET,
volume = "73",
number = "??",
pages = "3169--??",
day = "5",
month = dec,
year = "1994",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.73.3169",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comment \cite{Voss:1996:CLF} and reply
\cite{Mantegna:1996:MAR}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Nigrini:1994:UDF,
author = "Mark J. Nigrini",
title = "Using digital frequencies to detect fraud",
journal = "The White Paper",
volume = "??",
number = "2",
pages = "3--6",
month = apr # "\slash " # may,
year = "1994",
bibdate = "Sat Feb 16 18:53:08 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "The White Paper is the precursor to Fraud Magazine; I
cannot find it in the Library of Congress catalog.",
}
@Article{Pedrotti:1994:ALU,
author = "A. Pedrotti",
title = "Analysis of a list-update strategy",
journal = j-INFO-PROC-LETT,
volume = "52",
number = "3",
pages = "115--121",
day = "11",
month = nov,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
affiliation = "Scuola Normale Superiore",
affiliationaddress = "Pisa, Italy",
classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C
(Computational complexity); C6130 (Data handling
techniques)",
corpsource = "Scuola Normale Superiore, Pisa, Italy",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "Algorithms; analysis of algorithms; average-case
complexity; BIT; competitive algorithms; Computational
complexity; computational complexity; convergence;
Convergence of numerical methods; Data handling;
Function evaluation; Heuristic methods; list
processing; list update; Markov chains; Move to front
algorithm; move-to-front; Probability; Random number
generation; searching; Theorem proving; transpose;
Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Article{Sheppard:1994:TNA,
author = "Lee A. Sheppard",
title = "{Tax Notes} audits the {Clintons}",
journal = "Tax Notes Today",
volume = "??",
number = "??",
pages = "18--23",
day = "4",
month = apr,
year = "1994",
bibdate = "Fri Mar 22 09:13:48 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bankler.com/docs/Tax_Notes_Audits_the_Clintons.pdf",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Tritch:1994:MAC,
author = "Teresa Tritch and Mary L. Sprouse",
title = "{Money} audits the {Clintons}",
journal = "Money Magazine",
volume = "??",
number = "??",
pages = "84--98",
day = "1",
month = apr,
year = "1994",
bibdate = "Fri Mar 22 09:16:28 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://money.cnn.com/magazines/moneymag/moneymag_archive/1994/04/01/88775/index.htm",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Berton:1995:HGT,
author = "L. Berton",
title = "He's Got their Number. {Scholar} Uses Math to Foil
Financial Fraud",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "??--??",
day = "10",
month = jul,
year = "1995",
CODEN = "WSJOAF",
ISSN = "0099-9660",
ISSN-L = "0099-9660",
bibdate = "Sat Dec 10 11:17:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Wall Street Journal",
}
@Book{Bologna:1995:FAF,
author = "Jack Bologna and Robert J. Lindquist",
title = "Fraud auditing and forensic accounting: new tools and
techniques",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xv + 249",
year = "1995",
ISBN = "0-471-10646-1 (hardcover)",
ISBN-13 = "978-0-471-10646-3 (hardcover)",
LCCN = "HV8079.W47 B65 1995",
bibdate = "Tue Nov 22 10:31:53 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
http://www.loc.gov/catdir/description/wiley033/95005510.html;
http://www.loc.gov/catdir/toc/onix04/95005510.html",
acknowledgement = ack-nhfb,
remark = "This book does not discuss Benford's Law, but may be
helpful background for application of that law to the
detection of fraud.",
subject = "white collar crime investigation; United States;
forensic accounting; fraud investigation",
}
@Article{Chen:1995:LED,
author = "Ye-Sho Chen",
title = "Letters to the {Editor}: On the dynamic behavior of
{Bradford's Law} --- response",
journal = j-J-AM-SOC-INF-SCI,
volume = "46",
number = "10",
pages = "799--800",
month = dec,
year = "1995",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<799::AID-ASI19>3.0.CO%3B2-P",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:04 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Chen:1995:RDB,
author = "Ye-Sho Chen and P. Pete Chong and Morgan Y. Tong",
title = "Research: Dynamic behavior of {Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "46",
number = "5",
pages = "370--383",
month = jun,
year = "1995",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<370::AID-ASI7>3.0.CO%3B2-J",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:06 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Czirok:1995:CBS,
author = "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo
Havlin and H. Eugene Stanley",
title = "Correlations in binary sequences and a generalized
{Zipf} analysis",
journal = j-PHYS-REV-E,
volume = "52",
number = "??",
pages = "446--??",
day = "1",
month = jul,
year = "1995",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.52.446",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.446",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Filipponi:1995:SPA,
author = "Piero Filipponi and Renato Menicocci",
title = "Some Probabilistic Aspects of the Terminal Digits of
{Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "33",
number = "4",
pages = "325--331",
month = aug,
year = "1995",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:02:19 MDT 2011",
bibsource = "http://www.fq.math.ca/33-4.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Havlin:1995:DBZ,
author = "Shlomo Havlin",
title = "The distance between {Zipf} plots",
journal = j-PHYSICA-A,
volume = "216",
number = "1--2",
pages = "148--150",
day = "1",
month = jun,
year = "1995",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/0378-4371(95)00069-J",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037843719500069J",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Hill:1995:BII,
author = "Theodore P. Hill",
title = "Base-invariance implies {Benford's Law}",
journal = j-PROC-AM-MATH-SOC,
volume = "123",
number = "3",
pages = "887--895",
month = mar,
year = "1995",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2160815",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "60A10 (28D05)",
MRnumber = "1233974 (95d:60006)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2160815",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Hill:1995:SDP,
author = "Theodore P. Hill",
title = "The significant-digit phenomenon",
journal = j-AMER-MATH-MONTHLY,
volume = "102",
number = "4",
pages = "322--327",
month = apr,
year = "1995",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2974952",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K99 (60E99)",
MRnumber = "96f:11101",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Hill:1995:SDS,
author = "Theodore P. Hill",
title = "A statistical derivation of the significant-digit
law",
journal = j-STAT-SCI,
volume = "10",
number = "4",
pages = "354--363",
year = "1995",
CODEN = "STSCEP",
ISSN = "0883-4237 (print), 2168-8745 (electronic)",
ISSN-L = "0883-4237",
MRclass = "60E99 (60A10 62E99)",
MRnumber = "1421567 (98a:60021)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 10:09:36 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "2-P&origin=MSN;
http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
ZMnumber = "Zbl 0955.60509",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science. A Review Journal of the Institute
of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
}
@Article{Kanter:1995:MPL,
author = "I. Kanter and D. A. Kessler",
title = "{Markov} Processes: Linguistics and {Zipf's Law}",
journal = j-PHYS-REV-LET,
volume = "74",
number = "??",
pages = "4559--??",
day = "29",
month = may,
year = "1995",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.74.4559",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Koenig:1995:BCL,
author = "Michael Koenig and Toni Harrell",
title = "Brief Communications: {Lotka's Law}, {Price}'s urn,
and electronic publishing",
journal = j-J-AM-SOC-INF-SCI,
volume = "46",
number = "5",
pages = "386--388",
month = jun,
year = "1995",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<386::AID-ASI9>3.0.CO%3B2-V",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:06 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Makse:1995:MUG,
author = "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene
Stanley",
title = "Modelling urban growth patterns",
journal = j-NATURE,
volume = "377",
number = "6550",
pages = "608--612",
day = "19",
month = oct,
year = "1995",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/377608a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Feb 27 06:06:25 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Berlin (Germany) population; London (UK) population;
Zipf's Law",
}
@Article{Mantegna:1995:SAC,
author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
and S. Havlin and C.-K. Peng and M. Simons and H. E.
Stanley",
title = "Systematic analysis of coding and noncoding {DNA}
sequences using methods of statistical linguistics",
journal = j-PHYS-REV-E,
volume = "52",
number = "??",
pages = "2939--??",
day = "1",
month = sep,
year = "1995",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.52.2939",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.2939",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Mosimann:1995:DFC,
author = "James E. Mosimann and Claire V. Wiseman and Ruth E.
Edelman",
title = "Data Fabrication: Can People Generate Random Digits?",
journal = j-ACCOUNT-RES,
volume = "4",
number = "1",
pages = "31--55",
month = "????",
year = "1995",
CODEN = "ARQAEZ",
DOI = "https://doi.org/10.1080/08989629508573866",
ISSN = "0898-9621 (print), 1545-5815 (electronic)",
ISSN-L = "0898-9621",
bibdate = "Sat Dec 10 11:56:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
acknowledgement = ack-nhfb,
fjournal = "Accountability in Research",
journal-URL = "http://www.tandfonline.com/toc/gacr20",
keywords = "Benford's Law",
remark = "The abstract ends with: ``The difficulty that people
have in creating random error digits supports the
utility of examining such digits in investigations of
scientific misconduct.''",
}
@Article{Oluic-Vukovic:1995:LED,
author = "Vesna Olui{\'c}-Vukovi{\'c}",
title = "Letters to the {Editor}: On the dynamic behavior of
{Bradford's Law}",
journal = j-J-AM-SOC-INF-SCI,
volume = "46",
number = "10",
pages = "798--799",
month = dec,
year = "1995",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<798::AID-ASI18>3.0.CO%3B2-T",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:04 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "4 Jan 1999",
}
@Article{Stanley:1995:ZPS,
author = "Michael H. R. Stanley and Sergey V. Buldyrev and
Shlomo Havlin and Rosario N. Mantegna and Michael A.
Salinger and H. Eugene Stanley",
title = "{Zipf} plots and the size distribution of firms",
journal = j-ECONOM-LETT,
volume = "49",
number = "4",
pages = "453--457",
day = "15",
month = oct,
year = "1995",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/0165-1765(95)00696-D",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016517659500696D",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Wagner-Dobler:1995:DLL,
author = "Roland Wagner-D{\"o}bler and Jan Berg",
title = "The Dependence of {Lotka's Law} on the Selection of
Time Periods in the Development of Scientific Areas and
Authors",
journal = j-J-DOC,
volume = "51",
number = "1",
pages = "28--43",
month = "????",
year = "1995",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/eb026941",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:29:22 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{Zornig:1995:URZ,
author = "Peter Z{\"o}rnig and Gabriel Altmann",
title = "Unified representation of {Zipf} distributions",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "19",
number = "4",
pages = "461--473",
day = "1",
month = apr,
year = "1995",
CODEN = "CSDADW",
DOI = "https://doi.org/10.1016/0167-9473(94)00009-8",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
MRclass = "62E10 (62F10)",
MRnumber = "1333065 (96f:62029)",
MRreviewer = "Friedrich Liese",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0167947394000098",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
keywords = "Zipf's Law",
}
@Book{Bak:1996:HNW,
author = "Per Bak",
title = "How nature works: the science of self-organized
criticality",
publisher = "Copernicus",
address = "New York, NY, USA",
pages = "xiii + 212 + 8",
year = "1996",
ISBN = "0-387-94791-4 (hardcover)",
ISBN-13 = "978-0-387-94791-4 (hardcover)",
LCCN = "QC173.4.C74 B34 1996",
bibdate = "Thu Nov 24 13:34:22 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Critical phenomena (Physics); Complexity (Philosophy);
Physics; Philosophy",
}
@Article{Beirlant:1996:TIE,
author = "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
title = "Tail Index Estimation, {Pareto} Quantile Plots, and
Regression Diagnostics",
journal = j-J-AM-STAT-ASSOC,
volume = "91",
number = "436",
pages = "1659--??",
month = "????",
year = "1996",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon May 5 08:26:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Bonhoeffer:1996:NSH,
author = "Sebastian Bonhoeffer and Andreas V. M. Herz and
Maarten C. Boerlijst and Sean Nee and Martin A. Nowak
and Robert M. May",
title = "No Signs of Hidden Language in Noncoding {DNA}",
journal = j-PHYS-REV-LET,
volume = "76",
number = "11",
pages = "1977--1977",
month = mar,
year = "1996",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.76.1977",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Sat Sep 10 17:27:23 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1977",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Burgos:1996:ZSB,
author = "Javier D. Burgos and Pedro Moreno-Tovar",
title = "{Zipf}-scaling behavior in the immune system",
journal = j-BIOSYSTEMS,
volume = "39",
number = "3",
pages = "227--232",
day = "15",
month = nov,
year = "1996",
CODEN = "BSYMBO",
DOI = "https://doi.org/10.1016/0303-2647(96)01618-8",
ISSN = "0303-2647 (print), 1872-8324 (electronic)",
ISSN-L = "0303-2647",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0303264796016188",
acknowledgement = ack-nhfb,
fjournal = "Biosystems (A6E)",
journal-URL = "http://www.sciencedirect.com/science/journal/03032647",
keywords = "Zipf's Law",
}
@Article{Campanino:1996:IIM,
author = "Massimo Campanino and Stefano Isola",
title = "Infinite invariant measures for non-uniformly
expanding transformations of $ [0, 1] $: Weak law of
large numbers with anomalous scaling",
journal = j-FORUM-MATH,
volume = "8",
number = "1",
pages = "71--92",
year = "1996",
CODEN = "FOMAEF",
DOI = "https://doi.org/10.1515/form.1996.8.71",
ISSN = "0933-7741 (print), 1435-5337 (electronic)",
ISSN-L = "0933-7741",
bibdate = "Sat Nov 12 10:33:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0837.60022",
abstract = "We consider a class of maps of $ [0, 1] $ with an
indifferent fixed point at 0 and expanding everywhere
else. Using the invariant ergodic probability measure
of a suitable, everywhere expanding, induced
transformation we are able to study the infinite
invariant measure of the original map in some detail.
Given a continuous function with compact support in
$]0, 1]$, we prove that its time averages satisfy a
`weak law of large numbers' with anomalous scaling $ n
/ \log n $ and give an upper bound for the decay of
correlations.",
acknowledgement = ack-nhfb,
ajournal = "Forum Math.",
classmath = "60F05 (Weak limit theorems) 28D05 (Measure-preserving
transformations) 37A99 (Ergodic theory)",
fjournal = "Forum Mathematicum",
keywords = "decay of correlations; invariant ergodic probability
measure; weak law of large numbers",
}
@Article{Czirok:1996:POP,
author = "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and
Tam{\'a}s Vicsek",
title = "Possible origin of power-law behavior in $n$-tuple
{Zipf} analysis",
journal = j-PHYS-REV-E,
volume = "53",
number = "??",
pages = "6371--??",
day = "1",
month = jun,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.53.6371",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.6371",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Fuchs:1996:PDP,
author = "Aim{\'e} Fuchs and Giorgio Letta",
title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
les nombres premiers. ({French}) [The problem for the
first decimal digit of prime numbers]",
journal = j-ELECT-J-COMB,
volume = "3",
number = "2",
pages = "R25:1--R25:7",
month = "????",
year = "1996",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
bibdate = "Sat Feb 16 17:40:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The Foata Festschrift volume.",
URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
ZMnumber = "0853.11006",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
language = "French",
xxpages = "601--607",
}
@Article{Gunther:1996:ZLE,
author = "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
Wagner",
title = "{Zipf}'s law and the effect of ranking on probability
distributions",
journal = j-INT-J-THEOR-PHYS,
volume = "35",
number = "2",
pages = "395--417",
year = "1996",
CODEN = "IJTPBM",
DOI = "https://doi.org/10.1007/BF02083823",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
bibdate = "Sat Nov 12 10:53:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0843.60002",
abstract = "Ranking procedures are widely used in the description
of many different types of complex systems. Zipf's law
is one of the most remarkable frequency-rank
relationships and has been observed independently in
physics, linguistics, biology, demography, etc. We show
that ranking plays a crucial role in making it possible
to detect empirical relationships in systems that exist
in one realization only, even when the statistical
ensemble to which the systems belong has a very broad
probability distribution. Analytical results and
numerical simulations are presented which clarify the
relations between the probability distributions and the
behavior of expected values for unranked and ranked
random variables. This analysis is performed, in
particular, for the evolutionary model presented in our
previous papers which leads to Zipf's law and reveals
the underlying mechanism of this phenomenon in terms of
a system with interdependent and interacting components
as opposed to the ``ideal gas'' models suggested by
previous researchers. The ranking procedure applied to
this model leads to a new, unexpected phenomenon: a
characteristic ``staircase'' behavior of the mean
values of the ranked variables (ranked occupation
numbers). This result is due to the broadness of the
probability distributions for the occupation numbers
and does not follow from the ``ideal gas'' model. Thus,
it provides an opportunity, by comparison with
empirical data, to obtain evidence as to which model
relates to reality.",
acknowledgement = ack-nhfb,
classmath = "60A99 (Foundations of probability theory)",
fjournal = "International Journal of Theoretical Physics",
journal-URL = "http://link.springer.com/journal/10773",
keywords = "numerical simulations; ranking procedures; Zipf's
law",
}
@TechReport{Hill:1996:NDT,
author = "Theodore P. Hill",
title = "A note on distributions of true versus fabricated
data",
type = "Preprint",
institution = "Department of Mathematics, Georgia Institute of
Technology",
address = "Atlanta, GA, USA",
pages = "4",
year = "1996",
bibdate = "Sat Feb 16 17:47:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr",
acknowledgement = ack-nhfb,
}
@Article{Israeloff:1996:CZD,
author = "N. E. Israeloff and M. Kagalenko and K. Chan",
title = "Can {Zipf} Distinguish Language From Noise in
Noncoding {DNA}?",
journal = j-PHYS-REV-LET,
volume = "76",
number = "11",
pages = "1976--??",
day = "11",
month = mar,
year = "1996",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.76.1976",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Krugman:1996:CMU,
author = "Paul Krugman",
title = "Confronting the Mystery of Urban Hierarchy",
journal = j-J-JPN-INT-ECON,
volume = "10",
number = "4",
pages = "399--418",
month = dec,
year = "1996",
CODEN = "JJIEBD",
DOI = "https://doi.org/10.1006/jjie.1996.0023",
ISSN = "0889-1583 (print), 1095-8681 (electronic)",
ISSN-L = "0889-1583",
bibdate = "Wed Feb 27 06:15:55 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0889158396900234",
acknowledgement = ack-nhfb,
fjournal = "Journal of the {Japanese} and International
Economies",
keywords = "Zipf's Law",
}
@Book{Krugman:1996:SOE,
author = "Paul R. Krugman",
title = "The Self-Organizing Economy",
publisher = "Blackwell Publishers",
address = "Cambridge, MA, USA",
pages = "vi + 122",
year = "1996",
ISBN = "1-55786-699-6 (paperback)",
ISBN-13 = "978-1-55786-699-8 (paperback)",
LCCN = "HB199 .K75 1996",
bibdate = "Wed Feb 27 07:08:14 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Economics; Self-organizing systems",
}
@Article{Ley:1996:PDU,
author = "Eduardo Ley",
title = "On the Peculiar Distribution of the {U.S.} Stock
Indexes' Digits",
journal = j-AMER-STAT,
volume = "50",
number = "4",
pages = "311--313",
month = nov,
year = "1996",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 15:09:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2684926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Mantegna:1996:MAR,
author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
and S. Havlin and C.-K. Peng and M. Simons and H. E.
Stanley",
title = "{Mantegna} {\em et al.} Reply",
journal = j-PHYS-REV-LET,
volume = "76",
pages = "1979--1981",
month = mar,
year = "1996",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.76.1979",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Sat Sep 10 17:28:12 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mantegna:1994:LFN,Voss:1996:CLF}",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1979",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
issue = "11",
journal-URL = "http://prl.aps.org/browse",
}
@Article{Newman:1996:ASC,
author = "M. E. J. Newman and Kim Sneppen",
title = "Avalanches, scaling, and coherent noise",
journal = j-PHYS-REV-E,
volume = "54",
number = "6",
pages = "6226--6231",
month = dec,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.54.6226",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:44:51 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.6226",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@InProceedings{Nigrini:1996:DAR,
author = "Mark J. Nigrini",
editor = "M. Ettredge",
booktitle = "{Proceedings of the 1996 Deloitte \& Touche I
University of Kansas Symposium on Auditing Problems}",
title = "Digital Analysis and the Reduction of Auditor
Litigation Risk",
publisher = "University of Kansas",
address = "Lawrence, KS, USA",
pages = "69--81",
year = "1996",
bibdate = "Sat Sep 10 15:20:48 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Nigrini:1996:TCA,
author = "Mark J. Nigrini",
title = "A Taxpayer Compliance Application of {Benford's Law}",
journal = "Journal of the {American Taxation Association}",
volume = "18",
number = "1",
pages = "72--91",
month = "????",
year = "1996",
CODEN = "????",
ISSN = "0198-9073 (print), 1558-8017 (electronic)",
ISSN-L = "0198-9073",
bibdate = "Mon Nov 14 16:30:42 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Amer. Tax. Assoc.",
fjournal = "Journal of the {American Taxation Association}",
journal-URL = "http://aaajournals.org/loi/atax",
remark = "No journal issues online before 1999.",
}
@Article{Perline:1996:ZLC,
author = "Richard Perline",
title = "{Zipf}'s law, the {Central Limit Theorem}, and the
random division of the unit interval",
journal = j-PHYS-REV-E,
volume = "54",
number = "1",
pages = "220--223",
day = "1",
month = jul,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.54.220",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.220",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Mandelbrot's monkey-at-the-typewriter model of Zipf's
inverse power law; Zipf's Law",
}
@Article{Sole:1996:ESO,
author = "Ricard V. Sol{\'e} and Susanna C. Manrubia",
title = "Extinction and self-organized criticality in a model
of large-scale evolution",
journal = j-PHYS-REV-E,
volume = "54",
number = "1",
pages = "R42--R45",
month = jul,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.54.R42",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:32:32 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.R42",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Solomon:1996:SSE,
author = "Sorin Solomon and Moshe Levy",
title = "Spontaneous Scaling Emergence in Generic Stochastic
Systems",
journal = j-INT-J-MOD-PHYS-C,
volume = "7",
number = "5",
pages = "745--752",
month = oct,
year = "1996",
CODEN = "IJMPEO",
DOI = "https://doi.org/10.1142/S0129183196000624",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
bibdate = "Thu Feb 28 10:20:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
}
@Article{Voss:1996:CLF,
author = "Richard F. Voss",
title = "Comment on {``Linguistic Features of Noncoding DNA
Sequences''}",
journal = j-PHYS-REV-LET,
volume = "76",
number = "11",
pages = "1978--1978",
month = mar,
year = "1996",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.76.1978",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Sat Sep 10 14:35:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mantegna:1994:LFN} and reply
\cite{Mantegna:1996:MAR}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1978",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Benford's Law",
}
@Article{Watanabe:1996:EZL,
author = "Makoto S. Watanabe",
title = "Erratum: {Zipf}'s law in percolation",
journal = j-PHYS-REV-E,
volume = "54",
number = "??",
pages = "4483--4483",
day = "1",
month = oct,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.54.4483",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite {Watanabe:1996:ZLP}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.4483",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Watanabe:1996:ZLP,
author = "Makoto S. Watanabe",
title = "{Zipf}'s law in percolation",
journal = j-PHYS-REV-E,
volume = "53",
number = "??",
pages = "4187--4190",
day = "1",
month = apr,
year = "1996",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.53.4187",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See erratum \cite {Watanabe:1996:EZL}.",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.4187",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Allaart:1997:ISC,
author = "Pieter C. Allaart",
title = "An Invariant-Sum Characterization of {Benford's Law}",
journal = j-J-APPL-PROBAB,
volume = "34",
number = "1",
pages = "288--291",
month = mar,
year = "1997",
CODEN = "JPRBAM",
DOI = "https://doi.org/10.2307/3215195",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60E05",
MRnumber = "1429075 (98d:60029)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3215195",
abstract = "The accountant Nigrini remarked that in tables of data
distributed according to Benford's law, the sum of all
elements with first digit $ d (d = 1, 2, \ldots, 9) $
is approximately constant. In this note, a mathematical
formulation of Nigrini's observation is given and it is
shown that Benford's law is the unique probability
distribution such that the expected sum of all elements
with first digits $ d_1, \ldots, d_k $ is constant for
every fixed $k$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Castillo:1997:FGP,
author = "Enrique Castillo and Ali S. Hadi",
title = "Fitting the Generalized {Pareto} Distribution to
Data",
journal = j-J-AM-STAT-ASSOC,
volume = "92",
number = "440",
pages = "1609--1620",
month = dec,
year = "1997",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Oct 30 06:57:36 MST 2000",
bibsource = "http://www.amstat.org/publications/jasa/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
http://www.jstor.org/stable/2965432",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Chen:1997:NHS,
author = "Weishing Chen and Tai-Hsi Wu",
title = "A non-homogeneous software reliability model based on
{Zipf}'s law",
journal = "International Journal of Quality \& Reliability
Management",
volume = "14",
number = "4",
pages = "409--431",
month = "????",
year = "1997",
DOI = "https://doi.org/10.1108/02656719710170666",
ISSN = "0265-671X (print), 1758-6682 (electronic)",
ISSN-L = "0265-671X",
bibdate = "Fri Nov 25 07:08:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Denisov:1997:FBS,
author = "S. Denisov",
title = "Fractal binary sequences: {Tsallis} thermodynamics and
the {Zipf} law",
journal = j-PHYS-LET-A,
volume = "235",
number = "5",
pages = "447--451",
day = "17",
month = nov,
year = "1997",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/S0375-9601(97)00688-9",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0375960197006889",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
keywords = "Zipf's Law",
}
@InCollection{Gell-Mann:1997:ETZ,
author = "Murray Gell-Mann",
title = "Empirical Theory --- {Zipf}'s Law",
crossref = "Gell-Mann:1997:QJA",
pages = "92--97",
year = "1997",
bibdate = "Mon Sep 01 10:20:00 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Hill:1997:BL,
author = "Theodore Hill",
editor = "Michiel Hazewinkel",
booktitle = "Encyclopedia of Mathematics, Supplement {I}",
title = "{Benford's Law}",
volume = "1",
publisher = pub-SV,
address = pub-SV:adr,
pages = "102--103",
year = "1997",
ISBN = "90-481-4896-0",
ISBN-13 = "978-90-481-4896-7",
LCCN = "????",
bibdate = "Wed Nov 16 10:29:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Irmay:1997:RBZ,
author = "Shragga Irmay",
title = "The relationship between {Zipf}'s law and the
distribution of first digits",
journal = j-J-APPL-STAT,
volume = "24",
number = "4",
pages = "383--393",
day = "1",
month = aug,
year = "1997",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRclass = "62E15",
MRnumber = "1491308 (98h:62015)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.catchword.co.uk/titles/carfax/02664763/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; Zipf's Law",
xxpages = "383--394",
}
@Article{Jeevanand:1997:BEB,
author = "E. S. Jeevanand",
title = "{Bayes} Estimation of {$ P(X_2 < X_1) $} for a
Bivariate {Pareto} Distribution",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "46",
number = "1",
pages = "93--99",
month = "????",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.2307/2988496",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:24 MST 2015",
bibsource = "http://www.jstor.org/stable/i349996;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1990.bib",
URL = "http://www.jstor.org/stable/2988496",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@Manual{Nigrini:1997:DAT,
author = "Mark J. Nigrini",
title = "Digital Analysis Tests and Statistics",
organization = "The Nigrini Institute, Inc.",
address = "Allen, TX, USA",
month = "????",
year = "1997",
bibdate = "Sat Feb 16 18:55:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nigrini.com/data_software/Program_Details_2009.docx",
acknowledgement = ack-nhfb,
}
@Article{Nigrini:1997:UBL,
author = "Mark J. Nigrini and L. J. Mittermaier",
title = "The Use of {Benford's Law} as an Aid in Analytical
Procedures",
journal = j-AUDITING,
volume = "16",
number = "2",
pages = "52--67",
month = "????",
year = "1997",
CODEN = "????",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Sun Nov 13 11:37:48 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
remark = "No journal issues online before 1999.",
}
@Article{Oluic-Vukovic:1997:BDC,
author = "Vesna Olui{\'c}-Vukovi{\'c}",
title = "{Bradford}'s distribution: {From} the classical
bibliometric ``law'' to the more general stochastic
models",
journal = j-J-AM-SOC-INF-SCI,
volume = "48",
number = "9",
pages = "833--842",
month = sep,
year = "1997",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(199709)48:9<833::AID-ASI7>3.0.CO%3B2-S",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:21 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "7 Dec 1998",
}
@Book{Robertson:1997:FEM,
author = "Jack C. Robertson",
title = "Fraud Examination for Managers and Auditors",
publisher = "Viesca Books",
address = "Austin, TX, USA",
edition = "1997",
pages = "vii + 564",
year = "1997",
ISBN = "0-9656785-0-4",
ISBN-13 = "978-0-9656785-0-6",
LCCN = "HV8079.F7 R63 1997",
bibdate = "Thu Oct 13 09:04:19 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Fraud investigation",
}
@Article{Salsburg:1997:DPB,
author = "David Salsburg",
title = "Digit Preferences in the {Bible}",
journal = j-CHANCE,
volume = "10",
number = "4",
pages = "46--48",
month = "????",
year = "1997",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.1997.10542065",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Sat Feb 16 19:08:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
}
@InCollection{Smith:1997:EBL,
author = "Steven W. Smith",
booktitle = "The Scientist and Engineer's Guide to Digital Signal
Processing",
title = "Explaining {Benford's Law}",
chapter = "34",
publisher = "California Technical Publishing",
address = "San Diego, CA, USA",
bookpages = "xiv + 626",
pages = "701--722",
year = "1997",
ISBN = "0-9660176-3-3",
ISBN-13 = "978-0-9660176-3-2",
LCCN = "TK5102.9 .S57 1997",
bibdate = "Sat Sep 10 16:54:35 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.dspguide.com/ch34.htm",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "Chapters appear to stop at 31 in 1997 edition
(according to Amazon book preview), so a later addition
should have a new ISBN (the 2002 edition from Newnes is
\booktitle{Digital Signal Processing: A Practical Guide
for Engineers and Scientists}, with ISBN
0-7506-7444-X). However, the Web site says it is the
same book. The Web edition has 34 chapters, and all are
freely downloadable.",
}
@Article{Tsonis:1997:ZLS,
author = "A. A. Tsonis and C. Schultz and P. A. Tsonis",
title = "{Zipf's Law} and the structure and evolution of
languages",
journal = j-COMPLEXITY,
volume = "2",
number = "5",
pages = "12--13",
year = "1997",
CODEN = "COMPFS",
DOI = "https://doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO%3B2-C",
ISSN = "1076-2787 (print), 1099-0526 (electronic)",
ISSN-L = "1076-2787",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Complexity",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0526",
}
@Article{Zanette:1997:RIU,
author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
title = "Role of Intermittency in Urban Development: A Model of
Large-Scale City Formation",
journal = j-PHYS-REV-LET,
volume = "79",
number = "3",
pages = "523--526",
day = "3",
month = jul,
year = "1997",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.79.523",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 10:40:44 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.79.523",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Bach:1998:EPM,
author = "Eric Bach",
title = "Efficient prediction of {Marsaglia--Zaman} random
number generators",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "44",
number = "3",
pages = "1253--1257",
year = "1998",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.669305",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
MRclass = "65C10",
MRnumber = "99b:65007",
bibdate = "Thu Dec 22 07:42:24 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
ZMnumber = "0915.65003",
abstract = "This paper presents two properties of the random
number generator by {\em G. Marsaglia} and {\em A.
Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
0733.65005)]. First, it is shown that its successive
digits are digits of certain rational $b$-adic numbers.
Then, an efficient algorithm is derived to predict an
unknown pseudorandom sequence of this type. Two
examples of the prediction are given.",
acknowledgement = ack-nhfb,
classmath = "*65C10 Random number generation 11K45 Pseudo-random
numbers, etc.",
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
keywords = "$b$-adic number; algorithm; continued fraction;
pseudo-random number generator",
ZMreviewer = "K. Uosaki (Tottori)",
}
@Article{Browne:1998:FBL,
author = "Malcolm W. Browne",
title = "Following {Benford's Law}, or Looking Out for {No.
1}",
journal = j-NY-TIMES,
volume = "??",
number = "??",
pages = "F4--F4",
day = "4",
month = aug,
year = "1998",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Sat Feb 16 14:29:48 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Science section.",
URL = "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
}
@Article{Busta:1998:UBL,
author = "Bruce Busta and Randy Weinberg",
title = "Using {Benford's Law} and Neural Networks as a Review
Procedure",
journal = "Managerial Auditing Journal",
volume = "13",
number = "6",
pages = "356--366",
month = "????",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1108/02686909810222375",
ISSN = "0268-6902 (print), 1758-7735 (electronic)",
ISSN-L = "0268-6902",
bibdate = "Tue Nov 22 18:50:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Chongde:1998:EMB,
author = "Wang Chongde and Wang Zhe",
title = "Evaluation of the models for {Bradford's Law}",
journal = j-SCIENTOMETRICS,
volume = "42",
number = "1",
pages = "89--95",
month = may,
year = "1998",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/BF02465014",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:03:59 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
URL = "http://link.springer.com/article/10.1007/BF02465014",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{DeCeuster:1998:HPB,
author = "Marc J. K. {De Ceuster} and Geert Dhaene and Tom
Schatteman",
title = "On the hypothesis of psychological barriers in stock
markets and {Benford's Law}",
journal = j-J-EMPIR-FINANCE,
volume = "5",
number = "3",
pages = "263--279",
month = sep,
year = "1998",
CODEN = "JEFIEC",
DOI = "https://doi.org/10.1016/S0927-5398(97)00024-8",
ISSN = "0927-5398 (print), 1879-1727 (electronic)",
ISSN-L = "0927-5398",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
abstract = "We consider the hypothesis of psychological barriers
at round numbers of a stock index. This hypothesis is
often examined by testing the uniformity of the
distribution of the trailing digits in the stock index,
a rejection being interpreted as evidencing the
existence of psychological barriers. By virtue of
Benford's Law, we show that the uniform distribution is
not the right benchmark against which to test. As an
alternative we propose a test based on the cyclical
permutations of the actual returns. Applying this test
to the Dow Jones 30 Industrial Average, the Financial
Times Stock Exchange 100 and the Nikkei Stock Average
225, we find no convincing evidence of psychological
barriers, contrary to previous findings.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Empirical Finance",
keywords = "Benford's Law; Psychological barriers",
}
@Article{Herman:1998:TRI,
author = "Tom Herman",
title = "Tax report: An {IRS} blooper startles thousands of
taxpayers",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "1--1",
day = "18",
month = feb,
year = "1998",
CODEN = "WSJOAF",
ISSN = "0099-9660",
bibdate = "Fri Mar 22 09:17:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://online.wsj.com/article/SB887753996209804500.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Wall Street Journal",
keywords = "Benford's Law",
remark = "From the article: ``[a taxpayer] was expecting a \$513
tax refund. Instead, he recently received a letter from
the Internal Revenue Service informing him that he owes
the government \$300,000,007.57. \ldots{} about 3,000
other people around the nation got similar erroneous
notices, each showing a balance due of `three hundred
million dollars and change.'\,''",
}
@Article{Hill:1998:FDP,
author = "Theodore P. Hill",
title = "The First Digit Phenomenon",
journal = j-AM-SCI,
volume = "86",
number = "4",
pages = "358--363",
month = jul # "\slash " # aug,
year = "1998",
CODEN = "AMSCAC",
DOI = "https://doi.org/10.1511/1998.4.358",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Sat Dec 10 11:54:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
abstract = "A century ago, Simon Newcomb observed an unexpected
pattern in the first digits of logarithm tables: The
digit $1$ is significantly more likely to occur than
$2$, $2$ than $3$, and so on. More than a half-century
later, Frank Benford rediscovered the first-digit
phenomenon and found that it applied to many tables of
numerical data, including the stock market, census
statistics and accounting figures. New mathematical
insights establish the empirical law developed by
Newcomb and Benford as part of modern probability
theory, and recent applications include testing of
mathematical models, design of computers and detection
of fraud in accounting.",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Book{Knuth:1998:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1998",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/css.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
note = "See section 4.2.4V, The Fraction Parts, pages
254--262, for a discussion of Benford's Law.",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Knuth comments on page 255: ``The fact that the
leading digits tend to be small makes the most obvious
techniques of ``average error'' estimation for floating
point calculations invalid. The relative error due to
rounding is usually a little more than expected.",
tableofcontents = "3: Random Numbers / 1 \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 10 \\
3.2.1. The Linear Congruential Method / 10 \\
3.2 1.1. Choice of modulus / 12 \\
3.2.1.2 Choice of multiplier / 16 \\
3.2.1.3. Potency / 23 \\
3.2.2. Other Methods / 26 \\
3.3. Statistical Tests / 41 \\
3.3.1. General Test Procedures for Studying Random Data
/ 41 \\
3.3.2. Empirical Tests / 61 \\
*3.3.3. Theoretical Tests / 80 \\
3.3.4. The Spectral Test / 93 \\
3.4. Other Types of Random Quantities / 119 \\
3.4 1. Numerical Distributions / 119 \\
3.4.2. Random Sampling and Shuffling / 142 \\
*3.5. What Is a Random Sequence? / 149 \\
3.6. Summary / 184 \\
4: Arithmetic / 194 \\
4.1. Positional Number Systems / 195 \\
4.2. Floating Point Arithmetic / 214 \\
4.2.1. Single-Precision Calculations / 214 \\
4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
*4.2.3. Double-Precision Calculations / 246 \\
4.2.4. Distribution of Floating Point Numbers / 253 \\
4.3 Multiple Precision Arithmetic / 265 \\
4.3.1. The Classical Algorithms / 265 \\
*4.3.2. Modular Arithmetic / 284 \\
*4.3.3. How Fast Can We Multiply? / 294 \\
4.4. Radix Conversion / 319 \\
4.5. Rational Arithmetic / 330 \\
4.5.1. Fractions / 330 \\
4.5.2. The Greatest Common Divisor / 333 \\
*4.5.3. Analysis of Euclid's Algorithm / 356 \\
4.5.4. Factoring into Primes / 379 \\
4.6. Polynomial Arithmetic / 418 \\
4.6.1. Division of Polynomials / 420 \\
*4.6.2. Factorization of Polynomials / 439 \\
4.6.3. Evaluation of Powers / 461 \\
4.6.4. Evaluation of Polynomials / 485 \\
*4.7. Manipulation of Power Series / 525 \\
Answers to Exercises / 538 \\
Appendix A: Tables of Numerical Quantities / 726 \\
1. Fundamental Constants (decimal) / 726 \\
2; Fundamental Constants ( octal) / 727 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 728 \\
Appendix B: Index to Notations / 730 \\
Index and Glossary / 735",
}
@Article{Manrubia:1998:IMU,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
title = "Intermittency model for urban development",
journal = j-PHYS-REV-E,
volume = "58",
number = "1",
pages = "295--302",
month = jul,
year = "1998",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.58.295",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:42:23 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.295",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Marsili:1998:IIL,
author = "Matteo Marsili and Yi-Cheng Zhang",
title = "Interacting Individuals Leading to {Zipf's Law}",
journal = j-PHYS-REV-LET,
volume = "80",
number = "??",
pages = "2741--??",
day = "23",
month = mar,
year = "1998",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.80.2741",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Nigrini:1998:DIB,
author = "Mark J. Nigrini",
title = "{Dow} Illustrates {Benford's Law}",
journal = j-NY-TIMES,
volume = "??",
number = "??",
pages = "F4--F4",
day = "4",
month = aug,
year = "1998",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Sat Feb 16 15:46:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
}
@Article{NunesAmaral:1998:PLS,
author = "Lu{\'\i}s A. {Nunes Amaral} and Sergey V. Buldyrev and
Shlomo Havlin and Michael A. Salinger and H. Eugene
Stanley",
title = "Power Law Scaling for a System of Interacting Units
with Complex Internal Structure",
journal = j-PHYS-REV-LET,
volume = "80",
number = "7",
pages = "1385--1388",
day = "16",
month = feb,
year = "1998",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.80.1385",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Thu Feb 28 11:09:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Pietronero:1998:UDN,
author = "L. Pietronero and E. Tosatti and V. Tosatti and A.
Vespignani",
title = "The Uneven Distribution of Numbers in Nature",
journal = "ArXiv e-prints",
pages = "9",
day = "27",
month = aug,
year = "1998",
bibdate = "Mon Nov 21 06:58:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/cond-mat/9808305",
abstract = "Suppose you look at today's stock prices and bet on
the value of the first digit. One could guess that a
fair bet should correspond to the frequency of $ 1 / 9
= 11.11 \% $ for each digit from 1 to 9. This is by no
means the case, and one can easily observe a strong
prevalence of the small values over the large ones. The
first three integers 1, 2 and 3 alone have globally a
frequency of 60\% while the other six values 4, 5, 6,
7, 8 and 9 appear only in 40\% of the cases. This
situation is actually much more general than the stock
market and it occurs in a variety of number catalogs
related to natural phenomena. The first observation of
this property traces back to S. Newcomb in 1881 but a
more precise account was given by F. Benford in 1938.
In this note we illustrate these observations with the
enlightening specific example of the stock market. We
also identify the general mechanism for the origin of
this uneven distribution in the multiplicative nature
of fluctuations in economics and in many natural
phenomena. This provides a natural explanation for the
ubiquitous presence of the Benford's law in many
different phenomena with the common element that their
fluctuations refer to a fraction of their values. This
brings us close to the problem of the spontaneous
origin of scale invariant properties in various
phenomena which is a debated question at the frontier
of different fields.",
acknowledgement = ack-nhfb,
}
@Article{Pocheau:1998:SRS,
author = "A. Pocheau",
title = "Scale ratios, statistical symmetries and
intermittency",
journal = j-EUROPHYS-LETT,
volume = "43",
number = "4",
pages = "410--415",
month = aug,
year = "1998",
CODEN = "EULEEJ",
DOI = "https://doi.org/10.1209/epl/i1998-00103-6",
ISSN = "0295-5075 (print), 1286-4854 (electronic)",
ISSN-L = "0295-5075",
bibdate = "Sat Feb 16 16:02:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Europhysics Letters",
journal-URL = "http://iopscience.iop.org/0295-5075",
}
@Article{Ramsden:1998:ZLB,
author = "J. J. Ramsden and J. Vohradsk{\'y}",
title = "{Zipf}-like behavior in procaryotic protein
expression",
journal = j-PHYS-REV-E,
volume = "58",
number = "??",
pages = "7777--??",
day = "1",
month = dec,
year = "1998",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.58.7777",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.7777",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Rousset:1998:CPV,
author = "Olivier G. Rousset and Yilong Ma and Alan C. Evans",
title = "Correction for Partial Volume Effects in {PET}:
Principle and Validation",
journal = j-NUCL-MED,
volume = "39",
number = "5",
pages = "904--911",
month = may,
year = "1998",
CODEN = "JNMEAQ",
ISSN = "0161-5505 (print), 1535-5667 (electronic)",
ISSN-L = "0161-5505",
bibdate = "Sat Sep 10 16:10:46 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jnm.snmjournals.org/content/39/5/904.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nuclear Medicine",
journal-URL = "http://jnm.snmjournals.org/content/by/year",
keywords = "Benford's Law",
}
@Article{Schatte:1998:BLV,
author = "P. Schatte",
title = "On {Benford's law} to variable base",
journal = j-STAT-PROB-LETT,
volume = "37",
number = "4",
pages = "391--397",
day = "30",
month = mar,
year = "1998",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/S0167-7152(97)00142-9",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60F05 (60E15)",
MRnumber = "1624423 (99e:60072)",
MRreviewer = "Theodore P. Hill",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715297001429",
abstract = "Benford's law is studied in dependence on the base $ b
> 1 $. It can hold to large bases $b$ only
approximately. The quality of approximation is
estimated in cases of products and sums of random
variables, respectively, and in case of some
deterministic sequences. Always the approximation by
Benford's law becomes worse as $ b \to \infty $, but as
a rule also as $ b \to 1 + 0 $",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Discrepancy; First-digit problem;
Mantissa distribution; Products of random variables;
Sums of random variables",
}
@Article{Simon:1998:ADC,
author = "Jonathan Simon",
title = "An Analysis of the Distribution of Combinations Chosen
by {UK National Lottery} Players",
journal = j-J-RISK-UNCERT,
volume = "17",
number = "3",
pages = "243--277",
year = "1998",
CODEN = "JRUNEN",
DOI = "https://doi.org/10.1023/A:1007786901776",
ISSN = "0895-5646 (print), 1573-0476 (electronic)",
ISSN-L = "0895-5646",
bibdate = "Sat Sep 10 14:35:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Risk and Uncertainty",
journal-URL = "http://link.springer.com/journal/11166",
keywords = "Benford's Law",
}
@Article{Slijepcevic:1998:NID,
author = "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}",
title = "A Note on Initial Digits of Recurrence Sequences",
journal = j-FIB-QUART,
volume = "36",
number = "4",
pages = "305--308",
month = aug,
year = "1998",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:02:49 MDT 2011",
bibsource = "http://www.fq.math.ca/36-4.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/36-4/slijepcevic.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Troll:1998:ZLC,
author = "G. Troll and P. beim Graben",
title = "{Zipf}'s law is not a consequence of the {Central
Limit Theorem}",
journal = j-PHYS-REV-E,
volume = "57",
number = "3",
pages = "1347--1355",
day = "1",
month = feb,
year = "1998",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.57.1347",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.57.1347;
http://pre.aps.org/abstract/PRE/v57/i2/p1347_1",
abstract = "It has been observed that the rank statistics of
string frequencies of many symbolic systems (e.g., word
frequencies of natural languages) follows Zipf's law in
good approximation. We show that, contrary to claims in
the literature, Zipf's law cannot be realized by the
central limit theorem(s). The observation that a
log-normal distribution of string frequencies yields an
approximately Zipf-like rank statistics is actually
misleading. Indeed, Zipf's law for the rank statistics
is strictly equivalent to a power law distribution of
frequencies. There are two natural ways to perform the
infinite size limit for the vocabulary. The first one
is the method of choice in the literature; it makes the
upper word length bound tend to infinity and leads in
the case of a multistate Bernoulli process via a
central limit theorem to a log-normal frequency
distribution. An alternative and for text samples
actually better realizable way is to make the lower
frequency bound tend to zero. This limit procedure
leads to a power law distribution and hence to Zipf's
law --- at least for Bernoulli processes and to a very
good approximation for natural languages where it
passes the $ \chi^2 $ test. For the Bernoulli case we
will give a heuristic proof.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Book{Wirsching:1998:DSG,
author = "G{\"u}nther J. Wirsching",
title = "The dynamical system generated by the $ 3 n + 1 $
function",
volume = "1681",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vii + 158",
year = "1998",
ISBN = "3-540-63970-5 (softcover)",
ISBN-13 = "978-3-540-63970-1 (softcover)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
LCCN = "QA3 .L28 no. 1681",
bibdate = "Mon Nov 21 08:00:54 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNM,
URL = "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html;
http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Sequences (Mathematics); Combinatorial probabilities;
Convergence",
}
@Article{Ausloos:1999:PMK,
author = "M. Ausloos and K. Ivanova",
title = "Precise $ (m, k) $-{Zipf} diagram analysis of
mathematical and financial time series when $ m = 6 $,
$ k = 2 $",
journal = j-PHYSICA-A,
volume = "270",
number = "3--4",
pages = "526--542",
day = "15",
month = aug,
year = "1999",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(99)00178-8",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437199001788",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{AyllonBurguillo:1999:PDS,
author = "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera
Dom{\'\i}nguez}",
title = "El primer d{\'\i}gito significativo. ({Spanish}) [The
first significant digit]",
journal = "{Epsilon}: Revista de la {Sociedad Andaluza de
Educaci{\'o}n Matem{\'a}tica ``Thales''}",
volume = "15",
number = "3(45)",
pages = "339--352",
month = "????",
year = "1999",
ISSN = "1131-9321",
ISSN-L = "1131-9321",
MRnumber = "K60xx",
bibdate = "Sat Feb 16 14:32:14 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "MATHEDUC.02332710",
acknowledgement = ack-nhfb,
ajournal = "{Rev. Epsil{\'o}n SAEM `Thales'}",
journal-URL = "http://thales.cica.es/epsilon/;
http://dialnet.unirioja.es/servlet/revista?codigo=504",
language = "Spanish",
remark = "Reported in \cite{Torres:2007:HDN} to contain an
extensive bibliography on Benford's Law. The publisher
does not have issues before 2003, and no electronic
copy has yet been found on the Internet. Attempts to
get this paper via Interlibrary Loan failed on the
grounds that ``We are unable to verify any owning
libraries within the United States or those that we
have ILL privileges.''",
xxauthor = "Manuel {Perera Dom{\'\i}nguez} and Juan David
{Ayll{\'o}n Burguillo}",
}
@Article{Barabasi:1999:ESR,
author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
Albert",
title = "Emergence of scaling in random networks",
journal = j-SCIENCE,
volume = "286",
number = "5439",
pages = "509--512",
day = "15",
month = oct,
year = "1999",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.286.5439.509",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Tue Nov 15 09:57:42 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/286/5439/509",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "power-law distribution; Zipf's Law",
}
@Article{Brakman:1999:RZT,
author = "Steven Brakman and Harry Garretsen and Charles {Van
Marrewijk} and Marianne {Van Den Berg}",
title = "The Return of {Zipf}: Towards a Further Understanding
of the Rank--Size Distribution",
journal = j-J-REG-SCI,
volume = "39",
number = "1",
pages = "183--213",
year = "1999",
DOI = "https://doi.org/10.1111/1467-9787.00129",
ISSN = "0022-4146 (print), 1467-9787 (electronic)",
ISSN-L = "0022-4146",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Regional Science",
}
@Article{Coderre:1999:FDU,
author = "David Coderre",
title = "Fraud Detection Using Digital Analysis",
journal = j-EDPACS,
volume = "27",
number = "3",
pages = "1--8",
month = "????",
year = "1999",
CODEN = "EDPCDF",
DOI = "https://doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
ISSN = "0736-6981 (print), 1936-1009 (electronic)",
ISSN-L = "0736-6981",
bibdate = "Sat Jan 07 09:20:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
acknowledgement = ack-nhfb,
fjournal = "EDPACS",
keywords = "Benford's Law",
onlinedate = "21 Dec 2006",
}
@Article{Egghe:1999:LZM,
author = "L. Egghe",
title = "On the law of {Zipf--Mandelbrot} for multi-word
phrases",
journal = j-J-AM-SOC-INF-SCI,
volume = "50",
number = "3",
pages = "233--241",
month = "????",
year = "1999",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Mon Sep 10 06:09:31 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "17 Feb 1999",
}
@Article{Egghe:1999:RLZ,
author = "L. Egghe",
title = "Research: On the law of {Zipf--Mandelbrot} for
multi-word phrases",
journal = j-J-AM-SOC-INF-SCI,
volume = "50",
number = "3",
pages = "233--241",
month = "????",
year = "1999",
CODEN = "AISJB6",
DOI = "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Sep 11 09:04:32 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasis.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "17 Feb 1999",
}
@Article{Gabaix:1999:ZLC,
author = "Xavier Gabaix",
title = "{Zipf}'s law for cities: An explanation",
journal = j-Q-J-ECON,
volume = "114",
number = "3",
pages = "739--767",
year = "1999",
CODEN = "QJECAT",
DOI = "https://doi.org/10.1162/003355399556133",
ISSN = "0033-5533 (print), 1531-4650 (electronic)",
ISSN-L = "0033-5533",
bibdate = "Sat Nov 12 10:57:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0952.91059",
abstract = "Zipf's law is a very tight constraint on the class of
admissible models of local growth. It says that for
most countries the size distribution of cities
strikingly fits a power law: the number of cities with
populations greater than $S$ is proportional to $ 1 / S
$. Suppose that, at least in the upper tail, all cities
follow some proportional growth process (this appears
to be verified empirically). This automatically leads
their distribution to converge to Zipf's law.",
acknowledgement = ack-nhfb,
ajournal = "Q. J. Econ.",
classmath = "91B62 (Dynamic economic models etc.) 91B72 (Spatial
models)",
fjournal = "The Quarterly Journal of Economics",
keywords = "local growth; Zipf's law",
}
@Book{Gigerenzer:1999:SHM,
author = "Gerd Gigerenzer and Peter M. Todd",
title = "Simple heuristics that make us smart",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xv + 416",
year = "1999",
ISBN = "0-19-512156-2",
ISBN-13 = "978-0-19-512156-8",
LCCN = "BD260 .G54 1999",
bibdate = "Sat Sep 10 11:19:26 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Evolution and cognition",
URL = "http://www.loc.gov/catdir/enhancements/fy0640/98051084-d.html;
http://www.loc.gov/catdir/enhancements/fy0640/98051084-t.html;
http://www.loc.gov/catdir/enhancements/fy0726/98051084-b.html",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Heuristic",
tableofcontents = "The ABC Research Group \\
I. The Research Agenda \\
1. Fast and Frugal Heuristics: The Adaptive Toolbox /
Gerd Gigerenzer and Peter M. Todd \\
II. Ignorance-Based Decision Making \\
2. The Recognition Heuristic: How Ignorance Makes Us
Smart / Daniel G. Goldstein and Gerd Gigerenzer \\
3. Can Ignorance Beat the Stock Market? / Bernhard
Borges et al. \\
III. One-Reason Decision Making \\
4. Betting on One Good Reason: The Take The Best
Heuristic / Gerd Gigerenzer and Daniel G. Goldstein \\
5. How Good Are Simple Heuristics? / Jean Czerlinski,
Gerd Gigerenzer, and Daniel G. Goldstein \\
6. Why Does One-Reason Decision Making Work? A Case
Study in Ecological Rationality / Laura Martignon and
Ulrich Hoffrage \\
7. When Do People Use Simple Heuristics, and How Can We
Tell? / J{\"o}rg Rieskamp and Ulrich Hoffrage \\
8. Bayesian Benchmarks for Fast and Frugal Heuristics /
Laura Martignon and Kathryn Blackmond Laskey \\
IV. Beyond Choice: Memory, Estimation, and
Categorization \\
9. Hindsight Bias: A Price Worth Paying for Fast and
Frugal Memory / Ulrich Hoffrage and Ralph Hertwig \\
10. Quick Estimation: Letting the Environment Do the
Work / Ralph Hertwig, Ulrich Hoffrage, and Laura
Martignon \\
11. Categorization by Elimination: Using Few Cues to
Choose / Patricia M. Berretty, Peter M. Todd, and Laura
Martignon \\
V. Social Intelligence \\
12. How Motion Reveals Intention: Categorizing Social
Interactions / Philip W. Blythe, Peter M. Todd, and
Geoffrey F. Miller \\
13. From Pride and Prejudice to Persuasion: Satisficing
in Mate Search / Peter M. Todd and Geoffrey F. Miller
\\
14. Parental Investment by Simple Decision Rules /
Jennifer Nerissa Davis and Peter M. Todd \\
VI. A Look Around, A Look Back, A Look Ahead \\
15. Demons versus Heuristics in Artificial
Intelligence, Behavioral Ecology, and Economics / Adam
S. Goodie et al. \\
16. What We Have Learned (So Far) / Peter M. Todd and
Gerd Gigerenzer \\
References \\
Name Index \\
Subject Index",
}
@Article{Hill:1999:DFD,
author = "Theodore P. Hill",
title = "The Difficulty of Faking Data",
journal = j-CHANCE,
volume = "12",
number = "3",
pages = "27--31",
month = "????",
year = "1999",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.1999.10542154",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Tue Nov 22 18:54:44 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
keywords = "Benford's Law",
xxnote = "Check: Hurlimann bibliography says v26 pp. 8--13??;
that is wrong!",
}
@Article{Hill:1999:PCS,
author = "Theodore P. Hill",
title = "Le premier chiffre significatif fait sa loi.
({French}) [{The} first significant digit makes its
law]",
journal = "La Recherche: L'actualit{\'e} des sciences",
volume = "2",
number = "316",
pages = "72--76",
month = jan,
year = "1999",
CODEN = "RCCHBV",
ISSN = "0029-5671 (print), 1625-9955 (electronic)",
ISSN-L = "0029-5671",
bibdate = "Sat Feb 16 17:51:25 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970",
acknowledgement = ack-nhfb,
language = "French",
xxjournal = "La Recherche Hors S{\'e}rie",
}
@Article{Huberman:1999:IGD,
author = "Bernardo A. Huberman and Lada A. Adamic",
title = "{Internet}: Growth dynamics of the {World-Wide Web}",
journal = j-NATURE,
volume = "401",
number = "6749",
pages = "131--131",
day = "9",
month = sep,
year = "1999",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/43604",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Nov 15 09:52:36 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Zipf's Law",
}
@TechReport{Lowe:1999:FDL,
author = "Tomas Lowe and Sally Murphy and Justin Hayward",
title = "The First Digit Law",
type = "Report",
number = "??",
institution = "Department of Computing, Imperial College",
address = "London, UK",
month = jun,
year = "1999",
bibdate = "Wed Nov 23 16:59:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
acknowledgement = ack-nhfb,
lastaccess = "23 November 2011",
}
@Article{Malcai:1999:PLD,
author = "Ofer Malcai and Ofer Biham and Sorin Solomon",
title = "Power-law distributions and {L{\'e}vy}-stable
intermittent fluctuations in stochastic systems of many
autocatalytic elements",
journal = j-PHYS-REV-E,
volume = "60",
number = "2",
pages = "1299--1303",
month = aug,
year = "1999",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.60.1299",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 10:25:38 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.1299",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Manrubia:1999:SMP,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
title = "Stochastic multiplicative processes with reset
events",
journal = j-PHYS-REV-E,
volume = "59",
number = "5",
pages = "4945--4948",
month = may,
year = "1999",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.59.4945",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:25:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.59.4945",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "5",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's law",
}
@Article{Manrubia:1999:TDS,
author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette and
Ricard V. Sol{\'e}",
title = "Transient Dynamics and Scaling Phenomena in Urban
Growth",
journal = j-FRACTALS,
volume = "7",
number = "1",
pages = "1--8",
month = mar,
year = "1999",
CODEN = "FRACEG",
DOI = "https://doi.org/10.1142/S0218348X99000025",
ISSN = "0218-348X",
ISSN-L = "0218-348X",
bibdate = "Wed Feb 27 07:11:42 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025",
acknowledgement = ack-nhfb,
fjournal = "Fractals",
journal-URL = "http://www.worldscientific.com/loi/fractals",
keywords = "Zipf's Law",
}
@Article{Matthews:1999:PO,
author = "Robert Matthews",
title = "The Power of One",
journal = j-NEW-SCIENTIST,
volume = "163",
number = "2194",
pages = "27--30",
day = "10",
month = jul,
year = "1999",
CODEN = "NWSCAL",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Mon Nov 14 16:04:36 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fortunecity.com/emachines/e11/86/one.html;
http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
xxISSN = "0262-4079, 0028-6664",
}
@Article{Mercik:1999:SAI,
author = "Szymon Mercik and Karina Weron and Zuzanna Siwy",
title = "Statistical analysis of ionic current fluctuations in
membrane channels",
journal = j-PHYS-REV-E,
volume = "60",
number = "6",
pages = "7343--7348",
day = "1",
month = dec,
year = "1999",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.60.7343",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.7343",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Book{Miller:1999:JFM,
author = "Irwin Miller and Marylees Miller",
title = "{John E. Freund}'s mathematical statistics",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Sixth",
pages = "xii + 624",
year = "1999",
ISBN = "0-13-123613-X",
ISBN-13 = "978-0-13-123613-4",
LCCN = "QA276 .M4726 1999",
bibdate = "Thu Oct 13 07:00:13 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1928--",
remark = "Revised edition of John E. Freund,
\booktitle{Mathematical statistics}, 5th edition,
1992.",
subject = "Mathematical statistics",
}
@Article{Nigrini:1999:AVD,
author = "Mark J. Nigrini",
title = "Adding value with digital analysis",
journal = "The Internal Auditor: Journal of the {Institute of
Internal Auditors}",
volume = "56",
number = "1",
pages = "21--23",
month = "????",
year = "1999",
CODEN = "ITAUAB",
ISSN = "0020-5745",
ISSN-L = "0020-5745",
bibdate = "Sat Feb 16 18:56:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Nigrini:1999:IGY,
author = "Mark J. Nigrini",
title = "{I've} Got Your Number: How a Mathematical Phenomenon
Can Help {CPAs} Uncover Fraud and Other
Irregularities",
journal = j-J-ACCOUNTANCY,
volume = "187",
number = "2",
pages = "79--83",
month = may,
year = "1999",
CODEN = "JACYAD",
ISSN = "0021-8448 (print), 1945-0729 (electronic)",
ISSN-L = "0021-8448",
bibdate = "Mon Nov 14 16:31:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm;
http://www.journalofaccountancy.com/issues/1999/may/nigrini.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accountancy",
journal-URL = "http://www.journalofaccountancy.com/",
}
@Article{Nigrini:1999:PPF,
author = "Mark J. Nigrini",
title = "Peculiar patterns of first digits",
journal = j-IEEE-POT,
volume = "18",
number = "2",
pages = "24--27",
month = apr # "\slash " # may,
year = "1999",
CODEN = "IEPTDF",
DOI = "https://doi.org/10.1109/45.755849",
ISSN = "0278-6648 (print), 1558-1772 (electronic)",
ISSN-L = "0278-6648",
bibdate = "Mon Nov 21 22:18:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Despite seeing numbers all the time only occasionally
would one say that a list of numbers seems odd. For
this to occur, the numbers are typically highly rounded
or implausible (too much of a coincidence). However
digit pattern analysis, using a computer, can produce
valuable findings not revealed at a mere glance. The
most widely cited paper on digit frequencies was
published by Frank Benford in 1938. With powerful,
low-cost personal computers, Benford's law can help us
to efficiently test the integrity of data. The first
step is to assess whether Benford's law should apply to
the data. If the data is expected to conform, then
Benford's law becomes the expected distribution.
Conformity means that the actual distribution closely
approximates the expected distribution",
acknowledgement = ack-nhfb,
fjournal = "IEEE Potentials",
}
@Article{Okuyama:1999:ZLI,
author = "K. Okuyama and M. Takayasu and H. Takayasu",
title = "{Zipf}'s law in income distribution of companies",
journal = j-PHYSICA-A,
volume = "269",
number = "1",
pages = "125--131",
day = "1",
month = jul,
year = "1999",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(99)00086-2",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437199000862",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Growth rate of assets; Income distribution; Zipf's
Law",
}
@Article{Piqueira:1999:ZLO,
author = "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C.
de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E.
G. Cruz",
title = "{Zipf's Law} Organizes a Psychiatric Ward",
journal = j-J-THEOR-BIOL,
volume = "198",
number = "3",
pages = "439--443",
day = "7",
month = jun,
year = "1999",
CODEN = "JTBIAP",
DOI = "https://doi.org/10.1006/jtbi.1999.0923",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022519399909232",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@Article{Stanley:1999:SUR,
author = "H. Eugene Stanley",
title = "Scaling, universality, and renormalization: Three
pillars of modern critical phenomena",
journal = j-REV-MOD-PHYS,
volume = "71",
number = "2",
pages = "S358--S366",
month = mar,
year = "1999",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.71.S358",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Wed May 23 10:16:18 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v71/i2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.71.S358;
http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Article{Vandewalle:1999:ZAF,
author = "N. Vandewalle and M. Ausloos",
title = "The $n$-{Zipf} analysis of financial data series and
biased data series",
journal = j-PHYSICA-A,
volume = "268",
number = "1--2",
pages = "240--249",
day = "1",
month = jun,
year = "1999",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(99)00031-X",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843719900031X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Vardi:1999:PCS,
author = "Ilan Vardi",
title = "Premiers chiffres significatifs et nombres
alg{\'e}briques. ({French}) [Significant leading digits
and algebraic numbers]",
journal = j-C-R-ACAD-SCI-I,
volume = "328",
number = "9",
pages = "749--754",
month = may,
year = "1999",
CODEN = "CASMEI",
DOI = "https://doi.org/10.1016/S0764-4442(99)80265-1",
ISSN = "0764-4442 (print), 1778-3577 (electronic)",
ISSN-L = "0764-4442",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
abstract = "I show that there is a meromorphic continuation of $
\sigma \log_\beta n / a < \log_\beta a n^{-s} $ to the
whole plane if and only if $ \beta $ is a Pisot number,
$ \alpha \in Q(\beta) $, and either the second largest
conjugate of $ \beta $ is real or the conjugate of $
\alpha $ corresponding to the second largest conjugate
of $ \beta $ is positive.",
acknowledgement = ack-nhfb,
fjournal = "Comptes rendus de l'Acad{\'e}mie des sciences.
S{\'e}rie I, Math{'e}matique",
keywords = "Benford's Law",
language = "French",
}
@Article{Walthoe:1999:LNO,
author = "Jon Walthoe and Robert Hunt and Mike Pearson",
title = "Looking out for number one",
journal = "Plus Magazine",
volume = "??",
number = "??",
pages = "1--9",
month = sep,
year = "1999",
DOI = "????",
bibdate = "Mon Feb 18 06:59:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Published by the University of Cambridge Millennium
Mathematics Project.",
URL = "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Banyard:2000:NAF,
author = "Peter Banyard",
title = "A New Aid for Fraud Detection",
journal = "Credit Management: journal of the {Institute of Credit
Management}",
volume = "??",
number = "??",
address = "Stamford College, UK",
pages = "32--33",
month = mar,
year = "2000",
DOI = "",
ISSN = "0265-2099",
ISSN-L = "0265-2099",
bibdate = "Thu Oct 13 08:34:05 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
abstract = "A simple mathematical curiosity, discovered about a
century ago, may well prove a surefire way of sniffing
out swindlers. Benford's Law was just an observation
until the theory that proved it was discovered 3 years
ago. It seems unlikely, but about 30\% of numbers start
with the digit one. Another 18\% start with the digit 2
and only 4.6\% start with 9. It would be quite easy to
build a Benford fraud buster into any analysis of
figures, while it remains extremely difficult to
produce an artificial set of figures that will comply
with the law.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "I cannot find a Web site for this journal, or for its
archives, despite extensive searching.",
}
@Article{Blank:2000:PLC,
author = "Aharon Blank and Sorin Solomon",
title = "Power laws in cities population, financial markets and
{Internet} sites (scaling in systems with a variable
number of components)",
journal = j-PHYSICA-A,
volume = "287",
number = "1--2",
pages = "279--288",
day = "15",
month = nov,
year = "2000",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(00)00464-7",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 06:24:21 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437100004647",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@InProceedings{Burns:2000:SSR,
author = "B. D. Burns",
editor = "Niels A. Taatgen and Hedderik van Rijn",
booktitle = "{Proceedings of the 31st Annual Conference of the
Cognitive Science Society 2009 (CogSci 2009):
Amsterdam, Netherlands, 29 July--1 August 2009}",
title = "Sensitivity to Statistical Regularities: People
(Largely) Follow {Benford's Law}",
publisher = "Cognitive Science Society",
address = "Austin, TX, USA",
pages = "2872--2877",
year = "2010",
ISBN = "1-61567-407-1",
ISBN-13 = "978-1-61567-407-7",
LCCN = "????",
bibdate = "Sat Sep 10 10:53:37 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Drake:2000:CAA,
author = "Philip D. Drake and Mark J. Nigrini",
title = "Computer assisted analytical procedures using
{Benford's Law}",
journal = j-J-ACCOUNT-EDUC,
volume = "18",
number = "2",
pages = "127--146",
month = "Spring",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1016/S0748-5751(00)00008-7",
ISSN = "0748-5751 (print), 1873-1996 (electronic)",
ISSN-L = "0748-5751",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0748575100000087;
http://www.sciencedirect.com/science/journal/07485751",
abstract = "This case introduces students to Benford's Law and
Digital Analysis, which can be used as an analytical
procedure and fraud detection tool. Digital Analysis
(DA) is the analysis of digit and number patterns of a
data set. Actual digit frequencies in a data set are
compared to the expected frequencies according to
Benford's Law [Benford, F. (1938). The law of the
anomalous numbers, Proceedings of the American
Philosophical Society, 78, 551 572.]. Minor differences
suggest that the data have passed a reasonableness
test, while major differences signal possible financial
statement mis-statements. After describing Benford's
Law and the basic {DA} tests, the case requires
auditing students to download {DA} software and the
actual accounts payable file of a software company from
a designated Internet site. Students then, (1) analyse
the data using three {DA} tests as an analytical
procedure in an external audit context, and (2) graph
and a report the results and audit-related conclusions.
The teaching note includes the actual findings from the
audit of that data set and guidance on using the case
in an auditing course.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accounting Education",
keywords = "Benford's Law",
}
@Article{Lanza:2000:UDA,
author = "R. B. Lanza",
title = "Using digital analysis to detect fraud: Review of the
{DATAS\reg} statistical analysis tool",
journal = j-J-FORENSIC-ACCOUNT,
volume = "1",
number = "??",
pages = "291--296",
month = "????",
year = "2000",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Tue Nov 22 10:47:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.rtedwards.com/journals/JFA/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Leemis:2000:SDS,
author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
Evans",
title = "Survival Distributions Satisfying {Benford's Law}",
journal = j-AMER-STAT,
volume = "54",
number = "4",
pages = "236--241",
month = nov,
year = "2000",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62E15 (62N05)",
MRnumber = "1803620",
bibdate = "Fri Jan 27 18:16:34 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326510;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/publications/tas/Leemis.htm;
http://www.jstor.org/stable/2685773",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@InProceedings{Lei:2000:EIN,
author = "Skylar Lei and Michael Smith and Giancarlo Succi",
title = "Empirical investigation of a novel approach to check
the integrity of software engineering measuring
processes",
crossref = "ACM:2000:PIC",
pages = "773--773",
year = "2000",
DOI = "https://doi.org/10.1145/337180.337629",
bibdate = "Sat Feb 16 18:28:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Lowe:2000:BLF,
author = "R. Lowe",
title = "{Benford's Law} and fraud detection",
journal = "Chartered Accountants Journal of New Zealand",
volume = "79",
number = "10",
pages = "32--36",
month = "????",
year = "2000",
DOI = "",
ISSN = "1172-9929",
ISSN-L = "1172-9929",
bibdate = "Thu Oct 13 08:55:37 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
journal-URL = "http://www.nzica.com/journalarchive.aspx",
remark = "No archives online before 2012. Library of Congress
says that publication ceased in July 2005 at volume 84,
number 6.",
}
@Article{Lowe:2000:WBL,
author = "R. Lowe",
title = "When {Benford's Law} is broken",
journal = "Chartered Accountants Journal of New Zealand",
volume = "79",
number = "11",
pages = "24--27",
month = "????",
year = "2000",
DOI = "",
ISSN = "1172-9929",
ISSN-L = "1172-9929",
bibdate = "Thu Oct 13 08:55:37 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
journal-URL = "http://www.nzica.com/journalarchive.aspx",
remark = "No archives online before 2012. Library of Congress
says that publication ceased in July 2005 at volume 84,
number 6.",
}
@TechReport{Nigrini:2000:CA,
author = "Mark J. Nigrini",
title = "Continuous Auditing",
type = "Preprint",
institution = "Ernst \& Young Center for Auditing Research and
Advanced Technology, University of Kansas",
address = "Lawrence, KS, USA",
pages = "23",
day = "30",
month = aug,
year = "2000",
bibdate = "Sat Feb 16 18:57:40 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Book{Nigrini:2000:DAT,
author = "Mark J. Nigrini",
title = "Digital analysis tests and statistics: using digit and
number patterns and Benford's law to detect errors,
biases, fraud, irregularities, and processing
inefficiencies",
publisher = "Nigrini Institute Inc.",
address = "Allen, TX, USA",
pages = "242",
year = "2000",
LCCN = "????",
bibdate = "Sat Jan 23 07:53:08 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Nigrini:2000:DAU,
author = "Mark John Nigrini",
title = "Digital analysis using {Benford}'s law: tests and
statistics for auditors",
publisher = "Global Audit Publications",
address = "Vancouver, BC, Canada",
edition = "Second",
pages = "xvii + 278",
year = "2000",
ISBN = "189449709 (??invalid ISBN??)",
ISBN-13 = "189449709 (??invalid ISBN??)",
LCCN = "????",
bibdate = "Tue Nov 22 20:48:29 MST 2011",
bibsource = "amicus.nlc-bnc.ca:210/NL;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; Auditing;
Statistical methods; Analyse num{\'e}rique;
Informatique; V{\'e}rification comptable; M{\'e}thodes
statistiques",
}
@Article{Padmanabhan:2000:CAD,
author = "Venkata N. Padmanabhan and Lili Qiu",
title = "The content and access dynamics of a busy {Web} server
(poster session)",
journal = j-SIGMETRICS,
volume = "28",
number = "1",
pages = "122--123",
month = jun,
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1145/339331.339405",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Thu Jun 26 11:31:11 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "We study the MSNBC Web site, one of the busiest in the
Internet today. We analyze the dynamics of content
creation and modification as well as client accesses.
Our key findings are (a) files tend to change little
upon modification, (b) a small set of files get
modified repeatedly, (c) file popularity follows a
Zipf-like distribution with an $ \alpha $ much larger
than reported in previous, proxy-based studies, and (d)
there is significant temporal stability in file
popularity but not much stability in the domains from
which popular content is accessed. We discuss
implications of these findings.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
}
@Book{Sole:2000:SLH,
author = "Ricard Vicente Sol{\'e} and Brian Goodwin",
title = "Signs of Life: How Complexity Pervades Biology",
publisher = pub-BASIC-BOOKS,
address = pub-BASIC-BOOKS:adr,
pages = "xi + 322",
year = "2000",
ISBN = "0-465-01927-7, 0-465-01928-5 (paperback)",
ISBN-13 = "978-0-465-01927-4, 978-0-465-01928-1 (paperback)",
LCCN = "QH501 .S65 2000",
bibdate = "Thu Feb 28 09:59:50 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Mandelbrot; Zipf's law",
tableofcontents = "Nonlinearity, chaos, and emergence \\
Order, complexity, disorder \\
Genetic networks, cell differentiation, and development
\\
Physiology on the edge of chaos \\
Brain dynamics \\
Ants, brains, and chaos \\
The Baroque of nature \\
Life on the edge of catastrophe \\
Evolution and extinction \\
Fractal cities and market crashes",
}
@Article{Soliman:2000:BPP,
author = "Ahmed A. Soliman",
title = "{Bayes} Prediction in a {Pareto} Lifetime Model with
Random Sample Size",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "49",
number = "1",
pages = "51--62",
month = "????",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.2307/2681255",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:23 MST 2015",
bibsource = "http://www.jstor.org/stable/i326257;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-2000.bib",
URL = "http://www.jstor.org/stable/2681255",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@Article{Stanley:2000:SIU,
author = "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan
and P. Ch. Ivanov and T. H. Keitt and V. Plerou",
title = "Scale invariance and universality: organizing
principles in complex systems",
journal = j-PHYSICA-A,
volume = "281",
number = "1--4",
pages = "60--68",
day = "15",
month = jun,
year = "2000",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(00)00195-3",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu Feb 28 09:52:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437100001953",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "power law; scale invariance; Zipf's law",
}
@Article{Tapp:2000:UTD,
author = "D. J. Tapp and D. B. Burg",
title = "Using technology to detect fraud",
journal = "{Pennsylvania CPA} Journal",
volume = "71",
number = "4",
pages = "20--23",
month = "????",
year = "2000",
ISSN = "0746-1062",
ISSN-L = "0746-1062",
bibdate = "Thu Oct 13 09:05:22 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "https://www.picpa.org/keep-informed/pennsylvania-cpa-journal",
keywords = "Benford's Law",
remark = "No archives online before 2014.",
}
@Article{Tolle:2000:DDS,
author = "Charles R. Tolle and Joanne L. Budzien and Randall A.
Laviolette",
title = "Do dynamical systems follow {Benford}'s law?",
journal = j-CHAOS,
volume = "10",
number = "2",
pages = "331--336",
month = "????",
year = "2000",
CODEN = "CHAOEH",
DOI = "https://doi.org/10.1063/1.166498",
ISSN = "1054-1500",
ISSN-L = "1054-1500",
bibdate = "Mon Nov 14 17:35:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
http://link.aip.org/link/chaoeh/v10/i2/p331/s1;
http://link.aip.org/link/doi/10.1063/1.166498",
abstract = "Data compiled from a variety of sources follow
Benford's law, which gives a monotonically decreasing
distribution of the first digit (1 through 9). We
examine the frequency of the first digit of the
coordinates of the trajectories generated by some
common dynamical systems. One-dimensional cellular
automata fulfill the expectation that the frequency of
the first digit is uniform. The molecular dynamics of
fluids, on the other hand, provides trajectories that
follow Benford's law. Finally, three chaotic systems
are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The
Lorenz system generates trajectories that follow
Benford's law. The H{\'e}non system generates
trajectories that resemble neither the uniform
distribution nor Benford's law. Finally, the
R{\"o}ssler system generates trajectories that follow
the uniform distribution for some parameters choices,
and Benford's law for others.",
acknowledgement = ack-nhfb,
fjournal = "Chaos (Woodbury, NY)",
journal-URL = "http://scitation.aip.org/content/aip/journal/chaos",
xxpages = "331--337",
}
@Article{Urzua:2000:SET,
author = "Carlos M. Urz{\'u}a",
title = "A simple and efficient test for {Zipf}'s law",
journal = j-ECONOM-LETT,
volume = "66",
number = "3",
pages = "257--260",
day = "1",
month = mar,
year = "2000",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/S0165-1765(99)00215-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176599002153",
ZMnumber = "0951.91059",
abstract = "This paper presents a simple and locally optimal test
for Zipf's law. Its use is illustrated in the case of
the largest US metropolitan areas. An objection to the
general relevance of that law is also presented.",
acknowledgement = ack-nhfb,
classmath = "91B82 (Statistical methods in economics) 91B74 (Models
of real-world systems)",
fjournal = "Economics Letters",
keywords = "rank-size law; Zipf's law",
}
@Article{Vogt:2000:BGS,
author = "W. Vogt",
title = "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf
der Spur --- Zahlen l{\"u}gen nichts}. ({German})
[{Benford's Law}: tax and budget sinners lying on the
track --- Numbers do not lie]",
journal = "Schweizer Versicherung",
volume = "9",
number = "??",
pages = "27--29",
month = "????",
year = "2000",
DOI = "????",
bibdate = "Mon Feb 18 06:57:07 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
journal-URL = "http://www.schweizerversicherung.ch/de/archiv_suche",
language = "German",
remark = "No ISSN assigned. Not found in journal archive on 18
February 2013.",
}
@Article{York:2000:ATB,
author = "D. York",
title = "Auditing Technique --- {Benford}'s law",
journal = j-ACCOUNTANCY,
volume = "126",
number = "1283",
pages = "126--??",
month = "????",
year = "2000",
CODEN = "ACTYAD",
ISSN = "0001-4664",
ISSN-L = "0001-4664",
bibdate = "Wed Nov 23 11:30:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Accountancy",
journal-URL = "https://www.cchdaily.co.uk/magazine",
remark = "No archives online before 2014",
}
@Article{Axtell:2001:ZDU,
author = "R. L. Axtell",
title = "{Zipf} Distribution of {U.S.} Firm Sizes",
journal = j-SCIENCE,
volume = "293",
number = "5536",
pages = "1818--1820",
day = "7",
month = sep,
year = "2001",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.1062081",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Feb 27 06:38:34 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/293/5536/1818",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "Zipf's Law",
}
@Article{Dolgikh:2001:PCS,
author = "Dmitry G. Dolgikh and Andrei M. Sukhov",
title = "Parameters of cache systems based on a {Zipf}-like
distribution",
journal = j-COMP-NET-AMSTERDAM,
volume = "37",
number = "6",
pages = "711--716",
day = "15",
month = dec,
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1389-1286(01)00243-2",
ISSN = "1389-1286 (print), 1872-7069 (electronic)",
ISSN-L = "1389-1286",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "http://www.elsevier.com/locate/issn/13891286;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html;
http://www.sciencedirect.com/science/article/pii/S1389128601002432",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks (Amsterdam, Netherlands: 1999)",
journal-URL = "http://www.sciencedirect.com/science/journal/13891286",
keywords = "Zipf's Law",
}
@Article{Dubinsky:2001:MFF,
author = "Bruce G. Dubinsky",
title = "Math formula fights fraud",
journal = "Legal Times of {Washington}",
volume = "XXIV",
number = "9",
pages = "??--??",
day = "26",
month = feb,
year = "2001",
ISSN = "0732-7536",
ISSN-L = "0732-7536",
bibdate = "Sat Feb 16 17:35:39 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
xxjournal = "Legal Times",
}
@Article{Gelbukh:2001:ZHL,
author = "Alexander Gelbukh and Grigori Sidorov",
title = "{Zipf} and {Heaps Laws}' Coefficients Depend on
Language",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2004",
pages = "332--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:22 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Gent:2001:BL,
author = "Ian Gent and Toby Walsh",
title = "{Benford's Law}",
type = "Report",
institution = "School of Computer Science, University of St. Andrews,
and Department of Computer Science, University of
York",
address = "St. Andrews, Scotland and York, England",
pages = "7",
day = "2",
month = feb,
year = "2001",
bibdate = "Fri Nov 18 08:37:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
abstract = "Benford's Law predicts the frequency of the leading
digit in numbers met in a wide range of naturally
occurring phenomena. In data following Benford's Law,
numbers start with a small leading digit more often
those with a large leading digit. Here we demonstrate
that Benford's Law also describes a wide range of
computational phenomena. In particular, we show that a
number of different statistics associated with
computation like space and runtime often follow
Benford's Law. We also show that search cost on input
data that follows Benford's Law is often very different
to that on more uniform data. These results could be
used to improve algorithm performance (for example, for
load balancing or disk de-fragmentation), as well as to
help model algorithm performance. Benford's Law can
also be used to generate data for benchmarking
algorithms that may be more realistic than purely
random data.",
acknowledgement = ack-nhfb,
remark = "PDF file no longer at the St. Andrews URL on 18
November 2011, but recovered from
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}
@Article{Harremoes:2001:MEF,
author = "Peter Harremo{\"e}s and Flemming Tops{\o}e",
title = "Maximum Entropy Fundamentals",
journal = j-ENTROPY,
volume = "3",
number = "3",
pages = "191--226",
month = sep,
year = "2001",
CODEN = "ENTRFG",
DOI = "https://doi.org/10.3390/e3030191",
ISSN = "1099-4300",
ISSN-L = "1099-4300",
bibdate = "Thu Feb 28 10:55:45 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.mdpi.com/1099-4300/3/3/191",
acknowledgement = ack-nhfb,
fjournal = "Entropy",
keywords = "continuity of entropy; entropy loss; exponential
family; game theoretical equilibrium; hyperbolic
distributions; information topology; maximum entropy;
minimum risk; Nash equilibrium code; partition
function; Zipf's law",
remark = "Open access journal.",
}
@Article{Hobza:2001:NBL,
author = "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
title = "On the {Newcomb--Benford} law in models of statistical
data",
journal = "Revista Matem{\'a}tica Complutense",
volume = "14",
number = "2",
pages = "407--420",
year = "2001",
CODEN = "????",
ISSN = "1139-1138, 1696-8220, 1988-2807",
ISSN-L = "1139-1138",
MRclass = "62E10",
MRnumber = "1871305 (2002j:62015)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Rev. Mat. Complut.",
fjournal = "Revista Matem{\'a}tica Complutense",
}
@Article{Huang:2001:PLE,
author = "Z. F. Huang and S. Solomon",
title = "Power, {L{\'e}vy}, exponential and {Gaussian}-like
regimes in autocatalytic financial systems",
journal = j-EUR-PHYS-J-B,
volume = "20",
number = "4",
pages = "601--607",
month = apr,
year = "2001",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1007/PL00011114",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Thu Feb 28 10:26:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/PL00011114",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
keywords = "power law; scale invariance; Zipf's law",
}
@MastersThesis{Jamain:2001:BL,
author = "Adrien Jamain",
title = "{Benford's Law}",
type = "{Master}'s thesis",
school = "Department of Mathematics, Imperial College of London
and ENSIMAG",
address = "London, UK",
pages = "????",
year = "2001",
bibdate = "Sat Feb 16 18:06:41 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Not found in Imperial College Library or COPAC
catalogs on 16 February 2013. URL link is broken too.",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Jansen:2001:RNP,
author = "C. J. M. Jansen and M. M. W. Pollmann",
title = "On Round Numbers: Pragmatic Aspects of Numerical
Expressions",
journal = j-J-QUANT-LINGUISTICS,
volume = "8",
number = "3",
pages = "187--201",
month = "????",
year = "2001",
DOI = "https://doi.org/10.1076/jqul.8.3.187.4095",
ISSN = "0929-6174 (print), 1744-5035 (electronic)",
ISSN-L = "0929-6174",
bibdate = "Sat Jan 07 09:51:05 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
abstract = "This paper describes and explains some regularities in
the frequency of numbers in text. An analysis of number
frequencies in text corpora in Dutch, English, German,
and French confirms the expectation that frequency is
highly dependent on two factors: magnitude and
roundness. Roundness (defined as number frequency in an
approximation context) proves to be related to three
arithmetical properties: `10-ness', `2-ness', and
`5-ness'. In predicting the frequency of numbers
irrespective of their context `$ 2 1 / 2 $-ness' should
be added to these factors, as is suggested in the work
of Sigurd (1988). The role of the four number
characteristics found in this study can be explained by
the preference of the language user for using base
numbers, and for doubling and halving quantities.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
onlinedate = "09 Aug 2010",
}
@Article{Jolion:2001:IBL,
author = "Jean-Michel Jolion",
title = "Images and {Benford}'s law",
journal = j-J-MATH-IMAG-VIS,
volume = "14",
number = "1",
pages = "73--81",
year = "2001",
CODEN = "JMIVEK",
DOI = "https://doi.org/10.1023/A:1008363415314",
ISSN = "0924-9907 (print), 1573-7683 (electronic)",
ISSN-L = "0924-9907",
MRclass = "94A08 (68U10)",
MRnumber = "1818436 (2001m:94007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comments and extensions in \cite[Chapter
19]{Miller:2015:BLT}.",
URL = "http://link.springer.com/article/10.1023/A%3A1008363415314",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Imaging and Vision: JMIV",
}
@Article{Knudsen:2001:ZLC,
author = "Thorbj{\o}rn Knudsen",
title = "{Zipf}'s law for cities and beyond: the case of
{Denmark}",
journal = j-AM-J-ECON-SOCIOL,
volume = "60",
number = "1",
pages = "123--146",
month = jan,
year = "2001",
CODEN = "AJESA3",
DOI = "https://doi.org/10.1111/1536-7150.00057",
ISSN = "0002-9246 (print), 1536-7150 (electronic)",
ISSN-L = "0002-9246",
bibdate = "Sat Feb 16 18:14:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3487947",
acknowledgement = ack-nhfb,
fjournal = "The American Journal of Economics and Sociology",
}
@Article{Kretschmer:2001:RAI,
author = "Hildrun Kretschmer and Ronald Rousseau",
title = "Research: Author inflation leads to a breakdown of
{Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "52",
number = "8",
pages = "610--614",
month = "????",
year = "2001",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.1118",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:41:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "27 Apr 2001",
}
@Article{Levene:2001:ZLW,
author = "Mark Levene and Jos{\'e} Borges and George Loizou",
title = "{Zipf}'s law for {Web} surfers",
journal = j-KNOWL-INFO-SYS,
volume = "3",
number = "1",
pages = "120--129",
year = "2001",
CODEN = "KISNCR",
DOI = "https://doi.org/10.1007/PL00011657",
ISSN = "0219-1377",
bibdate = "Sat Nov 12 11:00:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "0991.68622",
abstract = "One of the main activities of Web users, known as
`surfing', is to follow links. Lengthy navigation often
leads to disorientation when users lose track of the
context in which they are navigating and are unsure how
to proceed in terms of the goal of their original
query. Studying navigation patterns of Web users is
thus important, since it can lead us to a better
understanding of the problems users face when they are
surfing. We derive Zipf's rank frequency law (i.e., an
inverse power law) from an absorbing Markov chain model
of surfers' behavior assuming that less probable
navigation trails are, on average, longer than more
probable ones. In our model the probability of a trail
is interpreted as the relevance (or `value') of the
trail. We apply our model to two scenarios: in the
first the probability of a user terminating the
navigation session is independent of the number of
links he has followed so far, and in the second the
probability of a user terminating the navigation
session increases by a constant each time the user
follows a link. We analyze these scenarios using two
sets of experimental data sets showing that, although
the first scenario is only a rough approximation of
surfers' behavior, the data is consistent with the
second scenario and can thus provide an explanation of
surfers' behavior.",
acknowledgement = ack-nhfb,
classmath = "68U99 (Computing methodologies) 68P15 (Database
theory) 68P20 (Information storage and retrieval)",
fjournal = "Knowledge and Information Systems",
keywords = "Markov chain; Web navigation; Zipf's law",
}
@Article{Losee:2001:TDB,
author = "Robert M. Losee",
title = "Term dependence: a basis for {Luhn} and {Zipf}
models",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "52",
number = "12",
pages = "1019--1025",
year = "2001",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.1155",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}
@Article{Malacarne:2001:QED,
author = "L. C. Malacarne and R. S. Mendes and E. K. Lenzi",
title = "$q$-exponential distribution in urban agglomeration",
journal = j-PHYS-REV-E,
volume = "65",
number = "??",
pages = "017106",
day = "21",
month = dec,
year = "2001",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.65.017106",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.65.017106",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf--Mandelbrot law",
}
@Article{Montemurro:2001:BZM,
author = "Marcelo A. Montemurro",
title = "Beyond the {Zipf--Mandelbrot} law in quantitative
linguistics",
journal = j-PHYSICA-A,
volume = "300",
number = "3--4",
pages = "567--578",
day = "15",
month = nov,
year = "2001",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(01)00355-7",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437101003557",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@PhdThesis{Morters:2001:BGV,
author = "Peter M{\"o}rters",
title = "{Benford's Gesetz {\"u}ber die Verteilung der
Ziffern}. (German) [{Benford}'s law on the distribution
of digits]",
type = "{Habilitationsvorlesung}",
school = "????",
address = "Kaiserslauten, Germany, and Bath, UK",
pages = "4",
month = "????",
year = "2001",
bibdate = "Sat Feb 16 18:47:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://people.bath.ac.uk/maspm/benford.ps",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Nigrini:2001:DAU,
author = "Mark Nigrini",
title = "Digital Analysis Using {Benford's} Law: Tests and
Statistics for Auditors",
journal = j-EDPACS,
volume = "28",
number = "9",
pages = "1--2",
month = "????",
year = "2001",
CODEN = "EDPCDF",
DOI = "https://doi.org/10.1201/1079/43266.28.9.20010301/30389.4",
ISSN = "0736-6981 (print), 1936-1009 (electronic)",
ISSN-L = "0736-6981",
bibdate = "Sat Jan 07 09:08:09 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4",
acknowledgement = ack-nhfb,
fjournal = "EDPACS",
onlinedate = "21 Dec 2006",
}
@Article{Pietronero:2001:EUD,
author = "L. Pietronero and E. Tosatti and V. Tosatti and A.
Vespignani",
title = "Explaining the uneven distribution of numbers in
nature: the laws of {Benford} and {Zipf}",
journal = j-PHYSICA-A,
volume = "293",
number = "1--2",
pages = "297--304",
day = "1",
month = apr,
year = "2001",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(00)00633-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2001PhyA..293..297P;
http://www.sciencedirect.com/science/article/pii/S0378437100006336",
abstract = "The distribution of first digits in numbers series
obtained from very different origins shows a marked
asymmetry in favor of small digits that goes under the
name of Benford's law. We analyze in detail this
property for different data sets and give a general
explanation for the origin of the Benford's law in
terms of multiplicative processes. We show that this
law can be also generalized to series of numbers
generated from more complex systems like the catalogs
of seismic activity. Finally, we derive a relation
between the generalized Benford's law and the popular
Zipf's law which characterize the rank order statistics
and has been extensively applied to many problems
ranging from city population to linguistics.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Reed:2001:PZO,
author = "William J. Reed",
title = "The {Pareto}, {Zipf} and other power laws",
journal = j-ECONOM-LETT,
volume = "74",
number = "1",
pages = "15--19",
day = "20",
month = dec,
year = "2001",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/S0165-1765(01)00524-9",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176501005249",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@TechReport{Scott:2001:BLE,
author = "P. D. Scott and M. Fasli",
title = "{Benford's Law}: An Empirical Investigation and a
Novel Explanation",
type = "CSM Technical Report",
number = "349",
institution = "Department of Computer Science, University Essex",
address = "Colchester, UK",
day = "26",
month = oct,
year = "2001",
bibdate = "Tue Nov 22 21:05:22 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf",
acknowledgement = ack-nhfb,
}
@Article{Sellke:2001:CVT,
author = "Thomas Sellke and M. J. Bayarri and James O. Berger",
title = "Calibration of $p$ Values for Testing Precise Null
Hypotheses",
journal = j-AMER-STAT,
volume = "55",
number = "1",
pages = "62--71",
month = feb,
year = "2001",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/000313001300339950",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 18:16:34 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326511;
https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/publications/tas/Sellke.htm;
http://www.jstor.org/stable/2685531;
http://www.tandfonline.com/doi/abs/10.1198/000313001300339950",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Snyder:2001:SAO,
author = "Mark A. Snyder and James H. Curry and Anne M.
Dougherty",
title = "Stochastic aspects of one-dimensional discrete
dynamical systems: {Benford}'s law",
journal = j-PHYS-REV-E,
volume = "64",
number = "2",
pages = "026222:1--026222:5",
month = aug,
year = "2001",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.64.026222",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Mon Nov 14 17:44:15 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S;
http://pre.aps.org/abstract/PRE/v64/i2/e026222",
abstract = "Benford's law owes its discovery to the ``Grubby Pages
Hypothesis,'' a 19th century observation made by Simon
Newcomb that the beginning pages of logarithm books
were grubbier than the last few pages, implying that
scientists referenced the values toward the front of
the books more frequently. If a data set satisfies
Benford's law, then its significant digits will have a
logarithmic distribution, which favors smaller
significant digits. In this article we demonstrate two
ways of creating discrete one-dimensional dynamical
systems that satisfy Benford's law. We also develop a
numerical simulation methodology that we use to study
dynamical systems when analytical results are not
readily available.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
pagecount = "5",
}
@InCollection{Solomon:2001:SPZ,
author = "Sorin Solomon and Peter Richmond",
booktitle = "Economics with heterogeneous interacting agents
({Marseille}, 2000)",
title = "Stability of {Pareto--Zipf} law in non-stationary
economies",
volume = "503",
publisher = pub-SV,
address = pub-SV:adr,
pages = "141--159",
year = "2001",
MRclass = "91B28 (91B62)",
MRnumber = "1838925",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Econom. and Math. Systems",
acknowledgement = ack-nhfb,
}
@Article{Zanette:2001:VTC,
author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
title = "Vertical transmission of culture and the distribution
of family names",
journal = j-PHYSICA-A,
volume = "295",
number = "1--2",
pages = "1--8",
day = "1",
month = jun,
year = "2001",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(01)00046-2",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:03:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437101000462",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Abe:2002:STE,
author = "Sumiyoshi Abe",
title = "Stability of {Tsallis} entropy and instabilities of
{R{\'e}nyi} and normalized {Tsallis} entropies: a basis
for $q$-exponential distributions",
journal = j-PHYS-REV-E,
volume = "66",
number = "??",
pages = "046134",
day = "24",
month = oct,
year = "2002",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.66.046134",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.046134",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Anonymous:2002:ZLM,
author = "Anonymous",
title = "{Zipf}'s law and maximum sustainable growth",
journal = j-STAT-PROB-LETT,
volume = "56",
number = "2",
pages = "??--??",
day = "15",
month = jan,
year = "2002",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.jedc.2013.02.004",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165188913000341",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Zipf's Law",
onlinedate = "19 February 2013",
}
@InProceedings{Bhattacharya:2002:KBT,
author = "S. Bhattacharya",
editor = "????",
booktitle = "9th World Congress of Accounting Historians, Deakin
University, Melbourne, Australia July 30--August 3,
2002",
title = "From {Kautilya} to {Benford} --- Trends in Forensic
and Investigative Accounting",
publisher = "Accounting Association of Australia and New Zealand",
address = "????",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:22:29 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://ach.sagepub.com/",
remark = "I cannot find the published proceedings in online
catalogs or bookstores, or in the Deakin University
library catalogs. Where only selected papers published
from the conference in the journal Accounting
History??",
review-doi = "https://doi.org/10.1177/103237320200700207",
review-url = "http://dro.deakin.edu.au/view/DU:30012663;
http://www.highbeam.com/doc/1G1-97484707.html",
}
@Article{Bolton:2002:SFD,
author = "Richard J. Bolton and David J. Hand",
title = "Statistical Fraud Detection: A Review",
journal = j-STAT-SCI,
volume = "17",
number = "3",
pages = "235--255",
month = aug,
year = "2002",
CODEN = "STSCEP",
ISSN = "0883-4237 (print), 2168-8745 (electronic)",
ISSN-L = "0883-4237",
bibdate = "Fri May 30 12:48:50 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statsci.bib",
URL = "http://projecteuclid.org/euclid.ss/1042727940",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
}
@Article{Brown:2002:ICF,
author = "Philip Brown and Angeline Chua and Jason Mitchell",
title = "The influence of cultural factors on price clustering:
Evidence from {Asia Pacific} stock markets",
journal = "Pacific-Basin Finance Journal",
volume = "10",
number = "3",
pages = "307--332",
year = "2002",
DOI = "https://doi.org/10.1016/S0927-538X(02)00049-5",
ISSN = "0927-538X (print), 1879-0585 (electronic)",
ISSN-L = "0927-538X",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "13th Annual PACAP/FMA Finance Conference",
URL = "http://www.sciencedirect.com/science/article/pii/S0927538X02000495",
abstract = "Price clustering is the tendency of prices to be
observed more frequently at some numbers than others.
It increases with haziness, or imprecision, about
underlying value. Most research on price clustering has
been conducted in Western financial markets, where
there is manifest preference for trading at round
numbers. We focus on number preferences under Chinese
culture. Many Chinese believe some numbers are unlucky
and to be avoided. For instance, the number 4 is
inauspicious because the Cantonese pronunciation of 4
is similar to the phrase to die. We first document
clustering of daily closing prices on six Asia Pacific
stock markets, three with predominantly Chinese
populations. Next, we fit binomial logit models within
these markets to estimate the association between
structural and economic factors, and culture, on price
clustering. We find some support for the influence of
Chinese culture and superstition on year-round number
preferences of traders, but it is located solely in the
Hong Kong market. Furthermore, in the Hong Kong market
Chinese culture and superstition help explain the
increased avoidance of the number 4 during the
auspicious Chinese New Year, Dragon Boat and Mid-Autumn
festivals.",
acknowledgement = ack-nhfb,
keywords = "Attraction; Benford's Law; Haziness; Negotiation;
Price clustering",
}
@TechReport{Diekmann:2002:DFM,
author = "Andreas Diekmann",
title = "{Diagnose von Fehlerquellen und methodische
Qualit{\"a}t in der sozialwissenschaftlichen
Forschung}. ({German}) [{Diagnosis} of errors and
methodological quality in social science research]",
type = "Report",
number = "ITA-02-04",
institution = "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
address = "Vienna, Austria",
pages = "????",
year = "2002",
bibdate = "Thu Nov 17 19:11:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Egghe:2002:DRC,
author = "L. Egghe and I. K. Ravichandra Rao",
title = "Duality revisited: {Construction} of fractional
frequency distributions based on two dual {Lotka}
laws",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "53",
number = "10",
pages = "789--801",
month = "????",
year = "2002",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.10103",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:41:59 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "11 Jun 2002",
}
@Article{FerreriCancho:2002:ZLR,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "{Zipf}'s law and random texts",
journal = j-ADV-COMPLEX-SYST,
volume = "5",
number = "1",
pages = "1--6",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1142/S0219525902000468",
ISSN = "0219-5259",
bibdate = "Sat Nov 12 11:00:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1090.91595",
abstract = "Random-text models have been proposed as an
explanation for the power law relationship between word
frequency and rank, the so-called Zipf's law. They are
generally regarded as null hypotheses rather than
models in the strict sense. In this context, recent
theories of language emergence and evolution assume
this law as a priori information with no need of
explanation. Here, random texts and real texts are
compared through (a) the so-called lexical spectrum and
(b) the distribution of words having the same length.
It is shown that real texts fill the lexical spectrum
much more efficiently and regardless of the word
length, suggesting that the meaningfulness of Zipf's
law is high.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics)",
fjournal = "Advances in Complex Systems",
journal-URL = "http://www.worldscinet.com/acs/acs.shtml",
keywords = "Human language; monkey languages; random texts;
scaling; Zipf's law",
}
@Article{Gottwald:2002:NBL,
author = "Georg A. Gottwald and Matthew Nicol",
title = "On the nature of {Benford's Law}",
journal = j-PHYSICA-A,
volume = "303",
number = "3--4",
pages = "387--396",
day = "15",
month = jan,
year = "2002",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(01)00497-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "60C05 (28D05 60E05 82B05)",
MRnumber = "1917635 (2003d:60015)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
http://www.sciencedirect.com/science/article/pii/S0378437101004976",
abstract = "We study multiplicative and affine sequences of real
numbers defined by $ N(j + 1) = \zeta (j) N(j) + \eta
(j) $, where \{\zeta(j)\} and \{\eta(j)\} are sequences
of positive real numbers (in the multiplicative case $
\eta (j) = 0 $ for all $j$). We investigate the
conditions under which the leading digits $k$ of
\{N(j)\} have the following probability distribution,
known as Benford's Law, $ P(k) = \log_{10}((k + 1) /
k)$. We present two main results. First, we show that
contrary to the usual assumption in the literature,
\{\zeta(j)\} does not necessarily need to come from a
chaotic or independent random process for Benford's Law
to hold. The multiplicative driving force may be a
deterministic quasiperiodic or even periodic forcing.
Second, we give conditions under which the distribution
of the first digits of an affine process displays
Benford's Law. Our proofs use techniques from ergodic
theory.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Law of Anomalous Numbers;
Multiplicative process; Scaling laws; Zipf's Law",
}
@Article{Hasan:2002:ADA,
author = "Bassam Hasan",
title = "Assessing data authenticity with {Benford}'s law",
journal = "Information Systems Control Journal",
volume = "6",
pages = "??--??",
year = "2002",
CODEN = "ISYJFS",
ISSN = "1526-7407",
bibdate = "Sat Feb 16 17:45:21 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx",
acknowledgement = ack-nhfb,
journal-URL = "http://www.isaca.org/",
remark = "Journal publication ceased at volume 6 in 2008,
according to one library catalog, but volumes up to
2013 are available at journal Web site.",
}
@InProceedings{Hill:2002:RAB,
author = "T. P. Hill",
editor = "????",
booktitle = "Conference, Leiden University",
title = "Recent applications of {Benford}'s law",
publisher = "????",
address = "????",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:55:46 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hoyle01042002,
author = "David C. Hoyle and Magnus Rattray and Ray Jupp and
Andrew Brass",
title = "Making sense of microarray data distributions",
journal = j-BIOINFORMATICS,
volume = "18",
number = "4",
pages = "576--584",
year = "2002",
DOI = "https://doi.org/10.1093/bioinformatics/18.4.576",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bioinformatics.oxfordjournals.org/content/18/4/576.abstract",
abstract = "Motivation: Typical analysis of microarray data has
focused on spot by spot comparisons within a single
organism. Less analysis has been done on the comparison
of the entire distribution of spot intensities between
experiments and between organisms.Results: Here we show
that mRNA transcription data from a wide range of
organisms and measured with a range of experimental
platforms show close agreement with Benford's law
(Benford, Proc. Am. Phil. Soc., 78, 551 572, 1938) and
Zipf's law (Zipf, The Psycho-biology of Language: an
Introduction to Dynamic Philology, 1936 and Human
Behaviour and the Principle of Least Effort, 1949). The
distribution of the bulk of microarray spot intensities
is well approximated by a log-normal with the tail of
the distribution being closer to power law. The
variance, 2, of log spot intensity shows a positive
correlation with genome size (in terms of number of
genes) and is therefore relatively fixed within some
range for a given organism. The measured value of 2 can
be significantly smaller than the expected value if the
mRNA is extracted from a sample of mixed cell types.
Our research demonstrates that useful biological
findings may result from analyzing microarray data at
the level of entire intensity distributions. Contact:
david.c.hoyle@man.ac.uk",
acknowledgement = ack-nhfb,
fjournal = "Bioinformatics",
journal-URL = "http://bioinformatics.oxfordjournals.org/",
keywords = "Zipf's Law",
}
@Article{Hoyle:2002:MSM,
author = "David C. Hoyle and Magnus Rattray and Ray Jupp and
Andrew Brass",
title = "Making sense of microarray data distributions",
journal = j-BIOINFORMATICS,
volume = "18",
number = "4",
pages = "576--584",
month = apr,
year = "2002",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Fri Nov 25 11:16:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bioinformatics",
journal-URL = "http://bioinformatics.oxfordjournals.org/",
keywords = "Benford's Law; mRNA transcription data",
}
@Article{Huber:2002:NMG,
author = "John C. Huber",
title = "A new model that generates {Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "53",
number = "3",
pages = "209--219",
month = "????",
year = "2002",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.10025",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:02 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "28 Dec 2001",
}
@Article{Jones:2002:LDR,
author = "B. K. Jones",
title = "Logarithmic distributions in reliability analysis",
journal = j-MICROELECT-RELIABILITY,
volume = "42",
number = "4--5",
pages = "779--786",
month = apr # "\slash " # may,
year = "2002",
CODEN = "MCRLAS",
DOI = "https://doi.org/10.1016/S0026-2714(02)00031-8",
ISSN = "0026-2714 (print), 1872-941X (electronic)",
ISSN-L = "0026-2714",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
abstract = "Real-life systems are complex, with many independent
parameters which can affect the system. Their behaviour
can therefore be very variable. This is especially true
of the more involved processes which occur in
reliability and degradation processes. However, there
are some characteristics which are observed which can
be understood simply because they are characteristic of
complex systems. These include distributions that are
very often logarithmic rather than uniform, log normal
failure distributions and $ 1 g / f $ noise. A wide
variety of diverse examples is given to illustrate the
common occurrence of such observations together with
the underlying unifying themes. There are several basic
reasons for the origin of logarithmic distributions.
One is that they arise from multiplicative processes.
Another is that although basic science is often
introduced as linear, with non-linear effects added as
a correction, complex systems are often inherently
non-linear. This produces multiplicative effects, such
as harmonic generation and fractal behaviour.",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics and Reliability",
keywords = "Benford's Law; Pareto distribution; Zipf's Law",
}
@Article{Kawamura:2002:UZL,
author = "Kenji Kawamura and Naomichi Hatano",
title = "Universality of {Zipf}'s law",
journal = j-J-PHYS-SOC-JAP,
volume = "71",
number = "5",
pages = "1211--1213",
year = "2002",
CODEN = "JUPSAU",
DOI = "https://doi.org/10.1143/JPSJ.71.1211",
ISSN = "0031-9015 (print), 1347-4073 (electronic)",
ISSN-L = "0031-9015",
bibdate = "Sat Nov 12 11:00:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jpsj.ipap.jp/",
ZMnumber = "1063.60114",
abstract = "The aim of the present paper is to propose and
simulate a simple and generic model that reproduces
Zipf's law. In the proposed model, the time evolution
is considered to be a random walk in the logarithmic
scale reflecting the company asset distribution and/or
the evolution of city populations (e.g. Zipf's law for
income distribution asserts that the size and number of
companies are in inverse proportional relationship).
The paper explains theoretically and shows by numerical
simulation that the introduced model of Zipf's law has
a very robust behaviour when applied to various natural
and social phenomena. The authors do not investigate
the famous case of Zipf's law application to the
frequency of English words, but they speculate that
this case might be also explained within the same time
development of the proposed model.",
acknowledgement = ack-nhfb,
classmath = "60J60 (Diffusion processes) 60J70 (Appl. of diffusion
theory) 76R50 (Diffusion) 82C24 (Interface problems
(dynamic and non-equilibrium))",
fjournal = "Journal of the Physical Society of Japan",
keywords = "city population evolution; company asset distribution;
diffusion; generic model of Zipf's law; natural and
social phenomena; random walk in logarithmic scale",
ZMreviewer = "Neculai Curteanu (Ia\c si)",
}
@TechReport{Kreiner:2002:FDL,
author = "W. A. Kreiner",
title = "First digit law",
type = "Preprint",
institution = "Abteilung Chemische Physik, Arbeitsgruppe
Laseranwendungen, Universit{\"a}t Ulm",
address = "Ulm, Germany",
pages = "7",
day = "3",
month = may,
year = "2002",
bibdate = "Sat Feb 16 18:18:49 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; First Digit Law; Newcomb; Statistisches
Fraktal",
language = "German",
}
@Article{Li:2002:ZLI,
author = "Wentian Li and Yaning Yang",
title = "{Zipf's Law} in Importance of Genes for Cancer
Classification Using Microarray Data",
journal = j-J-THEOR-BIOL,
volume = "219",
number = "4",
pages = "539--551",
day = "21",
month = dec,
year = "2002",
CODEN = "JTBIAP",
DOI = "https://doi.org/10.1006/jtbi.2002.3145",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
MRclass = "92C40 (92D10)",
MRnumber = "2044066",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022519302931450",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@Book{Livio:2002:GRS,
author = "Mario Livio",
title = "The Golden Ratio: the Story of Phi, the World's Most
Astonishing Number",
publisher = "Broadway Books",
address = "New York, NY, USA",
pages = "viii + 294",
year = "2002",
ISBN = "0-7679-0815-5",
ISBN-13 = "978-0-7679-0815-3",
LCCN = "QA466 .L58 2002",
bibdate = "Tue Jul 08 12:29:44 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is treated on pages 231--237.",
price = "US\$24.95, CAN\$37.95",
abstract = "Throughout history, thinkers from mathematicians to
theologians have pondered the mysterious relationship
between numbers and the nature of reality. In this
fascinating book, the author tells the tale of a number
at the heart of that mystery: phi, or
1.6180339887\ldots{}. This curious mathematical
relationship, widely known as ``The Golden Ratio,'' was
discovered by Euclid more than two thousand years ago
because of its crucial role in the construction of the
pentagram, to which magical properties had been
attributed. Since then it has shown a propensity to
appear in the most astonishing variety of places, from
mollusk shells, sunflower florets, and rose petals to
the shape of the galaxy. Psychological studies have
investigated whether the Golden Ratio is the most
aesthetically pleasing proportion extant, and it has
been asserted that the creators of the Pyramids and the
Parthenon employed it. It is believed to feature in
works of art from Leonardo da Vinci's Mona Lisa to
Salvador Dali's The Sacrament of the Last Supper, and
poets and composers have used it in their works. It has
even been found to be connected to the behavior of the
stock market! This book is a captivating journey
through art and architecture, botany and biology,
physics and mathematics. It tells the human story of
numerous phi-fixated individuals, including the
followers of Pythagoras who believed that this
proportion revealed the hand of God; astronomer
Johannes Kepler, who saw phi as the greatest treasure
of geometry; such Renaissance thinkers as mathematician
Leonardo Fibonacci of Pisa; and such masters of the
modern world as Goethe, Cezanne, Bartok, and physicist
Roger Penrose. Wherever his quest for the meaning of
phi takes him, the author reveals the world as a place
where order, beauty, and eternal mystery will always
coexist.",
acknowledgement = ack-nhfb,
tableofcontents = "Prelude to a number \\
The pitch and the pentagram \\
Under a star-Y-pointing pyramid? \\
The second treasure \\
Son of good nature \\
The divine proportion \\
Painters and poets have equal license \\
From the tiles to the heavens \\
Is God a mathematician?",
}
@InProceedings{Manaris:2002:PTR,
author = "B. Manaris and T. Purewal and C. McCormick",
editor = "{IEEE}",
booktitle = "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002,
Embassy Suites Hotel, Columbia, South Carolina, USA",
title = "Progress Towards Recognizing and Classifying Beautiful
Music with Computers: {MIDI}-Encoded Music and the
{Zipf-Mandelbrot Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xviii + 482",
pages = "52--57",
year = "2002",
DOI = "https://doi.org/10.1109/.2002.995557",
ISBN = "0-7803-7252-2",
ISBN-13 = "978-0-7803-7252-8",
LCCN = "TK7801 .I56 2002",
bibdate = "Mon Feb 18 10:40:27 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
acknowledgement = ack-nhfb,
}
@Article{Mochty:2002:AMI,
author = "L. Mochty",
title = "{Die Aufdeckung von Manipulationen im Rechnungswesen
--- Was leistet das Benford's Law?}. ({German}) [{The}
disclosure of accounting manipulations --- what does
{Benford's Law} mean?]",
journal = "Die Wirtschaftspr{\"u}fung",
volume = "14",
number = "??",
pages = "725--736",
month = "????",
year = "2002",
CODEN = "????",
ISSN = "0043-6313",
ISSN-L = "0043-6313",
bibdate = "Thu Nov 17 19:20:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Mosimann:2002:TDE,
author = "James Mosimann and John Dahlberg and Nancy Davidian
and John Krueger",
title = "Terminal Digits and the Examination of Questioned
Data",
journal = j-ACCOUNT-RES,
volume = "9",
number = "2",
pages = "75--92",
month = "????",
year = "2002",
CODEN = "ARQAEZ",
DOI = "https://doi.org/10.1080/08989620212969",
ISSN = "0898-9621 (print), 1545-5815 (electronic)",
ISSN-L = "0898-9621",
bibdate = "Sat Sep 10 15:08:21 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/08989620212969",
acknowledgement = ack-nhfb,
fjournal = "Accountability in Research",
journal-URL = "http://www.tandfonline.com/toc/gacr20",
keywords = "Benford's Law",
}
@Book{Newman:2002:ME,
author = "M. E. J. (Mark E. J.) Newman and Richard G. Palmer",
title = "Modeling extinction",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xii + 102",
year = "2002",
ISBN = "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)",
ISBN-13 = "978-0-19-515946-2 (paperback), 978-0-19-515945-5
(hardcover)",
LCCN = "QH78 .N48 2002",
bibdate = "Thu Feb 28 10:36:25 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Santa Fe Institute studies in the sciences of
complexity",
acknowledgement = ack-nhfb,
keywords = "power law; Zipf's law",
subject = "Extinction (Biology); Statistical methods;
Mathematical models",
}
@Misc{Popescu:2002:LNZ,
author = "Ioan-Iovitz Popescu",
title = "On the {Lavelette}'s nonlinear {Zipf}'s law",
howpublished = "Web preprint.",
month = feb,
year = "2002",
bibdate = "Sat Feb 16 19:02:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html",
acknowledgement = ack-nhfb,
}
@Article{Reed:2002:GFG,
author = "William J. Reed and Barry D. Hughes",
title = "From gene families and genera to incomes and
{Internet} file sizes: Why power laws are so common in
nature",
journal = j-PHYS-REV-E,
volume = "66",
number = "6",
pages = "067103",
month = dec,
year = "2002",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.66.067103",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Wed Feb 27 06:58:05 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.067103",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Pareto's Law; rank-size property; Zipf's Law",
pagecount = "4",
}
@Article{Sandon:2002:DPC,
author = "F. Sandon",
title = "Do Populations Conform to the Law of Anomalous
Numbers?",
journal = "Population",
volume = "57",
number = "4",
pages = "755--761",
month = "????",
year = "2002",
bibdate = "Sat Sep 10 16:15:28 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.persee.fr/doc/pop_1634-2941_2002_num_57_4_18419",
acknowledgement = ack-nhfb,
journal-URL = "http://www.persee.fr/collection/pop",
keywords = "Benford's Law",
}
@Article{Sandron:2002:DPC,
author = "Fr{\'e}d{\'e}ric Sandron",
title = "Do populations conform to the {Law of Anomalous
Numbers}?",
journal = "Population",
volume = "57",
number = "4--5",
pages = "755--761",
month = "????",
year = "2002",
CODEN = "????",
DOI = "????",
ISSN = "1169-1018",
ISSN-L = "1169-1018",
bibdate = "Sat Feb 16 19:08:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translation from French by S. R. Hayford.",
URL = "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753",
acknowledgement = ack-nhfb,
journal-URL = "http://www.jstor.org/journals/11691018.html",
}
@Article{Sandron:2002:PSE,
author = "Fr{\'e}d{\'e}ric Sandron",
title = "Les populations suivent-elles la loi des nombres
anomaux? ({French}). [{Do} populations conform to the
{Law of Anomalous Numbers}?]",
journal = "Population ({French} edition)",
volume = "57",
number = "4--5",
pages = "761--768",
month = "????",
year = "2002",
CODEN = "POPUAQ",
DOI = "????",
ISSN = "0032-4663 (print), 1957-7966 (electronic)",
ISSN-L = "0032-4663",
bibdate = "Sat Feb 16 19:08:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873",
acknowledgement = ack-nhfb,
language = "French",
}
@TechReport{Seaman:2002:BLB,
author = "R. S. Seaman",
title = "{Benford}'s law and and background field errors in
data assimilation",
type = "Preprint",
institution = "Bureau of Meteorology Research Centre",
address = "Melbourne, Australia",
month = "????",
year = "2002",
bibdate = "Sun Feb 17 14:01:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf",
acknowledgement = ack-nhfb,
}
@Article{Seaman:2002:RBL,
author = "R. S. Seaman",
title = "The relevance of {Benford's Law} to background field
errors in data assimilation",
journal = "Australian Meteorological Magazine",
volume = "51",
number = "1",
pages = "25--33",
month = "????",
year = "2002",
CODEN = "AMMGAS",
ISSN = "0004-9743",
ISSN-L = "0004-9743",
bibdate = "Mon Nov 14 16:08:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bom.gov.au/amm/docs/2002/seaman.pdf;
http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf",
acknowledgement = ack-nhfb,
ajournal = "Aust. Met. Mag.",
ajournal-2 = "Aust. Meteorol. Mag.",
fjournal = "Australian Meteorological Magazine",
journal-URL = "http://www.bom.gov.au/amm/",
}
@Article{Taylor:2002:STD,
author = "Rosemary N. Taylor and Damian J. McEntegart and
Eleanor C. Stillman",
title = "Statistical techniques to detect fraud and other data
irregularities in clinical questionnaire data",
journal = "Drug Information Journal",
volume = "36",
number = "1",
pages = "115--125",
month = jan,
year = "2002",
DOI = "https://doi.org/10.1177/009286150203600115",
ISSN = "0092-8615",
ISSN-L = "0092-8615",
bibdate = "Mon Feb 18 06:42:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{VanCaneghem:2002:EMI,
author = "T. {Van Caneghem}",
title = "Earnings Management Induced by Cognitive Reference
Points",
journal = "The British Accounting Review",
volume = "34",
number = "2",
pages = "167--178",
year = "2002",
DOI = "https://doi.org/10.1006/bare.2002.0190",
ISSN = "0890-8389 (print), 1095-8347 (electronic)",
ISSN-L = "0890-8389",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0890838902901903",
abstract = "Previous studies (Carslaw, 1988; Thomas, 1989;
Niskanen \& Keloharju, 2000) have shown that companies'
managers tend to round-up the first digits of reported
earnings (i.e. for companies reporting profits).
According to Carslaw (1988), this type of behaviour is
inspired by the existence of the so-called `\$1.99'
phenomenon where a price of \$1.99 is perceived as
being abnormally lower than one of \$2.00. In the
current study, we try to determine whether managers of
UK-listed companies also engage in this type of
`earnings rounding-up behaviour'. Analogous to the
earlier studies, our study compares observed and
expected frequencies for the second-from-the-left digit
in reported earnings. Our results suggest that managers
of UK-listed companies tend to round-up reported
pre-tax income, in a way that increases the first digit
by one, when they are faced with a nine in the
second-from-the-left position for this particular
earnings measure. The major contribution of the current
study is that it introduces discretionary accruals in
this line of research. Discretionary accruals were
estimated using both the Jones model (1991) and the
modified Jones model as proposed by Dechow et al.
(1995). Our results clearly suggest that discretionary
accruals are used in order to round-up reported
earnings figures. Moreover, discretionary accruals
enabled us to increase the power of the tests used in
previous studies.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Wallace:2002:AQD,
author = "W. A. Wallace",
title = "Assessing the quality of data used for benchmarking
and decision making",
journal = "Journal of Government Financial Management",
volume = "51",
number = "3",
pages = "16--22",
month = "????",
year = "2002",
DOI = "",
ISSN = "1533-1385",
ISSN-L = "1533-1385",
bibdate = "Thu Oct 13 09:17:04 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
journal-URL = "https://www.agacgfm.org/Resources/Journal-of-Government-Financial-Management/Archives.aspx",
keywords = "Benford's Law",
remark = "Online archive access, even for journal metadata,
requires member account!",
}
@Article{Yeh:2002:SMZ,
author = "Hsiaw-Chan Yeh",
title = "Six multivariate {Zipf} distributions and their
related properties",
journal = j-STAT-PROB-LETT,
volume = "56",
number = "2",
pages = "131--141",
day = "15",
month = jan,
year = "2002",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/S0167-7152(01)00149-3",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "62H10",
MRnumber = "1881166 (2002m:62084)",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715201001493",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Zipf's Law",
}
@Article{Abdel-All:2003:GPP,
author = "N. H. Abdel-All and M. A. W. Mahmoud and H. N.
Abd-Ellah",
title = "Geometrical properties of {Pareto} distribution",
journal = j-APPL-MATH-COMP,
volume = "145",
number = "2--3",
pages = "321--339",
day = "25",
month = dec,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:41:12 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Alvarez-Ramirez:2003:ZMS,
author = "Jose Alvarez-Ramirez and Monica Meraz and Gustavo
Gallegos",
title = "{Zipf--Mandelbrot} scaling law for world track
records",
journal = j-PHYSICA-A,
volume = "328",
number = "3--4",
pages = "545--560",
day = "15",
month = oct,
year = "2003",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(03)00579-X",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843710300579X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Book{Anastasi:2003:NFI,
author = "Joe Anastasi",
title = "The new forensics: investigating corporate fraud and
the theft of intellectual property",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 270",
year = "2003",
ISBN = "0-471-26994-8 (hardcover)",
ISBN-13 = "978-0-471-26994-6 (hardcover)",
LCCN = "HV8079.W47 A5 2003",
bibdate = "Tue Nov 22 11:42:36 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
http://www.loc.gov/catdir/description/wiley037/2003001697.html;
http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
acknowledgement = ack-nhfb,
remark = "Brief mention of Benford's Law on pp. 184--185.",
subject = "white collar crime investigation; data processing;
case studies; fraud investigation; forensic accounting;
computer security",
}
@Article{Ausloos:2003:SIZ,
author = "M. Ausloos and Ph. Bronlet",
title = "Strategy for investments from {Zipf} law(s)",
journal = j-PHYSICA-A,
volume = "324",
number = "1--2",
pages = "30--37",
day = "1",
month = jun,
year = "2003",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(02)01845-9",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B82",
MRnumber = "2030919",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "International Econophysics Conference IEC2002 (Bali)",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437102018459",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Book{Baldi:2003:MIW,
author = "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
title = "Modeling the {Internet} and the {Web}: probabilistic
methods and algorithms",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 285",
year = "2003",
ISBN = "0-470-86492-3 (e-book), 0-470-84906-1",
ISBN-13 = "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
LCCN = "TK5105.875.I57 B35 2003eb",
bibdate = "Fri Jun 3 10:03:23 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/pagerank.bib",
acknowledgement = ack-nhfb,
subject = "Internet; Mathematical models; Telecommunication;
Traffic; World Wide Web; Cyberspace; Probabilities;
Computers; Web; General; Networking; Intranets and
Extranets",
tableofcontents = "Mathematical Background \\
Probability and Learning from a Bayesian Perspective
\\
Parameter Estimation from Data \\
Basic principles \\
A simple die example \\
Mixture Models and the Expectation Maximization
Algorithm \\
Graphical Models \\
Bayesian networks \\
Belief propagation \\
Learning directed graphical models from data \\
Classification \\
Clustering \\
Power-Law Distributions \\
Scale-free properties (80/20 rule) \\
Applications to Languages: Zipf's and Heaps' Laws \\
Origin of power-law distributions and Fermi's model \\
Basic WWW Technologies \\
Web Documents \\
SGML and HTML \\
General structure of an HTML document \\
Links \\
Resource Identifiers: URI, URL, and URN \\
Protocols \\
Reference models and TCP/IP \\
The domain name system \\
The Hypertext Transfer Protocol \\
Programming examples \\
Log Files \\
Search Engines \\
Coverage \\
Basic crawling \\
Web Graphs \\
Internet and Web Graphs \\
Power-law size \\
Power-law connectivity \\
Small-world networks \\
Power law of PageRank \\
The bow-tie structure \\
Generative Models for the Web Graph and Other Networks
\\
Web page growth \\
Lattice perturbation models: between order and disorder
\\
Preferential attachment models, or the rich get richer
\\
Copy models \\
PageRank models \\
Applications \\
Distributed search algorithms \\
Subgraph patterns and communities \\
Robustness and vulnerability \\
Notes and Additional Technical References \\
Text Analysis \\
Indexing \\
Compression techniques \\
Lexical Processing \\
Tokenization",
}
@TechReport{Berger:2003:BLP,
author = "Arno Berger",
title = "{Benford}'s law in power-like nonautonomous dynamical
systems",
type = "Preprint",
institution = "Vienna University of Technology",
address = "Vienna, Austria",
year = "2003",
bibdate = "Sat Feb 16 17:18:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Canessa:2003:TAFa,
author = "Enrique Canessa",
title = "Theory of Analogous Force on Number Sets",
journal = "ArXiv e-prints",
year = "2003",
bibdate = "Mon Nov 21 06:56:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/cond-mat/0307703",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $ p_x $ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $ p_x $ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $ f_x $ on number sets
proportional to $ (\frac {\partial p_x}{\partial x})_T
$ at an analogous system temperature $T$. In
particular, this yields to an understanding of the
uneven distribution of integers of random sets in terms
of analogous scale invariance and a screened inverse
square force acting on the significant digits. The
theory also allows to establish recursion relations to
predict sequences of Fibonacci numbers and to give an
answer to the interesting theoretical question of the
appearance of the Benford's law in Fibonacci numbers. A
possible relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
remark = "To appear in Phys. A.",
}
@Article{Canessa:2003:TAFb,
author = "Enrique Canessa",
title = "Theory of analogous force on number sets",
journal = j-PHYSICA-A,
volume = "328",
number = "1--2",
pages = "44--52",
month = oct,
year = "2003",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(03)00526-0",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $ p_x $ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $ p_x $ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $ f_x $ on number sets
proportional to $ (\partial p_x / \partial x)T $ at an
analogous system temperature $T$. In particular, this
leads to an understanding of the uneven distribution of
integers of random sets in terms of analogous scale
invariance and a screened inverse square force acting
on the significant digits. The theory also allows to
establish recursion relations to predict sequences of
Fibonacci numbers and to give an answer to the
interesting theoretical question of the appearance of
the Benford's law in Fibonacci numbers. A possible
relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Fibonacci numbers; Number theory; prime
numbers; Probability theory; Statistical physics and
thermodynamics",
}
@Article{Das:2003:RRE,
author = "Somnath Das and Huai Zhang",
title = "Rounding-up in reported {EPS}, behavioral thresholds,
and earnings management",
journal = "Journal of Accounting and Economics",
volume = "35",
number = "1",
pages = "31--50",
year = "2003",
DOI = "https://doi.org/10.1016/S0165-4101(02)00096-4",
ISSN = "0165-4101 (print), 1879-1980 (electronic)",
ISSN-L = "0165-4101",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165410102000964",
abstract = "Reported earnings per share (EPS) are frequently
rounded to the nearest cent. This paper provides
evidence that firms manipulate earnings so that they
can round-up and report one more cent of EPS.
Specifically, we examine the digit immediately right of
the decimal in the calculated {EPS} number expressed in
cents. Evidence is presented that firms are more likely
to round-up when managers ex ante expect rounding-up to
meet analysts forecasts, report positive profits, or
sustain recent performance. Further investigation
provides evidence that working capital accruals are
used to round-up EPS.",
acknowledgement = ack-nhfb,
keywords = "Behavioral threshold; Benford's Law; Earnings
management; Earnings per share (EPS); Rounding",
}
@Article{Engel:2003:BLE,
author = "Hans-Andreas Engel and Christoph Leuenberger",
title = "{Benford}'s law for exponential random variables",
journal = j-STAT-PROB-LETT,
volume = "63",
number = "4",
pages = "361--365",
day = "15",
month = jul,
year = "2003",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/S0167-7152(03)00101-9",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60E99 (60C05)",
MRnumber = "1996184 (2004d:60050)",
MRreviewer = "Ulrich M. Hirth",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
abstract = "Benford's law assigns the probability $ \log_{10}(1 +
1 / d) $ for finding a number starting with specific
significant digit $d$. We show that exponentially
distributed numbers obey this law approximatively,
i.e., within bounds of $ 0.03$.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Exponential distribution; Significant
digit law",
}
@Article{FerreriCancho:2003:LEO,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "Least effort and the origins of scaling in human
language",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "100",
number = "3",
pages = "788--791",
day = "4",
month = feb,
year = "2003",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0335980100",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue Nov 15 09:44:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
keywords = "Zipf's Law",
onlinedate = "January 22, 2003",
}
@Book{Fleiss:2003:SMR,
author = "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho
Paik",
title = "Statistical Methods for Rates and Proportions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xxvii + 760",
year = "2003",
ISBN = "0-471-52629-0 (hardcover)",
ISBN-13 = "978-0-471-52629-2 (hardcover)",
LCCN = "QA279 .F58 2003",
bibdate = "Fri Mar 22 08:46:57 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in probability and statistics",
URL = "http://www.loc.gov/catdir/bios/wiley042/2002191005.html;
http://www.loc.gov/catdir/description/wiley034/2002191005.html;
http://www.loc.gov/catdir/toc/wiley031/2002191005.html",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Analysis of variance; Sampling (Statistics);
Biometry",
tableofcontents = "Preface \\
Preface to the Second Edition \\
Preface to the First Edition \\
1. An Introduction to Applied Probability \\
2. Statistical Inference for a Single Proportion \\
3. Assessing Significance in a Fourfold Table \\
4. Determining Sample Sizes Needed to Detect a
Difference Between Two Proportions \\
5. How to Randomize \\
\\
6. Comparative Studies: Cross-Sectional, Naturalistic,
or Multinomial Sampling \\
\\
7. Comparative Studies: Prospective and Retrospective
Sampling \\
8. Randomized Controlled Trials \\
9. The Comparison of Proportions from Several
Independent Samples \\
10. Combining Evidence from Fourfold Tables \\
11. Logistic Regression \\
12. Poisson Regression \\
13. Analysis of Data from Matched Samples \\
14. Regression Models for Matched Samples \\
15. Analysis of Correlated Binary Data \\
16. Missing Data \\
17. Misclassification Errors: Effects, Control, and
Adjustment \\
18. The Measurement of Interrater Agreement \\
19. The Standardization of Rates \\
Appendix A. Numerical Tables \\
Appendix B. The Basic Theory of Maximum Likelihood",
}
@Article{Furusawa:2003:ZLG,
author = "Chikara Furusawa and Kunihiko Kaneko",
title = "{Zipf's Law} in Gene Expression",
journal = j-PHYS-REV-LET,
volume = "90",
number = "??",
pages = "088102",
day = "26",
month = feb,
year = "2003",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.90.088102",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Gabaix:2003:TPL,
author = "Xavier Gabaix and Parameswaran Gopikrishnan and
Vasiliki Plerou and H. Eugene Stanley",
title = "A theory of power-law distributions in financial
market fluctuations",
journal = j-NATURE,
volume = "423",
number = "6937",
pages = "267--270",
day = "15",
month = may,
year = "2003",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/nature01624",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Feb 27 06:45:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Zipf's Law",
}
@InProceedings{Grekos:2003:RSC,
author = "G. Grekos and R. Giuliano-Antonini",
editor = "????",
booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July
6--12, 2003}",
title = "Regular sets and conditional density: an extension of
{Benford}'s law",
publisher = "????",
address = "????",
pages = "??--??",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:43:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hassan:2003:EDA,
author = "Bassam Hassan",
title = "Examining data accuracy and authenticity with leading
digit frequency analysis",
journal = "Industrial Management + Data Systems",
volume = "103",
number = "2",
pages = "121--125",
month = "????",
year = "2003",
CODEN = "MDSD8F",
ISSN = "0263-5577 (print), 1758-5783 (electronic)",
ISSN-L = "0263-5577",
bibdate = "Fri Nov 25 11:07:59 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Havil:2003:GEE,
author = "Julian Havil",
title = "{Gamma}: Exploring {Euler}'s Constant",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xxiii + 266",
year = "2003",
ISBN = "0-691-09983-9",
ISBN-13 = "978-0-691-09983-5",
LCCN = "QA41 .H23 2003",
bibdate = "Thu Sep 25 16:52:46 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$29.95",
URL = "http://www.loc.gov/catdir/description/prin031/2002192453.html",
abstract = "Among the myriad of constants that appear in
mathematics, $ \pi $, $e$, and $i$ are the most
familiar. Following closely behind is $ \gamma $ or
gamma, a constant that arises in many mathematical
areas yet maintains a profound sense of mystery. In a
tantalizing blend of history and mathematics, Julian
Havil takes the reader on a journey through logarithms
and the harmonic series, the two defining elements of
gamma, toward the first account of gamma's place in
mathematics. Introduced by the Swiss mathematician
Leonhard Euler (1707--1783), who figures prominently in
this book, gamma is defined as the limit of the sum of
$ 1 + 1 / 2 + 1 / 3 + \cdots + 1 / n - \ln n$, the
numerical value being $ 0.5772156 \ldots {}$. But
unlike its more celebrated colleagues $ \pi $ and $e$,
the exact nature of gamma remains a mystery --- we
don't even know if it can be expressed as a fraction.
Among the numerous topics that arise during this
historical odyssey into fundamental mathematical ideas
are the Prime Number Theorem and the most important
open problem in mathematics today, the Riemann
Hypothesis (though no proof of either is offered!).
Sure to be popular with not only students and
instructors but all math aficionados, Gamma takes us
through countries, centuries, lives, and works,
unfolding along the way the stories of some remarkable
mathematics from some remarkable mathematicians.",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword / xv \\
Acknowledgements / xvii \\
Introduction / xix \\
Chapter One: The Logarithmic Cradle / 1 \\
1.1 A Mathematical Nightmare- and an Awakening / 1 \\
1.2 The Baron's Wonderful Canon / 4 \\
1.3 A Touch of Kepler / 11 \\
1.4 A Touch of Euler / 13 \\
1.5 Napier's Other Ideas / 16 \\
Chapter Two: The Harmonic Series / 21 \\
2.1 The Principle / 21 \\
2.2 Generating Function for $H_n$ / 21 \\
2.3 Three Surprising Results / 22 \\
Chapter Three: Sub-Harmonic Series / 27 \\
3.1 A Gentle Start / 27 \\
3.2 Harmonic Series of Primes / 28 \\
3.3 The Kempner Series / 31 \\
3.4 Madelung's Constants / 33 \\
Chapter Four: Zeta Functions / 37 \\
4.1 Where $n$ Is a Positive Integer / 37 \\
4.2 Where $x$ Is a Real Number / 42 \\
4.3 Two Results to End With / 44 \\
Chapter Five: Gamma's Birthplace / 47 \\
5.1 Advent / 47 \\
5.2 Birth / 49 \\
Chapter Six: The Gamma Function / 53 \\
6.1 Exotic Definitions / 53 \\
6.2 Yet Reasonable Definitions / 56 \\
6.3 Gamma Meets Gamma / 57 \\
6.4 Complement and Beauty / 58 \\
Chapter Seven: Euler's Wonderful Identity / 61 \\
7.1 The All-Important Formula / 61 \\
7.2 And a Hint of Its Usefulness / 62 \\
Chapter Eight: A Promise Fulfilled / 65 \\
Chapter Nine: What Is Gamma Exactly? / 69 \\
9.1 Gamma Exists / 69 \\
9.2 Gamma Is What Number? 739.3 A Surprisingly Good
Improvement / 75 \\
9.4 The Germ of a Great Idea / 78 \\
Chapter Ten: Gamma as a Decimal / 81 \\
10.1 Bernoulli Numbers / 81 \\
10.2 Euler--Maclaurin Summation / 85 \\
10.3 Two Examples / 86 \\
10.4 The Implications for Gamma / 88 \\
Chapter Eleven: Gamma as a Fraction / 91 \\
11.1 A Mystery / 91 \\
11.2 A Challenge / 91 \\
11.3 An Answer / 93 \\
11.4 Three Results / 95 \\
11.5 Irrationals / 95 \\
11.6 Pell's Equation Solved / 97 \\
11.7 Filling the Gaps / 98 \\
11.8 The Harmonic Alternative / 98 \\
Chapter Twelve: Where Is Gamma? / 101 \\
12.1 The Alternating Harmonic Series Revisited / 101
\\
12.2 In Analysis / 105 \\
12.3 In Number Theory / 112 \\
12.4 In Conjecture / 116 \\
12.5 In Generalization / 116 \\
Chapter Thirteen: It's a Harmonic World / 119 \\
13.1 Ways of Means / 119 \\
13.2 Geometric Harmony / 121 \\
13.3 Musical Harmony / 123 \\
13.4 Setting Records / 125 \\
13.5 Testing to Destruction / 126 \\
13.6 Crossing the Desert / 127 \\
13.7 Shuffiing Cards / 127 \\
13.8 Quicksort / 128 \\
13.9 Collecting a Complete Set / 130 \\
13.10 A Putnam Prize Question / 131 \\
13.11 Maximum Possible Overhang / 132 \\
13.12 Worm on a Band / 133 \\
13.13 Optimal Choice / 134 \\
Chapter Fourteen: It's a Logarithmic World / 139 \\
14.1 A Measure of Uncertainty / 139 \\
14.2 Benford's Law / 145 \\
14.3 Continued-Fraction Behaviour / 155 \\
Chapter Fifteen: Problems with Primes / 163 \\
15.1 Some Hard Questions about Primes / 163 \\
15.2 A Modest Start / 164 \\
15.3 A Sort of Answer / 167 \\
15.4 Picture the Problem / 169 \\
15.5 The Sieve of Eratosthenes / 171 \\
15.6 Heuristics / 172 \\
15.7 A Letter / 174 \\
15.8 The Harmonic Approximation / 179 \\
15.9 Different-and Yet the Same / 180 \\
15.10 There are Really Two Questions, Not Three / 182
\\
15.11 Enter Chebychev with Some Good Ideas / 183 \\
15.12 Enter Riemann, Followed by Proof(s) / 186 \\
Chapter Sixteen: The Riemann Initiative / 189 \\
16.1 Counting Primes the Riemann Way / 189 \\
16.2 A New Mathematical Tool / 191 \\
16.3 Analytic Continuation / 191 \\
16.4 Riemann's Extension of the Zeta Function / 193 \\
16.5 Zeta's Functional Equation / 193 \\
16.6 The Zeros of Zeta / 193 \\
16.7 The Evaluation of $\Pi(x)$ and $\pi(x)$ / 196 \\
16.8 Misleading Evidence / 197 \\
16.9 The Von Mangoldt Explicit Formula --- and How It
Is Used to Prove the Prime Number Theorem / 200 \\
16.10 The Riemann Hypothesis / 202 \\
16.11 Why Is the Riemann Hypothesis Important? / 204
\\
16.12 Real Alternatives / 206 \\
16.13 A Back Route to Immortality-Partly Closed / 207
\\
16.14 Incentives, Old and New / 210 \\
16.15 Progress / 213 \\
Appendix A: The Greek Alphabet / 217 \\
Appendix B: Big Oh Notation / 219 \\
Appendix C: Taylor Expansions / 221 \\
C.1 Degree 1 / 221 \\
C.2 Degree 2 / 221 \\
C.3 Examples / 223 \\
C.4 Convergence / 223 \\
Appendix D: Complex Function Theory / 225 \\
D.1 Complex Differentiation / 225 \\
D.2 Weierstrass Function / 230 \\
D.3 Complex Logarithms / 231 \\
D.4 Complex Integration / 232 \\
D.5 A Useful Inequality / 235 \\
D.6 The Indefinite Integral / 235 \\
D.7 The Seminal Result / 237 \\
D.8 An Astonishing Consequence / 238 \\
D.9 Taylor Expansions-and an Important Consequence /
239 \\
D.10 Laurent Expansions --- and Another Important
Consequence / 242 \\
D.11 The Calculus of Residues / 245 \\
D.12 Analytic Continuation / 247 \\
Appendix E: Application to the Zeta Function / 249 \\
E.1 Zeta Analytically Continued / 249 \\
E.2 Zeta's Functional Relationship / 253",
}
@Article{Hurlimann:2003:GBL,
author = "Werner H{\"u}rlimann",
title = "A generalized {Benford} law and its application",
journal = j-ADV-APPL-STAT,
volume = "3",
number = "3",
pages = "217--228",
year = "2003",
CODEN = "????",
ISSN = "0972-3617",
ISSN-L = "0972-3617",
MRclass = "11K31 (11B73)",
MRnumber = "2034405 (2004k:11125)",
MRreviewer = "Vydas {\v{C}}ekanavi{\v{c}}ius",
bibdate = "Wed Aug 16 07:36:50 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances and Applications in Statistics",
}
@Article{Ioannides:2003:ZLC,
author = "Yannis M. Ioannides and Henry G. Overman",
title = "{Zipf}'s law for cities: an empirical examination",
journal = j-REG-SCI-URBAN-ECON,
volume = "33",
number = "2",
pages = "127--137",
day = "1",
month = mar,
year = "2003",
CODEN = "RSUEDM",
DOI = "https://doi.org/10.1016/S0166-0462(02)00006-6",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0166046202000066",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Kreiner:2003:NBL,
author = "W. A. Kreiner",
title = "On the {Newcomb--Benford} law",
journal = j-Z-NATURFORSCH,
volume = "58a",
number = "11",
pages = "618--622",
month = "????",
year = "2003",
CODEN = "ZNTFA2",
ISSN = "0372-9516",
ISSN-L = "0372-9516",
bibdate = "Sat Feb 16 18:19:41 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Naturforschung}",
journal-URL = "http://www.degruyter.com/view/j/zna",
}
@InCollection{Kumar:2003:BLA,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
editor = "Cheng-Few Lee",
booktitle = "Advances in Financial Planning and Forecasting",
title = "{Benford}'s law and its application in financial fraud
detection",
volume = "11",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
bookpages = "ix + 177",
pages = "57--70",
year = "2003",
ISBN = "0-7623-1016-2",
ISBN-13 = "978-0-7623-1016-6",
ISSN = "1046-5847",
LCCN = "????",
bibdate = "Wed Nov 23 16:45:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Lagarias:2003:PAB,
author = "Jeffrey C. Lagarias",
title = "The $ 3 x + 1 $ problem: An annotated bibliography
(1963--1999) (sorted by author)",
journal = "arxiv.org",
volume = "??",
number = "??",
month = sep,
year = "2003",
bibdate = "Sat Sep 10 12:58:10 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0309224",
abstract = "The $ 3 x + 1 $ problem concerns iteration of the map
on the integers given by $ T(n) = (3 n + 1) / 2 $ if
$n$ is odd; $ T(n) = n / 2$ if $n$ is even. The $ 3 x +
1$ Conjecture asserts that for every positive integer $
n > 1$ the forward orbit of $n$ under iteration by $T$
includes the integer 1. This paper is an annotated
bibliography of work done on the $ 3 x + 1$ problem and
related problems from 1963 through 1999. At present the
$ 3 x + 1$ Conjecture remains unsolved.",
acknowledgement = ack-nhfb,
pagecount = "74",
remark = "At least 13 updates have been made up to
11-Jan-2011.",
}
@Article{Lanza:2003:FSP,
author = "Richard B. Lanza",
title = "Fear Not the Software: Proactively Detecting
Occupational Fraud Using Computer Audit Reports",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = sep # "\slash " # feb,
year = "2003",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:14:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967868",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@InProceedings{Manaris:2003:EMZ,
author = "Bill Manaris and Dallas Vaughan and Christopher Wagner
and Juan Romero and Robert B. Davis",
title = "Evolutionary Music and the {Zipf--Mandelbrot Law}:
Developing Fitness Functions for Pleasant Music",
crossref = "Raidl:2003:AEC",
pages = "522--534",
year = "2003",
bibdate = "Mon Feb 18 10:49:54 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{McAllister:2003:ARE,
author = "James W. McAllister",
title = "Algorithmic randomness in empirical data",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "34",
number = "3",
pages = "633--646",
month = sep,
year = "2003",
CODEN = "SHPSB5",
DOI = "https://doi.org/10.1016/S0039-3681(03)00047-5",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See replies
\cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
abstract = "According to a traditional view, scientific laws and
theories constitute algorithmic compressions of
empirical data sets collected from observations and
measurements. This article defends the thesis that, to
the contrary, empirical data sets are algorithmically
incompressible. The reason is that individual data
points are determined partly by perturbations, or
causal factors that cannot be reduced to any pattern.
If empirical data sets are incompressible, then they
exhibit maximal algorithmic complexity, maximal entropy
and zero redundancy. They are therefore maximally
efficient carriers of information about the world.
Since, on algorithmic information theory, a string is
algorithmically random just if it is incompressible,
the thesis entails that empirical data sets consist of
algorithmically random strings of digits. Rather than
constituting compressions of empirical data, scientific
laws and theories pick out patterns that data sets
exhibit with a certain noise.",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part
{A}",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
keywords = "Algorithmic randomness; Benford's Law; Compression;
Empirical data; Information; Law; Pattern",
}
@Article{Mitzenmacher:2003:BHG,
author = "Michael Mitzenmacher",
title = "A Brief History of Generative Models for Power Law and
Lognormal Distributions",
journal = j-INTERNET-MATH,
volume = "1",
number = "2",
pages = "226--251",
month = dec,
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1080/15427951.2004.10129088",
ISSN = "1542-7951 (print), 1944-9488 (electronic)",
ISSN-L = "1542-7951",
bibdate = "Thu Nov 24 13:38:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.im/1089229510;
http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf;
http://www.tandfonline.com/toc/uinm20/1/2",
acknowledgement = ack-nhfb,
ajournal = "Internet Math.",
fjournal = "Internet Mathematics",
journal-URL = "http://projecteuclid.org/info/euclid.im",
keywords = "Fibonacci sequence; lognormal distribution; monkeys
typing randomly; Pareto distribution; power-law
distribution; Yule distribution; Zipf's Law",
remark = "This is a survey article with a six-page bibliography
of earlier work, and a clear description of the
differences between lognormal and power-law
distributions, which otherwise look similar on log-log
plots. Lognormal distributions have finite means and
moments, while power-law distributions may have
infinite means and/or moments, depending on the
exponent. The preprint at author's Web site (last URL)
contains additional material on the acrimonious debate
between Beno{\^\i}t Mandelbrot and Herbert A. Simon
(see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
other references in Mitzenmacher's paper) on the
derivation and modeling of Zipf's Law distributions.",
}
@PhdThesis{Muller:2003:AZP,
author = "Mathias M{\"u}ller",
title = "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der
Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}.
({German}) [Applications of the digit analysis in the
audit practice with a focus on {Benford's Law}]",
type = "{Diplomarbeit}",
school = "Wirtschaftsuniversit{\"a}t Wien",
address = "Wien, Austria",
pages = "v + 75",
month = "????",
year = "2003",
bibdate = "Sat Feb 16 18:44:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://permalink.obvsg.at/wuw/AC03895842",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Naldi:2003:CIZ,
author = "M. Naldi",
title = "Concentration indices and {Zipf}'s law",
journal = j-ECONOM-LETT,
volume = "78",
number = "3",
pages = "329--334",
month = mar,
year = "2003",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/S0165-1765(02)00251-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "91B82",
MRnumber = "1959355",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176502002513",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Newby:2003:OSS,
author = "Gregory B. Newby and Jane Greenberg and Paul Jones",
title = "Open source software development and {Lotka's Law}:
{Bibliometric} patterns in programming",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "54",
number = "2",
pages = "169--178",
day = "15",
month = jan,
year = "2003",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.10177",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:09 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
note = "See comments \cite{Burrell:2004:LEF}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "10 Dec 2002",
}
@Article{Nguyen:2003:DPL,
author = "H. T. Nguyen and V. Kreinovich and L. Longpre",
title = "Dirty pages of logarithm tables, lifetime of the
universe, and subjective (fuzzy) probabilities on
finite and infinite intervals",
journal = j-IEEE-TRANS-FUZZY-SYSTEMS,
volume = "1",
pages = "67--73",
year = "2003",
CODEN = "IEFSEV",
DOI = "https://doi.org/10.1109/FUZZ.2003.1209339",
ISSN = "1063-6706 (print), 1941-0034 (electronic)",
ISSN-L = "1063-6706",
bibdate = "Sat Feb 16 18:51:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The 12th IEE International Conference on Fuzzy
Systems. FUZZ'03",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Fuzzy Systems",
xxnote = "Is this the listed journal, or a conference paper??",
}
@Article{Peter:2003:ADE,
author = "Manfred Peter",
title = "The asymptotic distribution of elements in automatic
sequences",
journal = j-THEOR-COMP-SCI,
volume = "301",
number = "1 3",
pages = "285--312",
year = "2003",
CODEN = "TCSCDI",
DOI = "https://doi.org/10.1016/S0304-3975(02)00587-X",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S030439750200587X",
abstract = "In an automatic sequence an element need not have an
asymptotic density. In this paper a necessary and
sufficient criterion is proved for the existence of the
asymptotic density of a given element. If it does not
exist the asymptotic distribution of the element can be
described in terms of a function H whose graph is
self-similar. An algorithm is given to decide whether H
is piecewise continuously differentiable, and in this
case it can be computed effectively. Finally, it is
shown that the H -density of an element in an automatic
sequence always exists and equals its logarithmic
density.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "Asymptotics; Automata; Benford's Law; Density;
H{\"o}lder mean; Oscillating sum; Self-similarity",
}
@Article{Quick:2003:BLD,
author = "Reiner Quick and Matthias Wolz",
title = "{Benford's Law in deutschen Rechnungslegungsdaten}.
({German}) [{Benford's Law} in {German} accounting
data]",
journal = "Betriebswirtschaftliche Forschung und Praxis",
volume = "55",
number = "2",
pages = "208--224",
month = "????",
year = "2003",
CODEN = "????",
ISSN = "0340-5370",
ISSN-L = "0340-5370",
bibdate = "Sat Dec 10 12:01:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
remark = "Betriebswirtschaftliche Forschung und Praxis ==
Business Research and Practice.",
}
@Article{Reed:2003:PLI,
author = "William J. Reed",
title = "The {Pareto} law of incomes---an explanation and an
extension",
journal = j-PHYSICA-A,
volume = "319",
number = "1--4",
pages = "469--486",
year = "2003",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(02)01507-8",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B70",
MRnumber = "1965596",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Rose:2003:TEF,
author = "Anna M. Rose and Jacob M. Rose",
title = "Turn {Excel} into a financial sleuth: an easy-to-use
digital analysis tool can red-flag irregularities",
journal = j-J-ACCOUNTANCY,
volume = "196",
number = "2",
pages = "58--??",
month = aug,
year = "2003",
CODEN = "JACYAD",
ISSN = "0021-8448 (print), 1945-0729 (electronic)",
ISSN-L = "0021-8448",
bibdate = "Sat Feb 16 19:07:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accountancy",
journal-URL = "http://www.journalofaccountancy.com/",
}
@Article{Sinai:2003:SP,
author = "Ya. G. Sinai",
title = "Statistical $ (3 x + 1) $ problem",
journal = j-COMM-PURE-APPL-MATH,
volume = "56",
number = "7",
pages = "1016--1028",
month = jul,
year = "2003",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.10084",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Mon Nov 21 07:52:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Dedicated to the memory of J{\"u}rgen K. Moser.",
acknowledgement = ack-nhfb,
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}
@InProceedings{Swanson:2003:DPF,
author = "David Swanson and Moon Jung Cho and John Eltinge",
editor = "????",
booktitle = "Proceedings of the Survey Research Section",
title = "Detecting possibly fraudulent or error-prone survey
data using {Benford's Law}",
publisher = "American Statistical Association",
address = "Washington, DC, USA",
pages = "4172--4177",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Nov 16 10:21:39 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.",
acknowledgement = ack-nhfb,
}
@Article{Wales:2003:IWI,
author = "Elspeth Wales",
title = "Is it Worth Investing in Software to Combat Fraud?",
journal = "Computer Fraud \& Security",
volume = "2003",
number = "5",
pages = "6--8",
year = "2003",
DOI = "https://doi.org/10.1016/S1361-3723(03)05009-7",
ISSN = "1361-3723 (print), 1873-7056 (electronic)",
ISSN-L = "1361-3723",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1361372303050097",
abstract = "Despite the tendency for businesses to keep fraud to
themselves, the consensus is that the problem is
becoming worse. On the plus side though software
solutions that can detect potential fraudulent activity
are evolving in their scope and ability to
automatically track transactions in real-time.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Warren:2003:DLD,
author = "Henry S. Warren",
title = "The distribution of leading digits",
crossref = "Warren:2003:HD",
chapter = "15.3",
pages = "264--267",
year = "2003",
bibdate = "Fri Mar 16 08:02:56 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wu:2003:IPD,
author = "Shuo-Jye Wu and Chun-Tao Chang",
title = "Inference in the {Pareto} distribution based on
progressive {Type II} censoring with random removals",
journal = j-J-APPL-STAT,
volume = "30",
number = "2",
pages = "163--172",
month = "????",
year = "2003",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Dec 16 15:40:48 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Wu:2003:PDC,
author = "Wei Biao Wu and Chinya V. Ravishankar",
title = "The performance of difference coding for sets and
relational tables",
journal = j-J-ACM,
volume = "50",
number = "5",
pages = "665--693",
month = sep,
year = "2003",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/876638.876641",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Mon Sep 8 17:55:23 MDT 2003",
bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "We characterize the performance of difference coding
for compressing sets and database relations through an
analysis of the problem of estimating the number of
bits needed for storing the spacings between values in
sets of integers. We provide analytical expressions for
estimating the effectiveness of difference coding when
the elements of the sets or the attribute fields in
database tuples are drawn from the uniform and Zipf
distributions. We also examine the case where a
uniformly distributed domain is combined with a Zipf
distribution, and with an arbitrary distribution. We
present limit theorems for most cases, and
probabilistic convergence results in other cases. We
also examine the effects of attribute domain reordering
on the compression ratio. Our simulations show
excellent agreement with theory.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Aoyama:2004:KDP,
author = "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma",
title = "Kinematics and dynamics of {Pareto--Zipf}'s law and
{Gibrat}'s law",
journal = j-PHYSICA-A,
volume = "344",
number = "1--2",
pages = "117--121",
day = "1",
month = dec,
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2004.06.099",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009185",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@TechReport{Berger:2004:DDU,
author = "A. Berger",
title = "Dynamics and digits: on the ubiquity of {Benford's
Law}",
type = "Preprint",
institution = "Institute of Mechanics, Vienna University of
Technology",
address = "Vienna, Austria",
pages = "3",
day = "19",
month = nov,
year = "2004",
bibdate = "Sat Feb 16 17:20:58 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf",
acknowledgement = ack-nhfb,
}
@Article{Burrell:2004:LEF,
author = "Quentin L. Burrell",
title = "Letters to the {Editor}: Fitting {Lotka's Law}: {Some}
cautionary observations on a recent paper by {Newby} et
al. (2003)",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "55",
number = "13",
pages = "1209--1210",
month = nov,
year = "2004",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20086",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:16 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
note = "See \cite{Newby:2003:OSS}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "17 Aug 2004",
}
@Article{Challet:2004:BPD,
author = "Damien Challet and Andrea Lombardoni",
title = "Bug propagation and debugging in asymmetric software
structures",
journal = j-PHYS-REV-E,
volume = "70",
number = "4",
pages = "046109",
month = oct,
year = "2004",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.70.046109",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Thu Feb 28 08:15:07 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.046109;
http://pre.aps.org/abstract/PRE/v70/i4/e046109",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "4",
journal-URL = "http://pre.aps.org/browse",
keywords = "Linux; Unix; Zipf's Law",
pagecount = "5",
}
@Article{Chen:2004:MFM,
author = "Yanguang Chen and Yixing Zhou",
title = "Multi-fractal measures of city-size distributions
based on the three-parameter {Zipf} model",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "22",
number = "4",
pages = "793--805",
day = "1",
month = nov,
year = "2004",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2004.02.059",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0960077904001031",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
keywords = "Zipf's Law",
}
@Article{Cong:2004:WTP,
author = "Lin Cong and Zhipeng Li",
title = "On {Wilson}'s theorem and {Polignac} conjecture",
journal = "ArXiv e-prints",
day = "2",
month = aug,
year = "2004",
bibdate = "Mon Feb 18 07:03:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math.NT/0408018",
abstract = "We introduce Wilson's theorem and Clement's result and
present a necessary and sufficient condition for $p$
and $ p + 2 k $ to be primes where $k$ is a positive
integer. By using Simiov's Theorem, we derive an
improved version of Clement's result and
characterizations of Polignac twin primes which
parallel previous characterizations.",
acknowledgement = ack-nhfb,
}
@TechReport{Diekmann:2004:DEE,
author = "Andreas Diekmann",
title = "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
der Benford Verteilung}. ({German}) [{Data}
falsification. {Results} from experiments with the
{Benford} distribution]",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
year = "2004",
bibdate = "Fri Nov 18 12:09:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Diekmann:2004:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "26",
month = oct,
year = "2004",
bibdate = "Sat Dec 10 11:12:29 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by ``Benford's law''. Recently, a test
against this distribution was used to identify
fraudulent accounting data. This test is based on the
supposition that real data follow the Benford
distribution while fabricated data do not. Is it
possible to apply Benford tests to detect fabricated or
falsified scientific data as well as fraudulent
financial data? We approached this question in two
ways. First, we examined the use of the Benford
distribution as a standard by checking digit
frequencies in published statistical estimates. Second,
we conducted experiments in which subjects were asked
to fabricate statistical estimates (regression
coefficients). These experimental data were scrutinized
for possible deviations from the Benford distribution.
There were two main findings. First, the digits of the
published regression coefficients were approximately
Benford distributed. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. At least in the case of regression
coefficients, there were indications that checks for
digit-preference anomalies should focus less on the
first and more on the second and higher-digits",
acknowledgement = ack-nhfb,
}
@Article{Durtschi:2004:EUB,
author = "C. Durtschi and W. Hillison and C. Pacini",
title = "The Effective Use of {Benford's Law} to Assist in
Detecting Fraud in Accounting Data",
journal = j-J-FORENSIC-ACCOUNT,
volume = "5",
number = "1",
pages = "17--34",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Sun Nov 13 11:35:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Fontanari:2004:SNM,
author = "J. F. Fontanari and L. I. Perlovsky",
title = "Solvable null model for the distribution of word
frequencies",
journal = j-PHYS-REV-E,
volume = "70",
number = "??",
pages = "042901",
day = "25",
month = oct,
year = "2004",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.70.042901",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.042901",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:DPZ,
author = "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki
Aoyama and Mauro Gallegati and Wataru Souma",
title = "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An}
analysis with {European} firms",
journal = j-PHYSICA-A,
volume = "335",
number = "1--2",
pages = "197--216",
day = "1",
month = apr,
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2003.12.015",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011294",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:GPZ,
author = "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di
Guilmi} and Wataru Souma and Mauro Gallegati",
title = "{Gibrat} and {Pareto--Zipf} revisited with {European}
firms",
journal = j-PHYSICA-A,
volume = "344",
number = "1--2",
pages = "112--116",
day = "1",
month = dec,
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2004.06.098",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009173",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Fujiwara:2004:ZLF,
author = "Yoshi Fujiwara",
title = "{Zipf} law in firms bankruptcy",
journal = j-PHYSICA-A,
volume = "337",
number = "1--2",
pages = "219--230",
day = "1",
month = jun,
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2004.01.037",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B38",
MRnumber = "2092316",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437104001165",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Garcia-Berthou:2004:IBT,
author = "Emili Garc{\'i}a-Berthou and Carles Alcaraz",
title = "Incongruence between test statistics and {$P$} values
in medical papers",
journal = "BMC Medical Research Methodology",
volume = "4",
number = "1",
pages = "1--5",
year = "2004",
DOI = "https://doi.org/10.1186/1471-2288-4-13",
ISSN = "1471-2288",
ISSN-L = "1471-2288",
bibdate = "Sat Sep 10 11:16:07 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Given an observed test statistic and its degrees of
freedom, one may compute the observed P value with most
statistical packages. It is unknown to what extent test
statistics and P values are congruent in published
medical papers.",
acknowledgement = ack-nhfb,
journal-URL = "http://bmcmedresmethodol.biomedcentral.com/",
keywords = "Benford's Law; digit frequencies",
}
@Article{Geyer:2004:DFD,
author = "Christina Lynn Geyer and Patricia Pepple Williamson",
title = "Detecting fraud in data sets using {Benford's Law}",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "B33",
number = "1",
pages = "229--246",
month = "????",
year = "2004",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1081/SAC-120028442",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
MRclass = "62-07",
MRnumber = "2044866",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Statist. Simulation Comput.",
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Hurlimann:2004:IPB,
author = "Werner H{\"u}rlimann",
title = "Integer powers and {Benford}'s law",
journal = j-INT-J-PURE-APPL-MATH,
volume = "11",
number = "1",
pages = "39--46",
year = "2004",
CODEN = "????",
ISSN = "1311-8080 (print), 1314-3395 (electronic)",
ISSN-L = "1314-3395",
MRclass = "62E15 (11B83 11K31 62E20)",
MRnumber = "2033394 (2005c:62030)",
MRreviewer = "I. N. Volodin",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
journal-URL = "http://ijpam.eu/",
}
@Article{Ismail:2004:SES,
author = "Sanaa Isma{\"\i}l",
title = "A Simple Estimator for the Shape Parameter of the
{Pareto} Distribution with Economics and Medical
Applications",
journal = j-J-APPL-STAT,
volume = "31",
number = "1",
pages = "3--13",
month = jan,
year = "2004",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Sat Dec 4 12:10:37 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Janvresse:2004:UDB,
author = "{\'E}lise Janvresse and Thierry de la Rue",
title = "From uniform distributions to {Benford}'s law",
journal = j-J-APPL-PROBAB,
volume = "41",
number = "4",
pages = "1203--1210",
year = "2004",
CODEN = "JPRBAM",
DOI = "https://doi.org/10.1239/jap/1101840566",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60J20 (60J10)",
MRnumber = "2122815 (2006b:60161)",
MRreviewer = "Michael Drmota",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
http://www.jstor.org/stable/4141393;
https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf",
abstract = "We provide a new, probabilistic explanation for the
appearance of Benford's law in everyday-life numbers,
by showing that it arises naturally when we consider
mixtures of uniform distributions. Then we connect our
result to a result of Flehinger, for which we provide a
shorter proof, and the speed of convergence.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
}
@Book{Judson:2004:GBF,
author = "Horace Freeland Judson",
title = "The Great Betrayal: Fraud in Science",
publisher = "Harcourt",
address = "Orlando, FL, USA",
pages = "xiv + 463",
year = "2004",
ISBN = "0-15-100877-9",
ISBN-13 = "978-0-15-100877-3",
LCCN = "Q175.37 .J84 2004",
bibdate = "Sat Sep 10 12:29:21 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/har051/2004005906.html;
http://www.loc.gov/catdir/description/har051/2004005906.html;
http://www.loc.gov/catdir/samples/har051/2004005906.html;
http://www.loc.gov/catdir/toc/ecip0416/2004005906.html",
acknowledgement = ack-nhfb,
remark = "No mention of Benford's Law or first digit phenomenon,
but nevertheless relevant for applications of Benford's
Law to detection of fraud in data.",
subject = "Fraud in science",
tableofcontents = "Preface / xi \\
Prologue / 1 \\
1: A Culture of Fraud / 9 \\
2: What's It Like? A Typology of Scientific Fraud / 43
\\
3: Patterns of Complicity: Recent Cases / 98 \\
4: Hard to Measure, Hard to Define: The Incidence of
Scientific Fraud and the Struggle Over Its Definition /
155 \\
5: The Baltimore Affair / 191 \\
6: The Problems of Peer Review / 244 \\
7: Authorship, Ownership: The Problems of Credit,
Plagiarism, and Property / 287 \\
8: The Rise of Open Publication on the Internet / 325
\\
9: Laboratory to Law: The Problems of Institutions When
Misconduct is Charged / 369 \\
Epilogue / 404 \\
Notes / 419 \\
Index / 447",
}
@TechReport{Kollath-Romano:2004:DSD,
author = "P. Kollath-Romano",
title = "On the distribution of significant digits in numbers",
type = "Preprint",
institution = "Rensselaer Polytechnic Institute",
address = "Troy, NY, USA",
year = "2004",
bibdate = "Sat Feb 16 18:15:19 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Kotz:2004:FDP,
author = "Samuel Kotz and N. Balakrishnan and Campbell B. Read
and Brani Vidakovic",
editor = "Samuel Kotz and N. Balakrishnan and Campbell B. Read
and Brani Vidakovic",
booktitle = "Encyclopedia of Statistical Sciences",
title = "First-Digit Problem",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "??--??",
year = "2004",
DOI = "https://doi.org/10.1002/0471667196.ess0783.pub2",
ISBN = "0-471-66719-6 (e-book)",
ISBN-13 = "978-0-471-66719-3 (e-book)",
bibdate = "Sun Feb 24 10:49:25 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kristiansen:2004:BTZ,
author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
Skjeltorp",
title = "Braid theory and {Zipf} relation used in dynamics of
magnetic microparticles",
journal = j-ECONOM-LETT,
volume = "30",
number = "1",
pages = "2387--2388",
day = "1",
month = may,
year = "2004",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/j.jmmm.2003.12.1288",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304885303019127",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Kristiansen:2004:EOZ,
author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
Skjeltorp",
title = "Experimental observation of {Zipf--Mandelbrot}
relation",
journal = j-PHYSICA-A,
volume = "335",
number = "3--4",
pages = "413--420",
day = "15",
month = apr,
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2003.12.024",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82D10 (76T99 82-05)",
MRnumber = "2044153",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011804",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Kulikova:2004:OSS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "One-sided stable distributions and {Benford}'s law",
journal = "Teor. Veroyatn. Primen.",
volume = "49",
number = "1",
pages = "178--184",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1137/S0040585X97980944",
ISSN = "0040-361X",
ISSN-L = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2141338 (2005m:60028)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Lanza:2004:CBS,
author = "Richard B. Lanza",
title = "Comparing Best Software for Fraud Examinations: Fraud
Data Interrogation Tools",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = nov # "\slash " # dec,
year = "2004",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:17:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967837",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@Article{Lehner:2004:DVG,
author = "B. Lehner and P. Doll",
title = "Development and validation of a global database of
lakes",
journal = j-J-HYDROL,
volume = "296",
number = "1--4",
pages = "1--22",
day = "20",
month = aug,
year = "2004",
CODEN = "JHYDA7",
DOI = "https://doi.org/10.1016/j.jhydrol.2004.03.028",
ISSN = "0022-1694 (print), 1879-2707 (electronic)",
ISSN-L = "0022-1694",
bibdate = "Fri Mar 22 08:54:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022169404001404",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
fjournal = "Journal of Hydrology",
journal-URL = "http://www.sciencedirect.com/science/journal/00221694",
keywords = "Benford's Law",
}
@Article{Li:2004:DBL,
author = "Zhi-peng Li and Lin Cong and Hua-jia Wang",
title = "Discussion on {Benford's Law} and its Application",
journal = "ArXiv e-prints",
pages = "1--13",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 16:17:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2004math......8057L;
http://arxiv.org/abs/math/0408057",
abstract = "The probability that a number in many naturally
occurring tables of numerical data has first
significant digit $d$ is predicted by Benford's Law $
{\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over
d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's
Law from both theoretical and real-life sources on both
science and social science areas are shown in detail
with some novel ideas and generalizations developed
solely by the authors of this paper. Three tests,
Chi-Square test, total variation distance, and maximum
deviations are adopted to examine the fitness of the
datasets to Benford's distribution. Finally,
applications of Benford's Law are summarized and
explored to reveal the power of this mathematical
principle.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "math/0408057",
}
@Article{Lindsay:2004:DFD,
author = "D. H. Lindsay and P. S. Foote and A. Campbell and D.
R. Reilly",
title = "Detecting fraud in the data using automatic
intervention detection",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2004",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sat Feb 16 18:32:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
}
@Book{Miller:2004:JFM,
author = "Irwin Miller and Marylees Miller",
title = "{John E. Freund}'s mathematical statistics with
applications",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Seventh",
pages = "x + 614",
year = "2004",
ISBN = "0-13-142706-7",
ISBN-13 = "978-0-13-142706-8",
LCCN = "QA276 .M4726 2004",
bibdate = "Thu Oct 13 07:01:49 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1928--",
remark = "Revised edition of \cite{Miller:1999:JFM}.",
subject = "Mathematical statistics",
}
@TechReport{Miller:2004:STB,
author = "Steven J. Miller",
title = "Some thoughts on {Benford}'s law",
type = "Preprint",
institution = "Williams College",
address = "Williamstown, MA 01267 USA",
year = "2004",
bibdate = "Sat Feb 16 18:43:46 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf",
acknowledgement = ack-nhfb,
remark = "URL not found on 17 February 2013; perhaps in ReCALL
2004 proceedings",
}
@Article{Molchanov:2004:BEL,
author = "Stanislav Molchanov and Xian Wang",
title = "On the {Benford}'s empirical law",
journal = "Random Oper. Stochastic Equations",
volume = "12",
number = "3",
pages = "201--210",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1163/1569397042222495",
ISSN = "0926-6364 (print), 1569-397X (electronic)",
ISSN-L = "0926-6364",
MRclass = "11K16 (11B39 60B15)",
MRnumber = "2084074 (2005h:11162)",
MRreviewer = "A. N. Philippou",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Operators and Stochastic Equations",
}
@Article{Nabeshima:2004:ZLP,
author = "Terutaka Nabeshima and Yukio-Pegio Gunji",
title = "{Zipf}'s law in phonograms and {Weibull} distribution
in ideograms: comparison of {English} with {Japanese}",
journal = j-BIOSYSTEMS,
volume = "73",
number = "2",
pages = "131--139",
day = "20",
month = feb,
year = "2004",
CODEN = "BSYMBO",
DOI = "https://doi.org/10.1016/j.biosystems.2003.11.002",
ISSN = "0303-2647 (print), 1872-8324 (electronic)",
ISSN-L = "0303-2647",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0303264703002260",
acknowledgement = ack-nhfb,
fjournal = "Biosystems (A6E)",
journal-URL = "http://www.sciencedirect.com/science/journal/03032647",
keywords = "Zipf's Law",
}
@Article{Nguyen:2004:DPL,
author = "Hung T. Nguyen and Vladik Kreinovich and Luc
Longpr{\'e}",
title = "Dirty Pages of Logarithm Tables, Lifetime of the
Universe, and (Subjective) Probabilities on Finite and
Infinite Intervals",
journal = j-RELIABLE-COMPUTING,
volume = "10",
number = "2",
pages = "83--106",
month = apr,
year = "2004",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/B:REOM.0000015848.19449.12",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon Feb 6 07:42:05 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/rc.bib",
URL = "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@InProceedings{Pericchi:2004:LNB,
author = "Luis R{\'a}ul Pericchi and David Torres",
editor = "????",
booktitle = "{Third Universidad Simon Bolivar Seminar on
Statistical Analyses of the Venezuelan Recall
Referendum}",
title = "La {Ley de Newcomb--Benford} y sus aplicaciones al
Referendum Revocatorio en {Venezuela}. ({Spanish}) [The
{Newcomb--Benford Law} and its applications to the
recall referendum in {Venezuela}]",
publisher = "????",
address = "????",
pages = "1--7",
day = "1",
month = oct,
year = "2004",
bibdate = "Fri Feb 15 18:25:14 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reporte T{\'e}cnico no-definitivo 2a. Presented on
September 23, 2004.",
URL = "http://esdata.info/pdf/pericchi-torres.pdf;
https://sites.google.com/a/upr.edu/probability-and-statistics/home/techical-reports",
acknowledgement = ack-nhfb,
language = "Spanish",
}
@TechReport{Posch:2004:BBH,
author = "Peter N. Posch",
title = "{Benford} or not-{Benford}? {How} to test for the
first digit law",
type = "Working paper.",
institution = "Department of Finance, University of Ulm",
address = "Ulm, Germany",
year = "2004",
bibdate = "Sat Feb 16 19:05:45 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Posch:2004:SSD,
author = "Peter N. Posch",
title = "A survey on sequences and distribution functions
satisfying {Benford}'s law",
type = "Working paper.",
institution = "Department of Finance, University of Ulm",
address = "Ulm, Germany",
day = "25",
month = oct,
year = "2004",
bibdate = "Sat Feb 16 19:05:45 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.posch.org/paper/posch_benforddist.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Posch:2004:ZFB,
author = "Peter N. Posch",
title = "{Ziffernanalyse in der F{\"a}lschungsaufsp{\"u}rung.
Benford's Gesetz und Steuererkl{\"a}rungen in Theorie
und Praxis}. ({German}) [Digit analysis in fake
tracing. {Benford's Law} and tax returns in theory and
practice]",
type = "Arbeitspapier",
institution = "Abteilung Finanzwirtschaft, University Ulm",
address = "Ulm, Germany",
month = oct,
year = "2004",
bibdate = "Sat Feb 16 19:03:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Pustet:2004:ZHH,
author = "Regina Pustet",
title = "{Zipf} and his heirs",
journal = j-LANG-SCI,
volume = "26",
number = "1",
pages = "1--25",
day = "1",
month = jan,
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1016/S0388-0001(03)00018-4",
ISSN = "0388-0001 (print), 1873-5746 (electronic)",
ISSN-L = "0388-0001",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0388000103000184",
abstract = "During the first half of this century, George Kingsley
Zipf devised a comprehensive model of language mainly
on the empirical basis of frequency counts in
discourse. Although Zipf is remembered particularly for
establishing the general formula the higher the
discourse frequency of a linguistic item, the shorter
it will be, his model is complex enough to merit
re-evaluation especially in the light of more recent
findings of discourse-based models of language and
grammaticalization theory.",
acknowledgement = ack-nhfb,
fjournal = "Language Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/03880001",
keywords = "Benford's Law; Diachronic development of language;
Discourse analysis; George Kingsley Zipf; Usage-based
models of language; Word frequency; Zipf's Law",
}
@Article{Quarantelli:2004:ISA,
author = "Mario Quarantelli and Karim Berkouk and Anna Prinster
and Brigitte Landeau and Claus Svarer and Laszlo Balkay
and Bruno Alfano and Arturo Brunetti and Jean-Claude
Baron and Marco Salvatore",
title = "Integrated Software for the Analysis of Brain
{PET\slash SPECT} Studies with Partial-Volume Effect
Correction",
journal = j-NUCL-MED,
volume = "45",
number = "2",
pages = "192--201",
day = "1",
month = feb,
year = "2004",
CODEN = "JNMEAQ",
ISSN = "0161-5505 (print), 1535-5667 (electronic)",
ISSN-L = "0161-5505",
bibdate = "Sat Sep 10 15:45:29 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jnm.snmjournals.org/content/45/2/192.abstract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nuclear Medicine",
journal-URL = "http://jnm.snmjournals.org/content/by/year",
keywords = "Benford's Law",
}
@Article{Rawlings:2004:EBP,
author = "Philip K. Rawlings and David Reguera and Howard
Reiss",
title = "Entropic basis of the {Pareto} law",
journal = j-PHYSICA-A,
volume = "343",
number = "1--4",
pages = "643--652",
year = "2004",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2004.06.152",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B26 (91B82)",
MRnumber = "2094418 (2005e:91065)",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Rodriguez:2004:FSD,
author = "Ricardo J. Rodriguez",
title = "First Significant Digit Patterns From Mixtures of
Uniform Distributions",
journal = j-AMER-STAT,
volume = "58",
number = "1",
pages = "64--71",
month = feb,
year = "2004",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/0003130042782",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Feb 20 06:14:28 MST 2004",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law",
}
@TechReport{Saville:2004:SWN,
author = "Adrian D. Saville",
title = "Sorry, wrong number. {How} accounting data are wrong
and how the numbers can be fixed",
type = "Preprint",
institution = "????",
address = "????",
month = "????",
year = "2004",
bibdate = "Sat Feb 16 19:11:00 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Sigurd:2004:WLS,
author = "Bengt Sigurd and Mats Eeg-Olofsson and Joost {Van
Weijer}",
title = "Word length, sentence length and frequency --- {Zipf}
revisited",
journal = j-STUD-LINGUISTICA,
volume = "58",
number = "1",
pages = "37--52",
year = "2004",
DOI = "https://doi.org/10.1111/j.0039-3193.2004.00109.x",
ISSN = "0039-3193 (print), 1467-9582 (electronic)",
ISSN-L = "0039-3193",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Studia Linguistica",
}
@Article{Skousen:2004:AUP,
author = "Christopher J. Skousen and Liming Guan and T. Sterling
Wetzel",
title = "Anomalies and Unusual Patterns in Reported Earnings:
{Japanese} Managers Round Earnings",
journal = j-J-INT-FINANC-MANAG-ACCOUNT,
volume = "15",
number = "3",
pages = "212--234",
month = oct,
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1467-646X.2004.00108.x",
ISSN = "0954-1314 (print), 1467-646X (electronic)",
ISSN-L = "0954-1314",
bibdate = "Fri Nov 25 11:11:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of International Financial Management and
Accounting",
}
@Book{Tijms:2004:UPC,
author = "Henk C. Tijms",
title = "Understanding probability: chance rules in everyday
life",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 380",
year = "2004",
ISBN = "0-521-83329-9 (hardcover), 0-521-54036-4 (paperback)",
ISBN-13 = "978-0-521-83329-5 (hardcover), 978-0-521-54036-0
(paperback)",
LCCN = "QA273 .T48 2004",
bibdate = "Mon Feb 18 06:48:08 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Probabilities; Mathematical analysis; Chance;
Wahrscheinlichkeit; (Math.); Gesamtdarstellung",
}
@Article{Vanichpun:2004:OCU,
author = "Sarut Vanichpun and Armand M. Makowski",
title = "The output of a cache under the independent reference
model: where did the locality of reference go?",
journal = j-SIGMETRICS,
volume = "32",
number = "1",
pages = "295--306",
month = jun,
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1145/1012888.1005722",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:18 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "We consider a cache operating under a demand-driven
replacement policy when document requests are modeled
according to the Independent Reference Model (IRM). We
characterize the popularity pmf of the stream of misses
from the cache, the so-called output of the cache, for
a large class of demand-driven cache replacement
policies. We measure strength of locality of reference
in a stream of requests through the skewness of its
popularity distribution. Using the notion of
majorization to capture this degree of skewness, we
show that for the policy $ A_0 $ and the random policy,
the output always has less locality of reference than
the input. However, we show by counterexamples that
this is not always the case under the LRU and CLIMB
policies when the input is selected according to a
Zipf-like pmf. In that case, conjectures are offered
(and supported by simulations) as to when LRU or CLIMB
caching indeed reduces locality of reference.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "locality of reference; majorization; output of a
cache; popularity",
}
@InProceedings{Acebo:2005:BLN,
author = "E. Acebo and M. Sbert",
editor = "L. Neumann and M. Sbert and B. Gooch and W.
Purgathofer",
booktitle = "Conference: Computational Aesthetics 2005:
Eurographics Workshop on Computational Aesthetics in
Graphics, Visualization and Imaging 2005, Girona,
Spain, May 18--20, 2005",
title = "{Benford's Law} for Natural and Synthetic Images",
publisher = "????",
address = "????",
pages = "169--176",
year = "2005",
DOI = "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
bibdate = "Sat Sep 10 11:34:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Alexanderson:2005:BRG,
author = "Gerald L. Alexanderson",
title = "Book Review: {{\booktitle{Gamma: Exploring Euler's
Constant}}, by Julian Havil. Princeton, Princeton
University Press 2003. xxiii + 266 pages. US \$29.95.
ISBN 0-691-09983-9}",
journal = j-MATH-INTEL,
volume = "27",
number = "1",
pages = "86--88",
month = dec,
year = "2005",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF02984820",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/BF02984820",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
keywords = "Benford's Law",
}
@Article{Anonymous:2005:UZL,
author = "Anonymous",
title = "The use of {Zipf}'s law in animal communication
analysis",
journal = j-ANIM-BEHAV,
volume = "69",
number = "1",
pages = "??--??",
day = "20",
month = jan,
year = "2005",
CODEN = "ANBEA8",
DOI = "https://doi.org/10.1016/j.anbehav.2004.08.004",
ISSN = "0003-3472 (print), 1095-8282 (electronic)",
ISSN-L = "0003-3472",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0003347204003471",
acknowledgement = ack-nhfb,
fjournal = "Animal Behaviour",
journal-URL = "http://www.sciencedirect.com/science/journal/00033472",
keywords = "Zipf's Law",
}
@Article{Antonini:2005:RSC,
author = "Rita Giuliano Antonini and Georges Grekos",
title = "Regular sets and conditional density: an extension of
{Benford}'s law",
journal = j-COLLOQ-MATH,
volume = "103",
number = "2",
pages = "173--192",
year = "2005",
CODEN = "CQMAAQ",
DOI = "https://doi.org/10.4064/cm103-2-3",
ISSN = "0010-1354 (print), 1730-6302 (electronic)",
ISSN-L = "0010-1354",
MRclass = "11B05 (11K99)",
MRnumber = "2197847 (2006j:11012)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1092.11009",
acknowledgement = ack-nhfb,
fjournal = "Colloquium Mathematicum",
keywords = "asymptotic density; Benford's law; conditional
density; first digit problem; logarithmic density;
regular set; regular varying function",
ZMclass = "11B05 (Topology etc. of sets of numbers); 11K99
(Probabilistic theory)",
}
@Article{Berger:2005:BLP,
author = "Arno Berger",
title = "{Benford}'s law in power-like dynamical systems",
journal = j-STOCH-DYNAM,
volume = "5",
number = "4",
pages = "587--607",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S0219493705001602",
ISSN = "0219-4937",
ISSN-L = "0219-4937",
MRclass = "37B55 (11K06 37A50 37E05)",
MRnumber = "2185507 (2008i:37029)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Stoch. Dyn.",
fjournal = "Stochastics and Dynamics",
}
@InCollection{Berger:2005:DDU,
author = "A. Berger",
booktitle = "{EQUADIFF} 2003",
title = "Dynamics and digits: on the ubiquity of {Benford}'s
law",
publisher = "World Sci. Publ., Hackensack, NJ",
pages = "693--695",
year = "2005",
DOI = "https://doi.org/10.1142/9789812702067_0115",
MRclass = "37A45 (11K55)",
MRnumber = "2185113",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Berger:2005:MDD,
author = "Arno Berger",
title = "Multi-dimensional dynamical systems and {Benford}'s
law",
journal = j-DISCRETE-CONTIN-DYN-SYST,
volume = "13",
number = "1",
pages = "219--237",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.3934/dcds.2005.13.219",
ISSN = "1078-0947 (print), 1553-5231 (electronic)",
ISSN-L = "1078-0947",
MRclass = "37A45 (11K36 28D05 37A50 60F05)",
MRnumber = "2128801 (2005m:37016)",
MRreviewer = "Reinhard Winkler",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Continuous Dynamical Systems. Series A",
}
@Article{Berger:2005:ODD,
author = "Arno Berger and Leonid A. Bunimovich and Theodore P.
Hill",
title = "One-dimensional dynamical systems and {Benford}'s
law",
journal = j-TRANS-AM-MATH-SOC,
volume = "357",
number = "1",
pages = "197--219",
year = "2005",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-04-03455-5",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "37A45 (11K06 37A50 37E05 60F05 82B05)",
MRnumber = "2098092 (2005m:37017)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Bhattacharya:2005:CPA,
author = "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
Smarandache",
title = "Conditional probability of actually detecting a
financial fraud --- a neutrosophic extension to
{Benford}'s law",
journal = "International Journal of Applied Mathematics",
volume = "17",
number = "1",
pages = "7--14",
year = "2005",
CODEN = "????",
ISSN = "1311-1728",
MRclass = "62G10 (91B28)",
MRnumber = "2170667",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0504520",
abstract = "This study actually draws from and builds on an
earlier paper (Kumar and Bhattacharya, 2002). Here we
have basically added a neutrosophic dimension to the
problem of determining the conditional probability that
a financial fraud has been actually committed, given
that no Type I error occurred while rejecting the null
hypothesis H0: The observed first-digit frequencies
approximate a Benford distribution; and accepting the
alternative hypothesis H1: The observed first-digit
frequencies do not approximate a Benford distribution.
We have also suggested a conceptual model to implement
such a neutrosophic fraud detection system.",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Appl. Math.",
fjournal = "International Journal of Applied Mathematics",
}
@Article{Bhattacharyya:2005:COP,
author = "P. Bhattacharyya and A. Chatterjee and B. K.
Chakrabarti",
title = "A common origin of the power law distributions in
models of market and earthquake",
journal = "ArXiv e-prints",
year = "2005",
bibdate = "Sat Feb 16 17:25:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/physics/0510038",
acknowledgement = ack-nhfb,
}
@Article{Brown:2005:BLS,
author = "Richard J. C. Brown",
title = "{Benford}'s law and the screening of analytical data:
the case of pollutant concentrations in ambient air",
journal = j-ANALYST,
volume = "130",
number = "9",
pages = "1280--1285",
month = "????",
year = "2005",
CODEN = "ANALAO",
DOI = "https://doi.org/10.1039/B504462F",
ISSN = "0003-2654 (print), 1364-5528 (electronic)",
ISSN-L = "0003-2654",
bibdate = "Sat Feb 16 17:27:51 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/16096674",
acknowledgement = ack-nhfb,
fjournal = "The Analyst",
journal-URL = "http://pubs.rsc.org/en/journals/journalissues/an",
}
@Article{Campi:2005:ZLM,
author = "X. Campi and H. Krivine",
title = "{Zipf}'s law in multifragmentation",
journal = j-PHYS-REV-C,
volume = "72",
number = "??",
pages = "057602",
day = "30",
month = nov,
year = "2005",
CODEN = "PRVCAN",
DOI = "https://doi.org/10.1103/PhysRevC.72.057602",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.72.057602",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@TechReport{Ciofalo:2005:EBF,
author = "Michele Ciofalo",
title = "Entropy, {Benford}'s first digit law, and the
distribution of everything",
type = "Report",
institution = "Dipartimento di Ingegneria Nucleare, Universit{\`a}
degli Studi di Palermo",
address = "Palermo, Italy",
pages = "34",
year = "2005",
bibdate = "Sun Feb 17 08:23:55 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cleary:2005:ADA,
author = "Richard Cleary and Jay C. Thibodeau",
title = "Applying Digital Analysis Using {Benford's Law} to
Detect Fraud: The Dangers of Type {I} Errors",
journal = j-AUDITING,
volume = "24",
number = "1",
pages = "77--81",
month = may,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.2308/aud.2005.24.1.77",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:17:46 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@Article{Cohen:2005:PCL,
author = "Edith Cohen and Carsten Lund",
title = "Packet classification in large {ISPs}: design and
evaluation of decision tree classifiers",
journal = j-SIGMETRICS,
volume = "33",
number = "1",
pages = "73--84",
month = jun,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1145/1064212.1064222",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:27 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Packet classification, although extensively studied,
is an evolving problem. Growing and changing needs
necessitate the use of larger filters with more complex
rules. The increased complexity and size pose
implementation challenges on current hardware solutions
and drive the development of software classifiers, in
particular, decision-tree based classifiers. Important
performance measures for these classifiers are time and
memory due to required high throughput and use of
limited fast memory. We analyze Tier 1 ISP data that
includes filters and corresponding traffic from over a
hundred edge routers and thousands of interfaces. We
provide a comprehensive view on packet classification
in an operational network and glean insights that help
us design more effective classification algorithms. We
propose and evaluate decision tree classifiers with
{\em common branches}. These classifiers have linear
worst-case memory bounds and require much less memory
than standard decision tree classifiers, but
nonetheless, we show that on our data have similar
average and worst-case time performance. We argue that
common-branches exploit structure that is present in
real-life data sets. We observe a strong Zipf-like
pattern in the usage of rules in a classifier, where a
very small number of rules resolves the bulk of traffic
and most rules are essentially never used. Inspired by
this observation, we propose {\em traffic-aware\/}
classifiers that obtain superior average-case and
bounded worst-case performance. Good average-case can
boost performance of software classifiers that can be
used in small to medium sized routers and are also
important for traffic analysis and traffic
engineering.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "access control lists; decision trees; packet
filtering; routing",
}
@Article{Dahui:2005:TRZ,
author = "Wang Dahui and Li Menghui and Di Zengru",
title = "True reason for {Zipf}'s law in language",
journal = j-PHYSICA-A,
volume = "358",
number = "2--4",
pages = "545--550",
day = "15",
month = dec,
year = "2005",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2005.04.021",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437105004085",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@InProceedings{DelAcebo:2005:BLN,
author = "Esteve {Del Acebo} and Mateu Sbert",
title = "{Benford's Law} for Natural and Synthetic Images",
crossref = "Neumann:2005:CAE",
pages = "169--176",
year = "2005",
DOI = "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
bibdate = "Tue Nov 15 08:46:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
acknowledgement = ack-nhfb,
}
@Book{Durrett:2005:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Thomson Brooks\slash Cole",
address = "Belmont, CA, USA",
edition = "Third",
pages = "xi + 497",
year = "2005",
ISBN = "0-534-42441-4",
ISBN-13 = "978-0-534-42441-1",
LCCN = "QA273 .D865 2005",
bibdate = "Mon Nov 21 10:00:11 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Duxbury advanced series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 337ff. Hill \cite[page
893]{Hill:1995:BII} reports that the 1991 edition has a
proof that the $k$-th digit of powers of integers
follows Benford's Law.",
subject = "Probabilities",
}
@Book{Egghe:2005:PLI,
author = "Leo Egghe",
title = "Power laws in the information production process:
{Lotkaian} informetrics",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xvii + 427",
year = "2005",
ISBN = "0-12-088753-3, 0-08-048011-X (e-book)",
ISBN-13 = "978-0-12-088753-8, 978-0-08-048011-4 (e-book)",
LCCN = "Z669.8 .E44 2005",
bibdate = "Mon Feb 25 10:42:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See pages 204--205 for Benford's Law discussion.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject-dates = "Lotka, Alfred James, (1880--1949)",
tableofcontents = "Basic theory of Lotkaian informetrics \\
Three-dimensional Lotkaian informetrics \\
Lotkaian concentration theory \\
Lotkaian fractal complexity theory \\
Lotkaian informetrics of systems in which items can
have multiple sources \\
Further applications in Lotkaian informetrics \\
Lotkaian informetrics: an introduction",
}
@Article{Egghe:2005:PPL,
author = "L. Egghe",
title = "The power of power laws and an interpretation of
{Lotkaian} informetric systems as self-similar
fractals",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "56",
number = "7",
pages = "669--675",
month = may,
year = "2005",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20158",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:27 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "16 Mar 2005",
}
@Article{Egghe:2005:RBC,
author = "L Egghe",
title = "Relations between the continuous and the discrete
{Lotka} power function",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "56",
number = "7",
pages = "664--668",
month = may,
year = "2005",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20157",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:27 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "11 Mar 2005",
}
@Article{Egghe:2005:ZLC,
author = "L. Egghe",
title = "{Zipfian} and {Lotkaian} continuous concentration
theory",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "56",
number = "9",
pages = "935--945",
month = jul,
year = "2005",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20186",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:28 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "21 Apr 2005",
}
@Article{elSehity:2005:PDA,
author = "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
title = "Price developments after a nominal shock: {Benford's
Law} and psychological pricing after the euro
introduction",
journal = j-INT-J-RES-MARK,
volume = "22",
number = "4",
pages = "471--480",
month = dec,
year = "2005",
CODEN = "IJRME6",
DOI = "https://doi.org/10.1016/j.ijresmar.2005.09.002",
ISSN = "0167-8116 (print), 1873-8001 (electronic)",
ISSN-L = "0167-8116",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
abstract = "Retail managers use psychological pricing to make the
prices of goods appear to be just below a round number.
The euro introduction in 2002, with its various
exchange rates, distorted existing nominal price
patterns while at the same time retaining real prices.
We studied consumer prices before and after the
introduction of the euro by using Benford's Law as a
benchmark for price adjustments. Results indicate the
usefulness of this benchmark for detecting
irregularities in prices, and a clear trend towards
psychological pricing after the nominal shock of the
euro introduction. In addition, the tendency towards
psychological prices results in different inflation
rates in dependence of the price pattern.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Research in Marketing",
keywords = "Benford's Law; Digital analysis; Price endings; Retail
pricing",
}
@Article{Fairthorne:2005:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "171--193",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/00220410510585179",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Fairthorne:1969:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Article{FerreriCancho:2005:CZL,
author = "Ramon {Ferrer i Cancho} and Oliver Riordan and
B{\'e}la Bollob{\'a}s",
title = "The consequences of {Zipf}'s law for syntax and
symbolic reference",
journal = j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
volume = "272",
number = "1562",
pages = "561--565",
day = "7",
month = mar,
year = "2005",
CODEN = "PRLBA4",
DOI = "https://doi.org/10.1098/rspb.2004.2957",
ISSN = "0962-8452 (print), 1471-2954 (electronic)",
ISSN-L = "0962-8452",
bibdate = "Tue Nov 15 11:27:26 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series B.
Biological sciences",
}
@TechReport{Giles:2005:BLN,
author = "David E. Giles",
title = "{Benford's Law} and Naturally Occurring Prices in
Certain {ebaY} Auctions",
type = "Econometrics Working Paper",
number = "EWP0505",
institution = "Department of Economics, University of Victoria",
address = "Victoria, BC, Canada",
month = may,
year = "2005",
ISSN = "1485-6441",
bibdate = "Thu Feb 15 16:24:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://web.uvic.ca/econ/ewp0505.pdf",
abstract = "We show that certain the winning bids for certain ebaY
auctions obey Benford's Law. One implication of this is
that it is unlikely that these bids are subject to
collusion among bidders, or ``shilling'' on the part of
sellers. Parenthetically, we also show that numbers
from the naturally occurring Fibonacci and Lucas
sequences also obey Benford's Law.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Harremoes:2005:ZLHa,
author = "Peter Harremo{\"e}s and Flemming Topsoe",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
journal = j-PHYSICA-A,
volume = "328",
number = "3--4",
pages = "315--318",
day = "1",
month = aug,
year = "2005",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.endm.2005.07.075",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1571065305051450",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@InCollection{Harremoes:2005:ZLHb,
author = "Peter Harremo{\"e}s and Flemming Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics.",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "21",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "315--318",
year = "2005",
DOI = "https://doi.org/10.1016/j.endm.2005.07.075",
bibdate = "Sat Nov 12 11:07:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Electronic Notes in Discrete Mathematics",
ZMnumber = "1158.91482",
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
}
@Article{Hill:2005:RDS,
author = "Theodore P. Hill and Klaus Sch{\"u}rger",
title = "Regularity of digits and significant digits of random
variables",
journal = j-STOCH-PROC-APPL,
volume = "115",
number = "10",
pages = "1723--1743",
month = oct,
year = "2005",
CODEN = "STOPB7",
DOI = "https://doi.org/10.1016/j.spa.2005.05.003",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
abstract = "A random variable X is digit-regular (respectively,
significant-digit-regular) if the probability that
every block of $k$ given consecutive digits
(significant digits) appears in the b-adic expansion of
$X$ approaches $ b - k$ as the block moves to the
right, for all integers $ b > 1$ and $ k \geq 1$.
Necessary and sufficient conditions are established, in
terms of convergence of Fourier coefficients, and in
terms of convergence in distribution modulo 1, for a
random variable to be digit-regular
(significant-digit-regular), and basic relationships
between digit-regularity and various classical classes
of probability measures and normal numbers are given.
These results provide a theoretical basis for analyses
of roundoff errors in numerical algorithms which use
floating-point arithmetic, and for detection of fraud
in numerical data via using goodness-of-fit of the
least significant digits to uniform, complementing
recent tests for leading significant digits based on
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03044149",
keywords = "Benford's Law; Digit-regular random variable;
Floating-point numbers; Law of least significant
digits; Nonleading digits; Normal numbers; Significant
digits; Significant-digit-regular random variable;
Trailing digits",
}
@InProceedings{Hjorland:2005:BLS,
author = "Birger Hj{\o}rland and Jeppe Nicolaisen",
editor = "Fabio Crestani and Ian Ruthven",
booktitle = "Context: nature, impact, and role: {5th International
Conference on Conceptions of Library and Information
Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
proceedings}",
title = "{Bradford}'s law of scattering: ambiguities in the
concept of ``subject''",
volume = "3507",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xiii + 250",
pages = "96--106",
year = "2005",
ISBN = "3-540-26178-8",
ISBN-13 = "978-3-540-26178-0",
LCCN = "Z672.5 .I5616 2005",
bibdate = "Fri Nov 25 11:52:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Article{Ioannidis:2005:WMP,
author = "John P. A. Ioannidis",
title = "Why Most Published Research Findings Are False",
journal = j-PLOS-MED,
volume = "2",
number = "8",
pages = "696--701",
month = aug,
year = "2005",
CODEN = "PMLEAC",
DOI = "https://doi.org/10.1371/journal.pmed.0020124",
ISSN = "1549-1277 (print), 1549-1676 (electronic)",
ISSN-L = "1549-1277",
bibdate = "Fri Nov 18 12:42:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
abstract = "There is increasing concern that most current
published research findings are false. The probability
that a research claim is true may depend on study power
and bias, the number of other studies on the same
question, and, importantly, the ratio of true to no
relationships among the relationships probed in each
scientific field. In this framework, a research finding
is less likely to be true when the studies conducted in
a field are smaller; when effect sizes are smaller;
when there is a greater number and lesser preselection
of tested relationships; where there is greater
flexibility in designs, definitions, outcomes, and
analytical modes; when there is greater financial and
other interest and prejudice; and when more teams are
involved in a scientific field in chase of statistical
significance. Simulations show that for most study
designs and settings, it is more likely for a research
claim to be false than true. Moreover, for many current
scientific fields, claimed research findings may often
be simply accurate measures of the prevailing bias. In
this essay, I discuss the implications of these
problems for the conduct and interpretation of
research.",
acknowledgement = ack-nhfb,
articleno = "e124",
fjournal = "PLoS Medicine",
journal-URL = "http://medicine.plosjournals.org/",
remark = "This article does not discuss Benford's Law, but is
related to the use of that law in the detection of
fraud in research data. Ioannidis discusses the abuse
of statistics for limited experimental data, a topic
that receives book-length treatment in
\cite{Ziliak:2008:CSS}.",
}
@Article{Jolissaint:2005:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
Law, recurrence relations, and equidistributed
sequences]",
journal = j-ELEM-MATH,
volume = "60",
number = "1",
pages = "10--18",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.4171/EM/2",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "11K36 (37A45 60E99)",
MRnumber = "2188341 (2006j:11109)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Kechedzhi:2005:RDW,
author = "K. E. Kechedzhi and O. V. Usatenko and V. A.
Yampol{\cprime}skii",
title = "Rank distributions of words in correlated symbolic
systems and the {Zipf} law",
journal = j-PHYS-REV-E,
volume = "72",
number = "4",
pages = "046138",
day = "28",
month = oct,
year = "2005",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.72.046138",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82C31",
MRnumber = "2183723 (2006f:82069)",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.72.046138",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "6",
}
@Article{Kontorovich:2005:BLV,
author = "Alex V. Kontorovich and Steven J. Miller",
title = "{Benford}'s law, values of {$L$}-functions and the {$
3 x + 1 $} problem",
journal = j-ACTA-ARITHMETICA,
volume = "120",
number = "3",
pages = "269--297",
year = "2005",
CODEN = "AARIA9",
DOI = "https://doi.org/10.4064/aa120-3-4",
ISSN = "0065-1036 (print), 1730-6264 (electronic)",
ISSN-L = "0065-1036",
MRclass = "11K06 (11B37 11M06 37A45)",
MRnumber = "2188844 (2007c:11085)",
MRreviewer = "J. C. Lagarias",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
http://arxiv.org/abs/math/0412003",
abstract = "We show the leading digits of a variety of systems
satisfying certain conditions follow Benford's Law. For
each system proving this involves two main ingredients.
One is a structure theorem of the limiting
distribution, specific to the system. The other is a
general technique of applying Poisson Summation to the
limiting distribution. We show the distribution of
values of $L$-functions near the central line and (in
some sense) the iterates of the $ 3 x + 1 $ Problem are
Benford.",
acknowledgement = ack-nhfb,
fjournal = "Acta Arithmetica",
}
@Article{Kulikova:2005:CAS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "Completely Asymmetric Stable Laws and {Benford's
Law}",
journal = j-THEORY-PROBAB-APPL,
volume = "49",
number = "1",
pages = "163--169",
month = mar,
year = "2005",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/S0040585X97980944",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Thu Jul 7 19:15:48 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/98094",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
journal-URL = "http://epubs.siam.org/tvp",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Kulikova:2005:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H. F. D.} ({$H$}-function distribution) and the
{Benford} law. {I}",
journal = "Teor. Veroyatn. Primen.",
volume = "50",
number = "2",
pages = "366--371",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1137/S0040585X97981706",
ISSN = "0040-361X",
ISSN-L = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2221718 (2007b:60029)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Lagarias:2005:BLF,
author = "J. C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $ 3 x + 1 $ function",
journal = "ArXiv Mathematics e-prints",
month = sep,
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......9175L;
http://arxiv.org/abs/math/0509175",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0509175",
keywords = "Mathematics - Number Theory, Mathematics -
Probability",
}
@Article{Li:2005:ZLP,
author = "Yujian Li and Chuangbai Xiao",
title = "{Zipf}'s law probably existing in protein sequences",
journal = "J. Beijing Univ. Technol.",
volume = "31",
number = "4",
pages = "366--368",
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 11:10:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1084.92019",
abstract = "In order to analyze whether Zipf's law in linguistics
exists in protein sequences, this paper uses $ 1.735 \,
7 \times 10^4 $ protein sequences labeled with
secondary structures which are selected from the DSSP
database. The segments of successive amino acid
residues with a same code of secondary structure are
defined as words. The results show that the
distribution of words emerging frequency follows Zipf's
law with the exponent $ 0.981 $.",
acknowledgement = ack-nhfb,
classmath = "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
to biology): 92D20 (Protein sequences, DNA sequences)",
language = "Chinese. English summary",
xxremark = "Which journal is this? Beijing gong ye da xue xue bao
= Journal of Beijing Polytechnic University (ISSN
0254-0037), or Beijing ke ji da xue xue bao = Journal
of University of Science and Technology, Beijing (ISSN
1001-053X), or something different?",
}
@Article{Lu:2005:CZL,
author = "Tim Lu and Christine M. Costello and Peter J. P.
Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl
and Stefan Schreiber",
title = "Can {Zipf}'s law be adapted to normalize
microarrays?",
journal = j-BMC-BIOINFORMATICS,
volume = "6",
number = "??",
pages = "37--49",
month = "????",
year = "2005",
CODEN = "BBMIC4",
DOI = "https://doi.org/10.1186/1471-2105-6-37",
ISSN = "1471-2105",
ISSN-L = "1471-2105",
bibdate = "Sat Feb 16 18:38:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1186/1471-2105-6-37;
http://www.biomedcentral.com/1471-2105/6/37",
acknowledgement = ack-nhfb,
fjournal = "BMC Bioinformatics",
journal-URL = "http://www.biomedcentral.com/bmcbioinformatics/",
}
@InProceedings{Lu:2005:DFH,
author = "Fletcher Lu and J. Efrim Boritz",
title = "Detecting Fraud in Health Insurance Data: Learning to
Model Incomplete {Benford's Law} Distributions",
crossref = "Gama:2005:MLE",
pages = "633--640",
year = "2005",
DOI = "https://doi.org/10.1007/11564096_63",
bibdate = "Tue Nov 15 08:55:45 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
URL = "http://link.springer.com/chapter/10.1007/11564096_63",
acknowledgement = ack-nhfb,
}
@Article{Ma:2005:CBL,
author = "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel
and J. Wang and T. Keutgen and Z. Majka and M. Murray
and L. Qin and P. Smith and R. Alfaro and J. Cibor and
M. Cinausero and Y. El Masri and D. Fabris and E.
Fioretto and A. Keksis and M. Lunardon and A. Makeev
and N. Marie and E. Martin and A. Martinez-Davalos and
A. Menchaca-Rocha and G. Nebbia and G. Prete and V.
Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis
and P. Staszel and M. Veselsky and G. Viesti and E. M.
Winchester and S. J. Yennello",
title = "Critical behavior in light nuclear systems:
Experimental aspects",
journal = j-PHYS-REV-C,
volume = "71",
number = "5",
pages = "054606",
day = "26",
month = may,
year = "2005",
CODEN = "PRVCAN",
DOI = "https://doi.org/10.1103/PhysRevC.71.054606",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.71.054606",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Manaris:2005:ZLM,
author = "Bill Manaris and Juan Romero and Penousal Machado and
Dwight Krehbiel and Timothy Hirzel and Walter Pharr and
Robert B. Davis",
title = "{Zipf}'s law, music classification, and aesthetics",
journal = j-COMP-MUSIC-J,
volume = "29",
number = "1",
pages = "55--69",
month = "Spring",
year = "2005",
CODEN = "CMUJDY",
ISSN = "0148-9267 (print), 1531-5169 (electronic)",
ISSN-L = "0148-9267",
bibdate = "Sat Feb 16 18:40:14 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html;
http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer Music Journal",
keywords = "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law",
}
@Article{Martinson:2005:SBB,
author = "Brian C. Martinson and Melissa S. Anderson and Raymond
de Vries",
title = "Scientists Behaving Badly",
journal = j-NATURE,
volume = "435",
number = "7043",
pages = "737--738",
day = "9",
month = jun,
year = "2005",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1007/s00221-007-0889-0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sat Sep 10 13:14:54 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v435/n7043/pdf/435737a.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law",
remark = "No mention of Benford's Law or first digit phenomenon,
but nevertheless relevant for applications of Benford's
Law to detection of fraud in science.",
}
@Article{Maslov:2005:GTS,
author = "V. P. Maslov",
title = "On a general theorem of set theory that leads to the
{Gibbs}, {Bose--Einstein}, and {Pareto} distributions
and to the {Zipf--Mandelbrot} law for the stock
market",
journal = j-MAT-ZAMETKI,
volume = "78",
number = "6",
pages = "870--877",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11006-005-0186-9",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "91B28 (90C29)",
MRnumber = "2249037 (2007b:91077)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
journal-URL = "http://link.springer.com/journal/11006",
}
@Article{Maslov:2005:RZLa,
author = "V. P. Maslov",
title = "Refining {Zipf}'s law for frequency dictionaries",
journal = j-DOKL-AKAD-NAUK,
volume = "405",
number = "5",
pages = "591--594",
year = "2005",
CODEN = "DANKAS",
ISSN = "0869-5652",
ISSN-L = "0869-5652",
MRclass = "94A15 (60C05)",
MRnumber = "2340762",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
journal-URL = "http://istina.msu.ru/journals/366838/",
}
@Article{Maslov:2005:RZLb,
author = "V. P. Maslov",
title = "Refinement of {Zipf}'s law for frequency
dictionaries",
journal = j-DOKL-MATH,
volume = "72",
number = "3",
pages = "942--945",
year = "2005",
CODEN = "????",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:05:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1206.82009",
acknowledgement = ack-nhfb,
classmath = "82B10 (Quantum equilibrium statistical mechanics
(general)) 68T50 (Natural language processing) 68Q45
(Formal languages)",
fjournal = "Doklady Mathematics",
journal-URL = "http://link.springer.com/journal/11472",
keywords = "Bose--Einstein statistics",
language = "English. Russian original",
}
@Article{Maslov:2005:ZML,
author = "V. P. Maslov",
title = "The {Zipf--Mandelbrot} law: quantization and an
application to the stock market",
journal = j-RUSS-J-MATH-PHYS,
volume = "12",
number = "4",
pages = "483--488",
year = "2005",
CODEN = "RJMPEL",
ISSN = "1061-9208 (print), 1555-6638 (electronic)",
ISSN-L = "1061-9208",
MRclass = "91B28 (82B99)",
MRnumber = "2201312 (2006i:91053)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Russian Journal of Mathematical Physics",
}
@Article{McAllister:2005:ACE,
author = "James W. McAllister",
title = "Algorithmic compression of empirical data: reply to
{Twardy}, {Gardner}, and {Dowe}",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "403--410",
month = jun,
year = "2005",
CODEN = "SHPSB5",
DOI = "https://doi.org/10.1016/j.shpsa.2005.04.005",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
}
@Article{McCowan:2005:AUZ,
author = "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F.
Hanser",
title = "The appropriate use of {Zipf}'s law in animal
communication studies",
journal = j-ANIM-BEHAV,
volume = "69",
number = "1",
pages = "F1--F7",
day = "20",
month = jan,
year = "2005",
CODEN = "ANBEA8",
DOI = "https://doi.org/10.1016/j.anbehav.2004.09.002",
ISSN = "0003-3472 (print), 1095-8282 (electronic)",
ISSN-L = "0003-3472",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S000334720400346X",
acknowledgement = ack-nhfb,
fjournal = "Animal Behaviour",
journal-URL = "http://www.sciencedirect.com/science/journal/00033472",
keywords = "Zipf's Law",
}
@Article{Miller:2005:BLV,
author = "Steven J. Miller and A. Kontorovich",
title = "{Benford}'s law, values of {$L$}-functions and the $ 3
x + 1 $ problem",
journal = j-ACTA-ARITHMETICA,
volume = "120",
number = "3",
pages = "269--297",
month = "????",
year = "2005",
CODEN = "AARIA9",
DOI = "https://doi.org/10.4064/aa120-3-4",
ISSN = "0065-1036 (print), 1730-6264 (electronic)",
ISSN-L = "0065-1036",
MRclass = "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65,
46F12)",
bibdate = "Tue Feb 26 06:11:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Arithmetica",
}
@InProceedings{Nagasaka:2005:BLD,
author = "Kenji Nagasaka",
editor = "G. Barat and H. Daud{\'e} and M. Laurent and P.
Liardet and S. Louboutin and A. Thomas",
booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July
4--8, 2005, Universit{\'e} de Provence and
Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS
Marseilles, France}",
title = "{Benford}'s law with different basis",
publisher = "????",
address = "????",
pages = "1--2",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 18:49:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://atlas-conferences.com/c/a/r/e/47.htm",
acknowledgement = ack-nhfb,
}
@Article{Newman:2005:PLP,
author = "M. E. J. Newman",
title = "Power laws, {Pareto} distributions and {Zipf}'s law",
journal = j-CONTEMP-PHYS,
volume = "46",
number = "5",
pages = "323--351",
month = sep,
year = "2005",
CODEN = "CTPHAF",
DOI = "https://doi.org/10.1080/00107510500052444",
ISSN = "0010-7514 (print), 1366-5812 (electronic)",
ISSN-L = "0010-7514",
bibdate = "Thu Feb 18 20:07:22 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/contempphys.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When the probability of measuring a particular value
of some quantity varies inversely as a power of that
value, the quantity is said to follow a power law, also
known variously as Zipf's law or the Pareto
distribution. Power laws appear widely in physics,
biology, earth and planetary sciences, economics and
finance, computer science, demography and the social
sciences. For instance, the distributions of the sizes
of cities, earthquakes, forest fires, solar flares,
moon craters and people's personal fortunes all appear
to follow power laws. The origin of power-law behaviour
has been a topic of debate in the scientific community
for more than a century. Here we review some of the
empirical evidence for the existence of power-law forms
and the theories proposed to explain them.",
acknowledgement = ack-nhfb,
fjournal = "Contemporary Physics",
journal-URL = "http://www.tandfonline.com/loi/tcph20",
keywords = "Benford's Law; critical phenomena; Legendre beta
function; Pareto distribution; percolation; phase
transitions; power-law distributions; random walks;
Riemann zeta function; scale-free distributions; Yule
process; Zipf's Law",
remark = "This article is an excellent survey of continuous and
discrete distributions that follow a power law, and
some that do not. It is well worth reading.",
subject = "astrophysics; atomic and nuclear physics; chemical
physics; computational physics; condensed matter
physics; environmental physics; experimental physics;
general physics; particle and high energy physics;
plasma physics; space science; theoretical physics",
}
@Article{Nigrini:2005:ACI,
author = "Mark Nigrini",
title = "An assessment of the change in the incidence of
earnings management around the {Enron--Andersen}
episode",
journal = "Review of Accounting and Finance",
volume = "4",
number = "1",
pages = "92--110",
month = "????",
year = "2005",
DOI = "https://doi.org/10.1108/eb043420",
ISSN = "1475-7702 (print), 1758-7700 (electronic)",
ISSN-L = "1475-7702",
bibdate = "Fri Mar 22 09:08:37 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=1475-7702&volume=4&issue=1&articleid=1657234",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Article{Nitsch:2005:ZZ,
author = "Volker Nitsch",
title = "{Zipf} zipped",
journal = j-J-URBAN-ECON,
volume = "57",
number = "1",
pages = "86--100",
day = "15",
month = jan,
year = "2005",
CODEN = "JUECDW",
DOI = "https://doi.org/10.1016/j.jue.2004.09.002",
ISSN = "0094-1190 (print), 1095-9068 (electronic)",
ISSN-L = "0094-1190",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0094119004000981",
acknowledgement = ack-nhfb,
fjournal = "Journal of Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/00941190",
keywords = "Zipf's Law",
}
@Article{Perline:2005:SWF,
author = "Richard Perline",
title = "Strong, weak and false inverse power laws",
journal = j-STAT-SCI,
volume = "20",
number = "1",
pages = "68--88",
month = "????",
year = "2005",
CODEN = "STSCEP",
ISSN = "0883-4237 (print), 2168-8745 (electronic)",
ISSN-L = "0883-4237",
bibdate = "Fri Nov 18 12:15:56 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
keywords = "Benford's Law",
}
@Book{Posch:2005:ZTP,
author = "Peter N. Posch",
title = "{Ziffernanalyse in Theorie und Praxis: Testverfahren
zur F{\"a}lschungsaufsp{\"u}rung mit Benfords Gesetz}",
publisher = "Shaker",
address = "Aachen, Germany",
pages = "iv + 87 + v",
year = "2005",
ISBN = "3-8322-4492-1",
ISBN-13 = "978-3-8322-4492-7",
LCCN = "????",
bibdate = "Mon Feb 18 18:01:33 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
price = "EUR 29.80 (DE)",
series = "Berichte aus der Statistik",
URL = "http://www.gbv.de/dms/hbz/toc/ht014717371.pdf",
acknowledgement = ack-nhfb,
}
@Article{Rousseau:2005:RFE,
author = "Ronald Rousseau",
title = "{Robert Fairthorne} and the empirical power laws",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "194--202",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/00220410510585188",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:42:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
remark = "Review of
\cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.",
}
@Article{Rowlands:2005:EAD,
author = "Ian Rowlands",
title = "{Emerald} authorship data, {Lotka}'s law and research
productivity",
journal = j-ASLIB-PROC,
volume = "57",
number = "1",
pages = "5--10",
month = "????",
year = "2005",
CODEN = "ASLPAO",
DOI = "https://doi.org/10.1108/00012530510579039",
ISSN = "0001-253X (print), 1758-3748 (electronic)",
ISSN-L = "0001-253X",
bibdate = "Fri Nov 25 07:25:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "ASLIB Proceedings",
keywords = "brand loyalty; publishing; research results",
remark = "This paper applies Lotka's Law to the question of the
likelihood of an author remaining with a particular
publisher.",
}
@Article{Schaefer:2005:AIF,
author = "Christin Schaefer and J{\"o}rg-Peter Schr{\"a}pler and
Klaus-Robert M{\"u}ller and Gert G. Wagner",
title = "Automatic Identification of Faked and Fraudulent
Interviews in the {German SOEP}",
journal = "Journal of Applied Social Science Studies",
volume = "125",
number = "??",
pages = "183--193",
month = "",
year = "2005",
DOI = "",
bibdate = "Sat Sep 10 14:35:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.diw.de/documents/publikationen/73/diw_01.c.42515.de/dp441.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; SOEP (German Socio-Economic Panel
Study)",
remark = "Cannot find online archive of this journal: Web links
to it are dead.",
}
@Article{Shan:2005:GZD,
author = "Shi Shan",
title = "On the generalized {Zipf} distribution. {Part I}",
journal = j-INFO-PROC-MAN,
volume = "41",
number = "6",
pages = "1369--1386",
day = "1",
month = dec,
year = "2005",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/j.ipm.2005.03.003",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S030645730500018X",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
keywords = "Zipf's Law",
}
@Article{Soo:2005:ZLC,
author = "Kwok Tong Soo",
title = "{Zipf's Law} for cities: a cross-country
investigation",
journal = j-REG-SCI-URBAN-ECON,
volume = "35",
number = "3",
pages = "239--263",
day = "1",
month = may,
year = "2005",
CODEN = "RSUEDM",
DOI = "https://doi.org/10.1016/j.regsciurbeco.2004.04.004",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016604620400033X",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Stadje:2005:APD,
author = "Wolfgang Stadje",
title = "Asymptotic properties of digit sequences of random
numbers",
journal = j-MATH-NACHR,
volume = "278",
number = "10",
pages = "1209--1229",
month = "????",
year = "2005",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.200310303",
ISSN = "0025-584X",
ISSN-L = "0025-584X",
bibdate = "Mon Feb 18 06:36:36 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1073.11053",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
keywords = "ergodicity; limit theorem; Markov chain; moments;
occurrence probability; random digit sequence;
stationary digits; transition function",
ZMclass = "11K31 (Special sequences); 60G10 (Stationary
processes); 60J05 (Discrete-time Markov processes on
general state spaces); 60F99 (Limit theorems
(probability))",
}
@TechReport{Taylor:2005:TMT,
author = "Jonathan Taylor",
title = "Too many ties? {An} empirical analysis of the
{Venezuelan} recall referendum counts",
type = "Technical report",
number = "??",
institution = "Department of Statistics, Stanford University",
address = "Stanford, CA 94305, USA",
year = "2005",
bibdate = "Fri Feb 15 18:29:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://esdata.info/pdf/Taylor-Ties.pdf;
http://www.benfordonline.net/fullreference/577",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Pericchi:2011:QAD}, with ``Statist.
Sci. To appear 2009''. However, the article is not yet
found there in February 2013. This report was issued as
a result of the Carter Center's investigation of
fairness of 2004 voting in Venezuela. Its conclusion,
that there was no demonstrable electoral fraud, has
been challenged; see \cite{Pericchi:2011:QAD}.",
}
@Article{Twardy:2005:EDS,
author = "Charles Twardy and Steve Gardner and David L. Dowe",
title = "Empirical data sets are algorithmically compressible:
reply to {McAllister}?",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "391--402",
month = jun,
year = "2005",
CODEN = "SHPSB5",
DOI = "https://doi.org/10.1016/j.shpsa.2005.04.004",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S003936810500021X",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
journal-URL = "http://www.sciencedirect.com/science/journal/00393681",
}
@Article{vanLeijenhorst:2005:FDH,
author = "D. C. van Leijenhorst and Th. P. van der Weide",
title = "A formal derivation of {Heaps}' law",
journal = j-INFO-SCI,
volume = "170",
number = "2--4",
pages = "263--272",
year = "2005",
CODEN = "ISIJBC",
DOI = "https://doi.org/10.1016/j.ins.2004.03.006",
ISSN = "0020-0255 (print), 1872-6291 (electronic)",
ISSN-L = "0020-0255",
MRclass = "60C05",
MRnumber = "2120894 (2005h:60024)",
bibdate = "Sat Nov 12 10:28:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Word frequencies in text documents can be reasonably
described by the Mandelbrot distribution, which has
Zipf's law as a special case. Furthermore, the growth
of vocabulary size as a function of the text size (its
number of words) has been described in Heaps' law. It
has been shown that these two experimental laws are
related. In this paper we go a step further, and
provide a (formal) derivation of Heaps' law from the
Mandelbrot distribution. We also provide a
specification of the validity area for applying Heaps'
law.",
acknowledgement = ack-nhfb,
ajournal = "Inform. Sci.",
fjournal = "Information Sciences. An International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/00200255",
}
@Book{Wells:2005:PNM,
author = "D. G. (David G.) Wells",
title = "Prime Numbers: the Most Mysterious Figures in Math",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 272",
year = "2005",
ISBN = "0-471-46234-9 (hardcover), 0-471-71892-0 (ebook)",
ISBN-13 = "978-0-471-46234-7 (hardcover), 978-0-471-71892-5
(e-book)",
LCCN = "QA246 .W35 2005",
bibdate = "Wed Feb 21 14:25:53 MST 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0616/2004019974-b.html;
http://www.loc.gov/catdir/enhancements/fy0616/2004019974-d.html;
http://www.loc.gov/catdir/toc/ecip0422/2004019974.html",
abstract = "A fascinating journey into the mind-bending world of
prime numbers Cicadas of the genus Magicicada appear
once every 7, 13, or 17 years. Is it just a coincidence
that these are all prime numbers? How do twin primes
differ from cousin primes, and what on earth (or in the
mind of a mathematician) could be sexy about prime
numbers? What did Albert Wilansky find so fascinating
about his brother-in-law's phone number? Mathematicians
have been asking questions about prime numbers for more
than twenty-five centuries, and every answer seems to
generate a new rash of questions. In Prime Numbers: The
Most Mysterious Figures in Math, you'll meet the
world's most gifted mathematicians, from Pythagoras and
Euclid to Fermat, Gauss, and Erd{\H{o}}s, and you'll
discover a host of unique insights and inventive
conjectures that have both enlarged our understanding
and deepened the mystique of prime numbers. This
comprehensive, A-to-Z guide covers everything you ever
wanted to know-and much more that you never
suspected-about prime numbers, including: the unproven
Riemann hypothesis and the power of the zeta function,
the ``Primes is in P'' algorithm, the sieve of
Eratosthenes of Cyrene, Fermat and Fibonacci numbers,
the Great Internet Mersenne Prime Search, and much,
much more.",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "Introduction \\
List of Entries \\
abc conjecture \\
abundant number \\
AKS algorithm for primality testing \\
aliquot sequences (sociable chains) \\
almost-primes \\
amicable numbers \\
amicable curiosities \\
Andrica's conjecture \\
arithmetic progressions, of primes \\
Aurifeuillian factorization \\
average prime \\
Bang's theorem \\
Bateman's conjecture \\
Beal's conjecture, and prize \\
Benford's law \\
Bernoulli numbers \\
Bernoulli number curiosities \\
Bertrand's postulate \\
Bonse's inequality \\
Brier numbers \\
Brocard's conjecture \\
Brun's constant \\
Buss's function \\
Carmichael numbers \\
Catalan's conjecture \\
Catalan's Mersenne conjecture \\
Champion numbers \\
Chinese remainder theorem \\
cicadas and prime periods \\
circle, prime \\
circular prime \\
Clay prizes, the \\
compositorial \\
concatenation of primes \\
conjectures \\
consecutive integer sequence \\
consecutive numbers \\
consecutive primes, sums of \\
Conway's prime-producing machine \\
cousin primes \\
Cullen primes \\
Cunningham project \\
Cunningham chains \\
decimals, recurring (periodic) \\
deficient number \\
deletable and truncatable primes \\
Demlo numbers \\
descriptive primes \\
Dickson's conjecture \\
digit properties \\
Diophantus (c.200: died 284) \\
Dirichlet's theorem and primes in arithmetic series \\
distributed computing \\
divisibility tests \\
divisors (factors) \\
economical numbers \\
Electronic Frontier Foundation \\
elliptic curve primality proving \\
emirp \\
Eratosthenes of Cyrene, the sieve of \\
Erd{\H{o}}s, Paul (1913--1996) \\
errors \\
Euclid \\
Unique factorisation \\
$\sqrt{2}$ is irrational \\
Euclid and the infinity of primes \\
Consecutive composite numbers \\
Primes of the form $4 n + 3$ \\
A recursive sequence \\
Euclid and the first perfect number \\
Euclidean algorithm \\
Euler, Leonhard (1707--1783) \\
Euler's convenient numbers \\
The Basel problem \\
Euler's constant \\
Euler and the reciprocals of the primes \\
Euler's phi [totient] function \\
Carmichael's totient function conjecture \\
Curiosities of $\phi(n)$ \\
Euler's quadratic \\
The Lucky Numbers of Euler \\
factorial \\
factors of factorials \\
factorial primes \\
factorial sums \\
factorials, double, triple, \ldots{} \\
factorization, methods of \\
factors of particular forms \\
Fermat's algorithm \\
Legendre's method \\
How difficult is it to factor large numbers? \\
quantum computation \\
Feit--Thompson conjecture \\
Fermat Pierre de (1607--1665) \\
Fermat's Little Theorem \\
Fermat quotient \\
Fermat and primes of the form $x^2 + y^2$ \\
Fermat's conjecture, Fermat numbers and Fermat primes
\\
Fermat factorisation, from $F_6$ to $F_{30}$ \\
Generalized Fermat numbers \\
Fermat's Last Theorem \\
The first case of Fermat's Last Theorem: \\
Wall--Sun--Sun primes \\
Fermat--Catalan equation and conjecture \\
Fibonacci numbers \\
divisibility properties \\
Fibonacci curiosities \\
{\'E}douard Lucas and the Fibonacci numbers \\
Fibonacci composite sequences \\
formulae for primes \\
Fortunate numbers and Fortune's conjecture \\
gaps between primes, and composite runs \\
Gauss Johann Carl Friedrich (1777--1855) \\
Gauss and the distribution of primes \\
Gaussian primes \\
Gauss's circle problem \\
Gilbreath conjecture \\
GIMPS = Great Internet Mersenne Primes Search \\
Giuga's conjecture \\
Giuga numbers \\
Goldbach's conjecture \\
good primes \\
graph, prime number \\
Grimm's problem \\
Hardy, G. H. (1877--1947) \\
Hardy--Littlewood conjectures \\
heuristic reasoning \\
Hilbert's 23 problems \\
home prime \\
hypothesis H \\
illegal prime \\
inconsummate number \\
induction jumping champion \\
$k$-tuples conjecture, prime \\
knots, prime and composite \\
Landau, Edmund (1877--1938) \\
left-truncatable prime \\
Legendre A. M. (1752--1833) \\
Legendre's theorem (1808) \\
Lehmer, Derrick Norman (1867--1938) \\
Lehmer, Derrick Henry (1905--1991) \\
Linnik's constant \\
Liouville, Joseph (1809--1882) \\
Littlewood's theorem \\
the prime numbers race \\
Look and Say sequence \\
Lucas, {\'E}douard (1842--1891) \\
the Lucas sequence \\
primality testing \\
Lucas's game of calculation \\
the Lucas--Lehmer test \\
lucky numbers \\
the number of Lucky numbers and primes \\
`random' primes' \\
magic squares \\
Matijasevic and Hilbert's 10th problem \\
Mersenne numbers and Mersenne primes \\
Mersenne numbers \\
hunting for Mersenne primes \\
the coming of electronic computers \\
Mersenne prime conjectures \\
the New Mersenne Conjecture \\
how many Mersenne primes? \\
Eberhart's conjecture \\
factors of Mersenne Numbers \\
Lucas--Lehmer test for Mersenne primes \\
Mertens' theorem \\
Mertens' constant \\
Mill's theorem \\
Wright's theorem \\
mixed bag \\
multiplication, fast \\
Niven Numbers \\
odd numbers as $p + 2 a^2$ \\
Opperman's conjecture \\
palindromic primes \\
pandigital primes \\
Pascal's Triangle and the binomial coefficients \\
Pascal's triangle and Sierpinski's gasket \\
Pascal triangle curiosities \\
patents on prime numbers \\
P{\'e}pin's test for Fermat numbers \\
perfect numbers \\
odd perfect numbers \\
perfect, multiply \\
permutable primes \\
$o$, primes in the decimal expansion of \\
Pocklington's theorem \\
Polignac's conjectures \\
Polignac or obstinate numbers \\
powerful numbers \\
consecutive powerful numbers \\
primality testing \\
probabilistic methods \\
prime number graph \\
prime number theorem and the prime counting function
\\
history \\
elementary proof \\
record calculations \\
estimating $p(n)$ \\
calculating $p(n)$ \\
a curiosity \\
prime pretender \\
primitive prime factor \\
primitive roots \\
Artin's conjecture \\
a curiosity \\
primorial \\
primorial primes \\
Proth's Theorem \\
pseudoperfect numbers \\
bases and pseudpoprimes \\
pseudoprimes, strong \\
public key encryption \\
pyramid, prime \\
Pythagorean triangles, prime \\
quadratic residues \\
residual curiosities \\
polynomial congruences \\
quadratic reciprocity, law of \\
Euler's criterion \\
Ramanujan, Srinivasa (1887--1920) \\
Highly Composite Numbers \\
randomness, of primes \\
Von Sternach and a prime random walk \\
record primes \\
some records \\
repunits, prime \\
Rhonda numbers \\
Riemann hypothesis \\
Farey sequence and Riemann's Hypothesis \\
Riemann's hypothesis and $\sigma(n)$, the sum of
divisor function \\
squarefree and blue and red numbers \\
the Mertens conjecture \\
Riemann Hypothesis curiosities \\
Riesel number \\
right-truncatable prime \\
RSA algorithm \\
Martin Gardner's challenge \\
RSA Factoring Challenge, The New \\
Ruth--Aaron numbers \\
Scherk's conjecture \\
semi-primes \\
sexy primes \\
Shank's Conjecture \\
Siamese primes \\
Sierpinski numbers \\
Sierpinski strings \\
Sierpinski's quadratic \\
Sierpinski's $\phi(n)$ conjecture \\
Sloane's On-Line Encyclopedia of Integer Sequences \\
Smith numbers \\
Smith Brothers \\
smooth numbers \\
Sophie Germain primes \\
safe primes \\
square-free numbers \\
Stern prime \\
strong law of small numbers \\
triangular numbers \\
trivia \\
twin primes \\
twin curiosities \\
Ulam spiral \\
unitary divisors \\
unitary perfect \\
untouchable numbers \\
weird numbers \\
Wieferich primes \\
Wilson's theorem \\
twin primes \\
Wilson's quotient \\
Wilson primes \\
Wolstenholme's numbers, and theorems \\
more factors of Wolstenholme numbers \\
Woodall primes \\
zeta mysteries: the quantum connection \\
Appendix A: The First 500 Primes \\
Appendix B: Arithmetic Functions \\
Glossary \\
Bibliography \\
Index",
}
@Article{Aban:2006:PET,
author = "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
Panorska",
title = "Parameter Estimation for the Truncated {Pareto}
Distribution",
journal = j-J-AM-STAT-ASSOC,
volume = "101",
number = "473",
pages = "270--277",
month = mar,
year = "2006",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1198/016214505000000411",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Thu Aug 26 11:26:31 MDT 2010",
bibsource = "http://www.amstat.org/publications/jasa/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Baskerville:2006:SEM,
author = "Kim Baskerville and Maya Paczuski",
title = "Subgraph ensembles and motif discovery using an
alternative heuristic for graph isomorphism",
journal = j-PHYS-REV-E,
volume = "74",
number = "??",
pages = "051903",
day = "3",
month = nov,
year = "2006",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.74.051903",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.74.051903",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Bohachevsky:2006:DBL,
author = "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
Stein",
title = "A derivation of {Benford}'s law",
journal = j-AM-J-MATH-MANAGE-SCI,
volume = "26",
number = "3--4",
pages = "355--370",
year = "2006",
CODEN = "AMMSDX",
ISSN = "0196-6324",
ISSN-L = "0196-6324",
MRclass = "60E99 (11K36)",
MRnumber = "2312400 (2008h:60062)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematical and Management
Sciences",
}
@Article{Briscoe:2006:MLW,
author = "Bob Briscoe and Andrew Odlyzko and Benjamin Tilly",
title = "{Metcalfe's Law} is wrong --- communications networks
increase in value as they add members --- but by how
much?",
journal = j-IEEE-SPECTRUM,
volume = "43",
number = "7",
pages = "34--39",
month = jul,
year = "2006",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2006.1653003",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 12:29:46 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2000.bib",
abstract = "This paper argues that Metcalfe's law, which states
that the value of a communications network is
proportional to the square of the number of its users,
is incorrect. By seeming to assure that the value of a
network would increase quadratically - proportionately
to the square of the number of its participants - while
costs would, at most, grow linearly, Metcalfe's law
gave an air of credibility to the mad rush for growth
and the neglect of profitability. The paper discusses
the fundamental flaw of Metcalfe's law and describes
how Zipf's law can be used as basis to justify the $ n
\log (n) $ rule-of-thumb valuation of a general
communications network of size $n$.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Communication networks; communications network;
Computer networks; Costs; Ethernet networks; Internet;
Internet telephony; Investments; IP networks; Metcalfe
Law; Profitability; profitability; rule-of-thumb
valuation; Web pages; Web sites; Zipf law",
}
@InProceedings{Dallacasa:2006:TBS,
author = "F. Dallacasa and Valerio Dallacasa",
editor = "????",
booktitle = "{5th International Conference: APLIMAT 2006, Slovak
University of Technology, Bratislava}",
title = "Temporal behaviour of stock data from {Benford}'s
law",
publisher = "????",
address = "????",
pages = "425--432",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 17:32:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
price = "US\$",
URL = "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf",
acknowledgement = ack-nhfb,
}
@Article{deMarchi:2006:AAS,
author = "Scott de Marchi and James Hamilton",
title = "Assessing the Accuracy of Self-Reported Data: an
Evaluation of the Toxics Release Inventory",
journal = j-J-RISK-UNCERT,
volume = "32",
number = "1",
pages = "57--76",
month = jan,
year = "2006",
CODEN = "JRUNEN",
DOI = "https://doi.org/10.1007/s10797-006-6666-3",
ISSN = "0895-5646 (print), 1573-0476 (electronic)",
ISSN-L = "0895-5646",
bibdate = "Fri Nov 25 11:25:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Risk and Uncertainty",
journal-URL = "http://link.springer.com/journal/11166",
}
@Article{Dorogovtsev:2006:FON,
author = "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
Oliveira",
title = "Frequency of occurrence of numbers in the {World Wide
Web}",
journal = j-PHYSICA-A,
volume = "360",
number = "2",
pages = "548--556",
month = feb,
year = "2006",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2005.06.064",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://arxiv.org/abs/physics/0504185;
http://www.sciencedirect.com/science/article/pii/S0378437105006874",
abstract = "The distribution of numbers in human documents is
determined by a variety of diverse natural and human
factors, whose relative significance can be evaluated
by studying the numbers frequency of occurrence.
Although it has been studied since the 1880's, this
subject remains poorly understood. Here, we obtain the
detailed statistics of numbers in the World Wide Web,
finding that their distribution is a heavy-tailed
dependence which splits in a set of power-law ones. In
particular, we find that the frequency of numbers
associated to western calendar years shows an uneven
behavior: 2004 represents a singular critical point,
appearing with a strikingly high frequency; as we move
away from it, the decreasing frequency allows us to
compare the amounts of existing information on the past
and on the future. Moreover, while powers of ten occur
extremely often, allowing us to obtain statistics up to
the huge 10 127, non-round numbers occur in a much more
limited range, the variations of their frequencies
being dramatically different from standard statistical
fluctuations. These findings provide a view of the
array of numbers used by humans as a highly
non-equilibrium and inhomogeneous system, and shed a
new light on an issue that, once fully investigated,
could lead to a better understanding of many
sociological and psychological phenomena.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Critical point; Fluctuations; Power-law
distributions; Search engines; Statistics of natural
numbers; The World Wide Web",
}
@Article{Duranton:2006:SFZ,
author = "Gilles Duranton",
title = "Some foundations for {Zipf}'s law: Product
proliferation and local spillovers",
journal = j-REG-SCI-URBAN-ECON,
volume = "36",
number = "4",
pages = "542--563",
day = "1",
month = jul,
year = "2006",
CODEN = "RSUEDM",
DOI = "https://doi.org/10.1016/j.regsciurbeco.2006.03.008",
ISSN = "0166-0462 (print), 1879-2308 (electronic)",
ISSN-L = "0166-0462",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0166046206000354",
acknowledgement = ack-nhfb,
fjournal = "Regional Science and Urban Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/01660462",
keywords = "Zipf's Law",
}
@Article{Egghe:2006:DHL,
author = "L. Egghe",
title = "The dependence of the height of a {Lorenz} curve of a
{Zipf} function on the size of the system",
journal = j-MATH-COMP-MODELLING,
volume = "43",
number = "7--8",
pages = "870--879",
day = "15",
month = apr,
year = "2006",
CODEN = "MCMOEG",
DOI = "https://doi.org/10.1016/j.mcm.2005.09.033",
ISSN = "0895-7177 (print), 1872-9479 (electronic)",
ISSN-L = "0895-7177",
MRclass = "94A15 (91B82)",
MRnumber = "2218323 (2006k:94033)",
MRreviewer = "Ulrich Tamm",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S089571770500508X",
acknowledgement = ack-nhfb,
fjournal = "Mathematical and Computer Modelling",
keywords = "Zipf's Law",
}
@Article{Gaite:2006:CSZ,
author = "Jos{\'e} Gaite",
title = "Cut-out sets and the {Zipf} law for fractal voids",
journal = j-PHYSICA-D,
volume = "223",
number = "2",
pages = "248--255",
day = "15",
month = nov,
year = "2006",
CODEN = "PDNPDT",
DOI = "https://doi.org/10.1016/j.physd.2006.09.021",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
MRclass = "28A80",
MRnumber = "2307212",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167278906003848",
acknowledgement = ack-nhfb,
fjournal = "Physica. D, Nonlinear phenomena",
journal-URL = "http://www.sciencedirect.com/science/journal/01672789",
keywords = "Zipf's Law",
}
@Article{Gan:2006:ZLS,
author = "Li Gan and Dong Li and Shunfeng Song",
title = "Is the {Zipf} law spurious in explaining city-size
distributions?",
journal = j-ECONOM-LETT,
volume = "92",
number = "2",
pages = "256--262",
day = "1",
month = aug,
year = "2006",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/j.econlet.2006.03.004",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176506000772",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Handurukande:2006:PSB,
author = "S. B. Handurukande and A.-M. Kermarrec and F. {Le
Fessant} and L. Massouli{\'e} and S. Patarin",
title = "Peer sharing behaviour in the {eDonkey} network, and
implications for the design of server-less file sharing
systems",
journal = j-OPER-SYS-REV,
volume = "40",
number = "4",
pages = "359--371",
month = oct,
year = "2006",
CODEN = "OSRED8",
DOI = "https://doi.org/10.1145/1218063.1217970",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Fri Jun 20 17:14:10 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper we present an empirical study of a
workload gathered by crawling the eDonkey network --- a
dominant peer-to-peer file sharing system --- for over
50 days. We first confirm the presence of some known
features, in particular the prevalence of free-riding
and the Zipf-like distribution of file popularity. We
also analyze the evolution of document popularity. We
then provide an in-depth analysis of several clustering
properties of such workloads. We measure the
geographical clustering of peers offering a given file.
We find that most files are offered mostly by peers of
a single country, although popular files don't have
such a clear home country. We then analyze the overlap
between contents offered by different peers. We find
that peer contents are highly clustered according to
several metrics of interest. We propose to leverage
this property by allowing peers to search for content
without server support, by querying suitably identified
semantic neighbours. We find via trace-driven
simulations that this approach is generally effective,
and is even more effective for rare files. If we
further allow peers to query both their semantic
neighbours, and in turn their neighbours' neighbours,
we attain hit rates as high as over 55\% for neighbour
lists of size 20.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
keywords = "file sharing; peer-to-peer; simulation; trace",
}
@InCollection{Harremoes:2006:ZLH,
author = "P. Harremo{\"e}s and F. Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "4123",
publisher = pub-SV,
address = pub-SV:adr,
pages = "788--792",
year = "2006",
DOI = "https://doi.org/10.1007/11889342_50",
bibdate = "Sat Nov 12 11:15:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
ZMnumber = "1158.91481",
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
}
@Article{Horn:2006:DSA,
author = "B. Horn and M. Kreuzer and E. Kochs and G. Schneider",
title = "Different States of Anesthesia Can Be Detected by
{Benford's Law}",
journal = "Journal of Neurosurgical Anesthesiology",
volume = "18",
number = "4",
pages = "328--329",
month = oct,
year = "2006",
ISSN = "0898-4921 (print), 1537-1921 (electronic)",
ISSN-L = "0898-4921",
bibdate = "Sat Sep 10 12:15:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Neurosurgical Anesthesiology",
journal-URL = "http://www.edmgr.com/JNA/;
http://journals.lww.com/jnsa/pages/default.aspx",
keywords = "Benford's Law",
}
@TechReport{Humenberger:2006:BGV,
author = "Hans Humenberger",
title = "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der
ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on
the distribution of the first digit of numbers]",
type = "Report",
institution = "Institut f{\"u}r Mathematik und Angewandte Statistik,
Universit{\"a}t f{\"u}r Bodenkultur",
address = "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria",
month = aug,
year = "2006",
bibdate = "Sun Feb 17 09:37:40 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Hurlimann:2006:BLB,
author = "Werner H{\"u}rlimann",
title = "{Benford's Law} from 1881 to 2006: a bibliography",
type = "Report",
address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
pages = "15",
day = "5",
month = jul,
year = "2006",
bibdate = "Fri Mar 30 11:32:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/pdf/math.ST/0607168",
abstract = "On the occasion of the 125-th anniversary of Newcomb's
paper, a bibliography of academic work related to
Benford's law from its year of origin 1881 to 2006 has
been compiled.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "This bibliography lists 325 references on the title
subject, with these (years) and counts: (1881) 1,
(1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
(1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
(1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
(1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
(1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
(1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
(1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
(1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
(1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
(1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
(1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
(2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
(2005) 34, (2006) 18.",
}
@Article{Hurlimann:2006:GBL,
author = "Werner H{\"u}rlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = "ArXiv Mathematics e-prints",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7166H",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607166",
keywords = "Mathematics - Statistics, Mathematics - Number Theory,
11B73, 11B83, 11K31, 62E15, 62E17",
}
@Article{Izsak:2006:MLE,
author = "F. Izs{\'a}k",
title = "Maximum likelihood estimation for constrained
parameters of multinomial distributions --- Application
to {Zipf--Mandelbrot} models",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "51",
number = "3",
pages = "1575--1583",
day = "1",
month = dec,
year = "2006",
CODEN = "CSDADW",
DOI = "https://doi.org/10.1016/j.csda.2006.05.008",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
MRnumber = "2307527",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016794730600154X",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
keywords = "Zipf's Law",
}
@TechReport{Judge:2006:DPS,
author = "George Judge and Laura Schechter",
title = "Detecting problems in survey data using {Benford}'s
law",
type = "Preprint",
institution = "University of California at Berkeley and University of
Wisconsin at Madison",
address = "Berkeley, CA, USA and Madison, WI, USA",
pages = "30",
day = "1",
month = nov,
year = "2006",
bibdate = "Sat Feb 16 18:12:29 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.aae.wisc.edu/lschechter/benford.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kossovsky:2006:TBU,
author = "Alex Ely Kossovsky",
title = "Towards a Better Understanding of the Leading Digits
Phenomena",
journal = "ArXiv Mathematics e-prints",
year = "2006",
bibdate = "Mon Nov 21 06:46:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0612627",
abstract = "This article on leading digits (Benford's Law)
contains the following: (i) An attempt at a
comprehensive account on the leading digits phenomena,
incorporating many of its existing explanations,
proofs, and differing points of view. (ii) The finding
that leading digits of random numbers derived from a
chain of distributions that are linked via parameter
selection are logarithmic in the limit as the number of
sequences approaches infinity, and that empirically
only around 5 or 6 sequences of such a distribution
chain are needed to obtain results that are close
enough to the logarithmic (i.e., rapid convergence).
(iii) An outright exact logarithmic behavior for a
2-sequence chain whenever parametrical density is
exactly logarithmic. (iv) An account on the existence
of singularities in exponential growth rates with
regards to the leading digits distributions of their
series. (v) An account on several distributions that
are intrinsically logarithmic or approximately so. (vi)
A conceptual justification of Flehinger's iterated
averaging scheme --- an algorithm that was presented
without any clear motivation. (vii) A note on the close
relationship of Flehinger's scheme and the chain of
distribution to Hill's super distribution. (viii) A
conceptual argument justifying the scale invariance
principle --- a principle invoked in derivations of
Benford's law. (ix) A note on the intimate connection
between one-sided tail to the right in density
distributions and logarithmic leading digit behavior.",
acknowledgement = ack-nhfb,
remark = "On 18 February 2013, the archive has 17 revisions of
this article.",
xxjournal = "CoRR",
}
@Article{Kristiansen:2006:BTZ,
author = "K. de Lange Kristiansen and G. Helgesen and A. T.
Skjeltorp",
title = "Braid theory and {Zipf--Mandelbrot} relation used in
microparticle dynamics",
journal = j-EUR-PHYS-J-B,
volume = "51",
number = "3",
pages = "363--371",
month = jun,
year = "2006",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1140/epjb/e2006-00241-7",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Sat Sep 8 18:31:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Book{Kuipers:2006:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 390",
year = "2006",
ISBN = "0-486-45019-8 (paperback)",
ISBN-13 = "978-0-486-45019-3 (paperback)",
LCCN = "QA292 .K84 2006",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
acknowledgement = ack-nhfb,
remark = "Originally published in \cite{Kuipers:1974:UDS}.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@Article{Kulikova:2006:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's
Law}. {I}",
journal = j-THEORY-PROBAB-APPL,
volume = "50",
number = "2",
pages = "311--315",
month = jan,
year = "2006",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/S0040585X97981706",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Wed May 19 18:14:51 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
journal-URL = "http://epubs.siam.org/tvp",
}
@Article{Lagarias:2006:BLF,
author = "Jeffrey C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $ 3 x + 1 $ function",
journal = "J. London Math. Soc. (2)",
volume = "74",
number = "2",
pages = "289--303",
year = "2006",
CODEN = "JLMSAK",
DOI = "https://doi.org/10.1112/S0024610706023131",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
ISSN-L = "0024-6107",
MRclass = "37A45",
MRnumber = "2269630 (2007h:37007)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the London Mathematical Society. Second
Series",
}
@Article{Leinicke:2006:FFN,
author = "Linda M. Leinicke and Joyce A. Ostrosky and W. Max
Rexroad",
title = "Fighting fraud by the numbers: Digital analysis
primer",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2006",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:13:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294967620",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
keywords = "Benford's Law",
}
@Article{Leydesdorff:2006:CPL,
author = "Loet Leydesdorff and Stephen Bensman",
title = "Classification and power laws: the logarithmic
transformation",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "57",
number = "11",
pages = "1470--1486",
month = sep,
year = "2006",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20467",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Sat Feb 16 18:31:04 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
keywords = "Benford's Law",
}
@Article{Lim:2006:BRB,
author = "Nena Lim",
title = "Book Review: {{\booktitle{The new forensics:
investigating corporate fraud and the theft of
intellectual property}}, J. Anastasi. John Wiley \&
Sons, New Jersey (2003)}",
journal = "Digital Investigation",
volume = "3",
number = "4",
pages = "245--246",
year = "2006",
DOI = "https://doi.org/10.1016/j.diin.2006.10.002",
ISSN = "1742-2876 (print), 1873-202X (electronic)",
ISSN-L = "1742-2876",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S174228760600106X",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Lu:2006:AFD,
author = "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
booktitle = "Advances in artificial intelligence",
title = "Adaptive fraud detection using {Benford}'s law",
volume = "4013",
publisher = pub-SV,
address = pub-SV:adr,
pages = "347--358",
year = "2006",
DOI = "https://doi.org/10.1007/11766247_30",
MRnumber = "2280590",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@InProceedings{Lu:2006:BCF,
author = "F. Lu and J. E. Boritz",
editor = "????",
booktitle = "{Uncertainty in Artificial Intelligence: Proceedings
of the 22nd Conference}",
title = "Building a case for fraud using {Benford}'s law with
reinforcement learning",
publisher = "????",
address = "????",
pages = "??--??",
year = "2006",
bibdate = "Sat Feb 16 18:34:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Manaris:2006:IES,
author = "Bill Manaris and Luca Pellicoro and George Pothering
and Harland Hodges",
editor = "????",
booktitle = "{2006 IASTED International Conference on Artificial
Intelligence and Applications (AIA 2006), February
13--16, 2006, Innsbruck, Austria}",
title = "Investigating {Esperanto}'s statistical proportions
relative to other languages using neural networks and
{Zipf}'s law",
publisher = "Acta Press",
address = "????",
pages = "1--7",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 18:41:37 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf",
acknowledgement = ack-nhfb,
}
@Article{Maslov:2006:BGA,
author = "V. P. Maslov",
title = "{Bose} gas of anharmonic oscillators and a refinement
of {Zipf}'s law",
journal = j-TEORET-MATH-FIZ,
volume = "148",
number = "3",
pages = "495--496",
year = "2006",
CODEN = "TMFZAL",
DOI = "https://doi.org/10.1007/s11232-006-0117-2",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B10",
MRnumber = "2283664",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
journal-URL = "http://link.springer.com/journal/11232",
}
@Article{Maslov:2006:NAD,
author = "V. P. Maslov",
title = "Negative asymptotic dimension, a new condensate, and
their relation to the quantized {Zipf} law",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "6",
pages = "856--863",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11006-006-0203-7",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "82B10 (20F69 53C23 81S10 91F20)",
MRnumber = "2311613 (2008e:82005)",
MRreviewer = "Artur E. Ruuge",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
journal-URL = "http://link.springer.com/journal/11006",
}
@Article{Maslov:2006:RZM,
author = "V. P. Maslov",
title = "A refinement of the {Zipf--Mandelbrot} law and
lacunarity in an ideal gas",
journal = j-TEORET-MATH-FIZ,
volume = "147",
number = "3",
pages = "511--512",
year = "2006",
CODEN = "TMFZAL",
DOI = "https://doi.org/10.1007/s11232-006-0083-8",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B10",
MRnumber = "2254729 (2007d:82007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
journal-URL = "http://link.springer.com/journal/11232",
}
@Article{Maslov:2006:ZLR,
author = "V. P. Maslov and T. V. Maslova",
title = "On {Zipf}'s law and rank distributions in linguistics
and semiotics",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "5",
pages = "718--732",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11006-006-0189-1",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "60C05 (62-07 62P99)",
MRnumber = "2311586 (2008g:60027)",
MRreviewer = "Konstantin E. Feldman",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "Zbl 1134.62086",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
journal-URL = "http://link.springer.com/journal/11006",
}
@Article{Maslova:2006:ZLM,
author = "T. V. Maslova",
title = "{Zipf}'s law and {Maslov}'s formula as applied to
semiotic systems",
journal = j-DOKL-MATH,
volume = "74",
number = "3",
pages = "917--920",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1134/S1064562406060330",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:13:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "pre05824774",
acknowledgement = ack-nhfb,
classmath = "62E20 (Asymptotic distribution theory in statistics)
82B03 (Foundations of equilibrium statistical
mechanics)",
fjournal = "Doklady Mathematics",
journal-URL = "http://link.springer.com/journal/11472",
language = "English. Russian original",
}
@Article{Maslova:2006:ZLV,
author = "T. V. Maslova",
title = "On the {Zipf} law and the {V. P. Maslov} formula for
semiotic systems",
journal = j-DOKL-AKAD-NAUK,
volume = "411",
number = "6",
pages = "754--757",
year = "2006",
CODEN = "DANKAS",
ISSN = "0869-5652",
ISSN-L = "0869-5652",
MRclass = "62E20 (82B03)",
MRnumber = "2451374",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
journal-URL = "http://istina.msu.ru/journals/366838/",
}
@InProceedings{Mebane:2006:DAE,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2006 Annual Meeting of the Midwest Political Science
Association, April 20--23, Palmer House, Chicago}",
title = "Detecting Attempted Election Theft: Vote Counts,
Voting Machines and {Benford's Law}",
publisher = "????",
address = "????",
pages = "i + 50",
day = "19",
month = apr,
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:14:14 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/mw06.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2006:EFS,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{Election Fraud Conference, Salt Lake City, Utah,
September 29--30, 2006}",
title = "Election Forensics: The Second-digit {Benford's Law}
Test and Recent {American Presidential} Elections",
publisher = "????",
address = "????",
pages = "??--??",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Feb 15 18:22:27 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www-personal.umich.edu/~wmebane/fraud06.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2006:EFV,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2006 Summer Meeting of the Political Methodology
Society, UC-Davis, July 20--22, 2006}",
title = "Election Forensics: Vote Counts and {Benford's Law}",
publisher = "????",
address = "????",
pages = "ii + 48",
day = "18",
month = jul,
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:01:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm06.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Second Digit Benford Law (2BL)",
}
@Article{Mellor:2006:GKZ,
author = "Andy Mellor",
title = "Book Review: {G. K. Zipf, \booktitle The
Psycho-biology of Language (1935) MIT Press, Cambridge,
MA}",
journal = j-SYSTEM,
volume = "34",
number = "3",
pages = "455--457",
day = "20",
month = sep,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.system.2006.07.004",
ISSN = "0346-251X (print), 1879-3282 (electronic)",
ISSN-L = "0346-251X",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0346251X06000674",
acknowledgement = ack-nhfb,
fjournal = "System",
journal-URL = "http://www.sciencedirect.com/science/journal/0346251X",
keywords = "Zipf's Law",
}
@Article{Metwally:2006:IES,
author = "Ahmed Metwally and Divyakant Agrawal and Amr {El
Abbadi}",
title = "An integrated efficient solution for computing
frequent and top-$k$ elements in data streams",
journal = j-TODS,
volume = "31",
number = "3",
pages = "1095--1133",
month = sep,
year = "2006",
CODEN = "ATDSD3",
DOI = "https://doi.org/10.1145/1166074.1166084",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Tue Oct 17 05:41:01 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comments in \cite{Liu:2010:CIE}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Database Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
}
@Book{Miller:2006:IMN,
author = "Steven J. Miller and Ramin Takloo-Bighash",
title = "An Invitation to Modern Number Theory",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xx + 503",
year = "2006",
ISBN = "0-691-12060-9 (hardcover)",
ISBN-13 = "978-0-691-12060-7 (hardcover)",
LCCN = "QA241 .M5344 2006",
bibdate = "Fri Mar 22 08:57:57 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Number theory",
tableofcontents = "Part 1. Basic Number Theory \\
1. Mod p Arithmetic, Group Theory and Cryptography \\
2. Arithmetic Functions \\
3. Zeta and L-Functions \\
4. Solutions to Diophantine Equations \\
Part 2. Continued Fractions and Approximations \\
5. Algebraic and Transcendental Numbers \\
6. The Proof of Roth's Theorem \\
7. Introduction to Continued Fractions \\
Part 3. Probabilistic Methods and Equidistribution \\
8. Introduction to Probability \\
9. Applications of Probability: Benford's Law and
Hypothesis Testing \\
10. Distribution of Digits of Continued Fractions \\
11. Introduction to Fourier Analysis \\
12. f n k g and Poissonian Behavior \\
Part 4. The Circle Method \\
13. Introduction to the Circle Method \\
14. Circle Method: Heuristics for Germain Primes \\
Part 5. Random Matrix Theory and L-Functions \\
15. From Nuclear Physics to L-Functions \\
16. Random Matrix Theory: Eigenvalue Densities \\
17. Random Matrix Theory: Spacings between Adjacent
Eigenvalues \\
18. The Explicit Formula and Density Conjectures \\
Appendix A. Analysis Review \\
Appendix B. Linear Algebra Review \\
Appendix C. Hints and Remarks on the Exercises \\
Appendix D. Concluding Remarks",
}
@Article{Miller:2006:MCL,
author = "Steven J. Miller and M. J. Nigrini",
title = "The {Modulo 1 Central Limit Theorem} and {Benford's
Law} for Products",
journal = "International Journal of Algebra",
volume = "3",
number = "3",
pages = "119--130",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "1312-8868 (print), 1314-7595 (electronic)",
ISSN-L = "1312-8868",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7686M;
http://arxiv.org/abs/math/0607686",
abstract = "We derive a necessary and sufficient condition for the
sum of $M$ independent continuous random variables
modulo $1$ to converge to the uniform distribution in $
L^1 ([0, 1]) $, and discuss generalizations to discrete
random variables. A consequence is that if $ X_1,
\ldots {}, X_M $ are independent continuous random
variables with densities $ f_1, \ldots {}, f_M $, for
any base $B$ as $ M \to \infty $ for many choices of
the densities the distribution of the digits of $ X_1 *
\cdots {} * X_M $ converges to Benford's law base $B$.
The rate of convergence can be quantified in terms of
the Fourier coefficients of the densities, and provides
an explanation for the prevalence of Benford behavior
in many diverse systems.",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607686",
journal-URL = "http://www.m-hikari.com/ija/index.html",
keywords = "Mathematics - Probability, Mathematics - Classical
Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
42A10, 42A61, 62E15 (Secondary)",
}
@Article{Miller:2006:OSB,
author = "Steven J. Miller and M. J. Nigrini",
title = "Order Statistics and {Benford's Law}",
journal = "ArXiv Mathematics e-prints",
month = jan,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......1344M",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0601344",
keywords = "Mathematics - Probability, Mathematics - Number
Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
(Secondary)",
}
@Article{Moret:2006:NBL,
author = "M. A. Moret and V. de Senna and M. G. Pereira and G.
F. Zebende",
title = "{Newcomb--Benford} Law in Astrophysical Sources",
journal = j-INT-J-MOD-PHYS-C,
volume = "17",
number = "11",
pages = "1597--1604",
month = "????",
year = "2006",
CODEN = "IJMPEO",
DOI = "https://doi.org/10.1142/S0129183106010054",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
ISSN-L = "0129-1831",
bibdate = "Mon Nov 14 17:37:59 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
}
@TechReport{Morrow:2006:BLF,
author = "John Morrow",
title = "{Benford's Law}, Families of Distributions and a Test
Basis",
type = "Report",
institution = "University of Wisconsin--Madison",
address = "Madison, WI, USA",
month = "????",
year = "2006",
bibdate = "Tue Nov 22 20:44:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Revised draft of 9 October 2010.",
URL = "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
acknowledgement = ack-nhfb,
lastaccess = "22 November 2011",
}
@Article{Moura:2006:ZLB,
author = "Newton J. {Moura, Jr.} and Marcelo B. Ribeiro",
title = "{Zipf} law for {Brazilian} cities",
journal = j-J-THEOR-BIOL,
volume = "219",
number = "4",
pages = "441--448",
day = "15",
month = jul,
year = "2006",
CODEN = "JTBIAP",
DOI = "https://doi.org/10.1016/j.physa.2005.11.038",
ISSN = "0022-5193 (print), 1095-8541 (electronic)",
ISSN-L = "0022-5193",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437105012422",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00225193",
keywords = "Zipf's Law",
}
@TechReport{Nigrini:2006:BLA,
author = "M. J. Nigrini and Steven J. Miller",
title = "{Benford}'s law applied to hydrology data --- results
and relevance to other geophysical data",
type = "Preprint",
institution = "????",
address = "????",
month = "????",
year = "2006",
bibdate = "Sat Feb 16 18:58:34 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Ogasawara:2006:ZLH,
author = "Osamu Ogasawara and Shoko Kawamoto and Kousaku Okubo",
title = "{Zipf}'s law and human transcriptomes: an explanation
with an evolutionary model",
journal = j-C-R-BIOL,
volume = "326",
number = "10--11",
pages = "1097--1101",
day = "1",
month = jul,
year = "2006",
CODEN = "CRBOCM",
DOI = "https://doi.org/10.1016/j.crvi.2003.09.031",
ISSN = "1631-0691 (print), 1768-3238 (electronic)",
ISSN-L = "1631-0691",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1631069103002294",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Biologies",
journal-URL = "http://sciencedirect.com/science/journal/16310691",
keywords = "Zipf's Law",
}
@Article{Pocheau:2006:SDL,
author = "A. Pocheau",
title = "The significant digit law: a paradigm of statistical
scale symmetries",
journal = j-EUR-PHYS-J-B,
volume = "49",
number = "4",
pages = "491--511",
month = feb,
year = "2006",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1140/epjb/e2006-00084-2",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Sat Feb 16 15:06:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1140/epjb/e2006-00084-2",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Article{Posch:2006:ADP,
author = "Peter N. Posch and Welf A. Kreiner",
title = "Analysing digits for portfolio formation and index
tracking",
journal = j-J-ASSET-MANAGE,
volume = "7",
number = "1",
pages = "69--80",
month = may,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1057/palgrave.jam.2240203",
ISSN = "1470-8272 (print), 1479-179X (electronic)",
ISSN-L = "1470-8272",
bibdate = "Fri Nov 25 11:19:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A general methodology is proposed for using digit
distributions as an approach to examining arbitrary
datasets. With the Newcomb--Benford law as a starting
point, a more general framework for digital analysis is
developed. A new measure is proposed based on this
framework, namely the Digital-Fit Factor (DFF). The use
of index comparison on the S\&P500 and the Dow Jones
Industrial Average is demonstrated. The DFF is then
used to construct portfolios and measure their
performance compared with that of the index. The
average returns using the measure exceed the index
composition by 6--14 percentage points per year by
being more stable at the same time. Furthermore, these
measures require only a very small proportion of the
available information and are thus very efficient.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Asset Management",
keywords = "Benford's Law",
}
@Article{Ree:2006:PLD,
author = "Suhan Ree",
title = "Power-law distributions from additive preferential
redistributions",
journal = j-PHYS-REV-E,
volume = "73",
number = "??",
pages = "026115",
day = "15",
month = feb,
year = "2006",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.73.026115",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.73.026115",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@InProceedings{Sanches:2006:IRU,
author = "Jo{\~a}o M. Sanches and Jorge S. Marques",
booktitle = "{2006 IEEE International Conference on Image
Processing, Atlanta, Georgia, 8--11 October 2006}",
title = "Image Reconstruction using the {Benford Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2029--2032",
year = "2006",
DOI = "https://doi.org/10.1109/ICIP.2006.312845",
ISBN = "1-4244-0480-0",
ISBN-13 = "978-1-4244-0480-3",
ISSN = "1522-4880",
bibdate = "Tue Nov 15 09:03:24 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Tt has been claimed that the first digit of real
signals follows a logarithmic distribution, called
Benford law. This paper shows that this distribution is
a natural prior for the gradient of several types of
medical images (MRI, CT, ultrasound) and proposes a
reconstruction algorithm based on the Benford law which
does not require any parameter tuning. Experimental
results are presented to illustrate the performance of
the reconstruction algorithm",
acknowledgement = ack-nhfb,
}
@Article{Saville:2006:UBL,
author = "Adrian D. Saville",
title = "Using {Benford's} Law to detect data error and fraud:
An examination of companies listed on the {Johannesburg
Stock Exchange}",
journal = "South African Journal of Economic and Management
Sciences",
volume = "9",
number = "3",
pages = "341--354",
month = "????",
year = "2006",
CODEN = "????",
ISSN = "1015-8812 (print), 2222-3436 (electronic)",
ISSN-L = "1015-8812",
bibdate = "Fri Mar 22 09:12:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
journal-URL = "http://sajems.org/index.php/sajems/issue/archive",
keywords = "Benford's Law",
remark = "No issues online before volume 10, number 1, 2007.",
}
@Article{Schneider:2006:RAS,
author = "Reto U. Schneider",
title = "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber
hundert Jahren stiess ein Astronom auf ein
merkw{\"u}rdiges statistisches Gesetz, das heute
Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The}
puzzle of the worn pages: More than a hundred years ago
an astronomer came across a strange statistical law
that will now expose tax cheats]",
journal = "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher
Zeitung}",
volume = "??",
number = "1/06",
month = "????",
year = "2006",
bibdate = "Fri Nov 18 12:18:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html;
http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Schuette:2006:TFZ,
author = "Paul Schuette and Marcus C. Spruill",
title = "Tail fit and the {Zipf--Pareto} law",
journal = "Extremes",
volume = "9",
number = "3--4",
pages = "243--261",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10687-007-0030-6",
ISSN = "1386-1999",
ISSN-L = "1386-1999",
MRnumber = "2367837",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Extremes. Statistical Theory and Applications in
Science, Engineering and Economics",
xxyear = "2007",
}
@Article{Sugimoto:2006:AFP,
author = "Toyoaki Sugimoto and Naoto Miyoshi",
title = "On the asymptotics of fault probability in
least-recently-used caching with {Zipf}-type request
distribution",
journal = j-RAND-STRUCT,
volume = "29",
number = "3",
pages = "296--323",
year = "2006",
CODEN = "RSALFD",
DOI = "https://doi.org/10.1002/rsa.20098",
ISSN = "1042-9832 (print), 1098-2418 (electronic)",
ISSN-L = "1042-9832",
MRclass = "68N25 (60C05 62E20 62P30 68P05 68U35)",
MRnumber = "2254493 (2008h:68028)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Structures and Algorithms",
keywords = "distributional tail asymptotics; least-recently-used
caching; move-to-front algorithm; negative association;
Zipf-type distribution",
}
@MastersThesis{TorresNunez:2006:NBL,
author = "David A. {Torres N{\'u}{\~n}ez}",
title = "{Newcomb--Benford's Law}: Applications to Electoral
Processes, Bioinformatics, and the Stock Index",
type = "{M.S.} thesis",
school = "Center for Bioststatistics and Bioinformatics,
University of Puerto Rico, R{\'\i}o Piedras Campus",
address = "PO Box 23355, San Juan, PR 00931-3355",
month = may,
year = "2006",
bibdate = "Fri Feb 15 18:34:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
advisor = "Luis R{\'a}ul Pericchi Guerra",
}
@Article{VandeWalle:2006:ZGK,
author = "J. {Van de Walle} and K. Willems",
title = "{Zipf, George Kingsley (1902--1950)}",
journal = j-J-ECON-DYN-CONTROL,
volume = "31",
number = "7",
pages = "756--757",
day = "15",
month = jul,
year = "2006",
CODEN = "JEDCDH",
DOI = "https://doi.org/10.1016/B0-08-044854-2/04726-X",
ISSN = "0165-1889 (print), 1879-1743 (electronic)",
ISSN-L = "0165-1889",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B008044854204726X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Economic Dynamics and Control",
keywords = "Zipf's Law",
}
@Article{Wilkinson:2006:RPC,
author = "Leland Wilkinson",
title = "Revising the {Pareto} Chart",
journal = j-AMER-STAT,
volume = "60",
number = "4",
pages = "332--334",
month = nov,
year = "2006",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/000313006X152243",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Ackermann:2007:DMB,
author = "Heiner Ackermann and Alantha Newman and Heiko
R{\"o}glin and Berthold V{\"o}cking",
title = "Decision-making based on approximate and smoothed
{Pareto} curves",
journal = j-THEOR-COMP-SCI,
volume = "378",
number = "3",
pages = "253--270",
day = "9",
month = jun,
year = "2007",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 08:55:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/03043975",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Amin:2007:TVA,
author = "Zeinab H. Amin",
title = "Tests for the Validity of the Assumption that the
Underlying Distribution of Life is {Pareto}",
journal = j-J-APPL-STAT,
volume = "34",
number = "2",
pages = "195--201",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Misc{Anonymous:2007:ZL,
author = "Anonymous",
key = "Zipf's Law",
title = "{Zipf}'s law",
year = "2007",
bibdate = "Sat Jan 26 12:46:16 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib",
URL = "http://en.wikipedia.org/wiki/Zipf's_law",
acknowledgement = ack-ds,
lastaccess = "27 January 2013",
rawdata = "Zipf's Law (2007)
|http://en.wikipedia.org/wiki/Zipf's_law|",
}
@Article{Bakulina:2007:AZL,
author = "M. P. Bakulina",
title = "Application of {Zipf}'s law for text compression",
journal = "Diskretn. Anal. Issled. Oper. Ser. 2",
volume = "14",
number = "2",
pages = "3--13",
year = "2007",
CODEN = "????",
ISSN = "1560-9901",
ISSN-L = "1560-9901",
MRclass = "94A15",
MRnumber = "2542308 (2010i:94076)",
MRreviewer = "I. Vajda",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
Seriya 2",
}
@Article{Baskerville:2007:GAS,
author = "Kim Baskerville and Peter Grassberger and Maya
Paczuski",
title = "Graph animals, subgraph sampling, and motif search in
large networks",
journal = j-PHYS-REV-E,
volume = "76",
number = "??",
pages = "036107",
day = "11",
month = sep,
year = "2007",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.76.036107",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036107",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Beeli:2007:FCG,
author = "Gian Beeli and Michaela Esslen and Lutz J{\"a}ncke",
title = "Frequency Correlates in Grapheme-Color Synaesthesia",
journal = "Psychological Science",
volume = "18",
number = "9",
pages = "788--792",
year = "2007",
DOI = "https://doi.org/10.1111/j.1467-9280.2007.01980.x",
bibdate = "Sat Sep 10 10:35:44 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pss.sagepub.com/content/18/9/788.abstract",
abstract = "Individuals with synaesthesia experience certain
stimuli in more than one sensory modality. Most common
is the linkage of letters and digits (graphemes) to
colors. Whereas synaesthesia might be partly
genetically determined, the linkages to specific colors
are assumed to be learned. We present a systematic
statistical analysis of synaesthetic color perception
based on subjects' reproduction of individual colors
for each grapheme, instead of simple verbal
categorizations. The statistical analysis revealed that
the color perceptions, measured with the HSL (hue,
saturation, and luminance) scale, varied systematically
among the different digits and letters. The frequencies
of the digits and letters (in the German language)
partly explained these systematic variations. However,
digit frequency was more strongly related to color
perception in the synaesthetes than was letter
frequency. The results for digit and letter frequency
indicate that experience with graphemes may shape
synaesthetic color perception.",
acknowledgement = ack-nhfb,
eprint = "http://pss.sagepub.com/content/18/9/788.full.pdf+html",
keywords = "Benford's Law",
}
@Article{Benguigui:2007:DMC,
author = "Lucien Benguigui and Efrat Blumenfeld-Lieberthal",
title = "A dynamic model for city size distribution beyond
{Zipf}'s law",
journal = j-PHYSICA-A,
volume = "384",
number = "2",
pages = "613--627",
day = "15",
month = oct,
year = "2007",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2007.05.059",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437107006061",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Berger:2007:DMN,
author = "A. Berger and S. Siegmund",
title = "On the distribution of mantissae in nonautonomous
difference equations",
journal = j-J-DIFFERENCE-EQU-APPL,
volume = "13",
number = "8--9",
pages = "829--845",
month = "????",
year = "2007",
CODEN = "JDEAEA",
DOI = "https://doi.org/10.1080/10236190701388039",
ISSN = "1023-6198 (print), 1563-5120 (electronic)",
ISSN-L = "1023-6198",
MRclass = "37A45 (37B55 39A11)",
MRnumber = "2343033 (2008j:37010)",
MRreviewer = "Reinhard Winkler",
bibdate = "Tue Feb 19 09:37:52 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Second Memorial Issue in Honour of Bernd Aulbach.",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Difference Equations and Applications",
journal-URL = "http://www.informaworld.com/1023-6198",
}
@Article{Berger:2007:NMO,
author = "Arno Berger and Theodore P. Hill",
title = "{Newton}'s Method Obeys {Benford}'s Law",
journal = j-AMER-MATH-MONTHLY,
volume = "114",
number = "7",
pages = "588--601",
month = aug # "\slash " # sep,
year = "2007",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65G50 (37N30)",
MRnumber = "2341322 (2008h:65016)",
MRreviewer = "Uwe Sch{\"a}fer",
bibdate = "Mon Jan 30 12:00:29 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i27642270;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/27642274",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Bernik:2007:BLA,
author = "V. I. Bernik and N. I. Kalosha",
title = "{Benford}'s law and the approximation of logarithms of
natural numbers by rational numbers",
journal = "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
F{\=\i}z.-Mat. Navuk",
volume = "??",
number = "3",
pages = "68--73, 127",
year = "2007",
CODEN = "????",
ISSN = "0002-3574",
ISSN-L = "0002-3574",
MRclass = "11J83 (11A63 11K36)",
MRnumber = "2398318 (2008j:11084)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Vests{\=\i} Natsyyanal\cprime na{\u\i}
Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
National Academy of Sciences of Belarus. Physics and
Mathematics Series",
}
@Article{Brown:2007:UZL,
author = "R. J. C. Brown",
title = "The use of {Zipf}'s law in the screening of analytical
data: a step beyond {Benford}",
journal = j-ANALYST,
volume = "132",
number = "4",
pages = "344",
year = "2007",
CODEN = "ANALAO",
DOI = "https://doi.org/10.1039/b618255k",
ISSN = "0003-2654 (print), 1364-5528 (electronic)",
ISSN-L = "0003-2654",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
abstract = "This study shows for the first time the effectiveness
of Zipf's law in screening analytical data sets for
outliers, data formatting and data transcription
errors, particularly when the data sets are small. In
the case of pollutant concentrations in ambient air,
the multivariate nature of the measurement, and the
relationship between the measured values of these
multivariant quantities are the characteristics that
allow a Zipf's law approach to data screening to be
successful. Furthermore, it has been shown that Zipf's
law has advantages over other novel data screening
techniques, such as Benford's law, in terms of
sensitivity and scope",
acknowledgement = ack-nhfb,
fjournal = "The Analyst",
journal-URL = "http://pubs.rsc.org/en/journals/journalissues/an",
}
@Article{Chacko:2007:EPB,
author = "Manoj Chacko and P. Yageen Thomas",
title = "Estimation of a Parameter of Bivariate {Pareto}
Distribution by Ranked Set Sampling",
journal = j-J-APPL-STAT,
volume = "34",
number = "6",
pages = "703--714",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Cho:2007:BBL,
author = "Wendy K. Tam Cho and Brian J. Gaines",
title = "Breaking the ({Benford}) law: statistical fraud
detection in campaign finance",
journal = j-AMER-STAT,
volume = "61",
number = "3",
pages = "218--223",
month = aug,
year = "2007",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/000313007X223496",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2393725",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
abstract = "Benford's law is seeing increasing use as a diagnostic
tool for isolating pockets of large datasets with
irregularities that deserve closer inspection. Popular
and academic accounts of campaign finance are rife with
tales of corruption, but the complete dataset of
transactions for federal campaigns is enormous.
Performing a systematic sweep is extremely arduous;
hence, these data are a natural candidate for initial
screening by comparison to Benford's distributions.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Clauset:2007:FST,
author = "Aaron Clauset and Maxwell Young and Kristian Skrede
Gleditsch",
title = "On the Frequency of Severe Terrorist Events",
journal = j-J-CONFL-RESOLUT,
volume = "51",
number = "1",
pages = "58--87",
month = feb,
year = "2007",
CODEN = "JCFRAL",
DOI = "https://doi.org/10.1177/0022002706296157",
ISSN = "0022-0027 (print), 1552-8766 (electronic)",
ISSN-L = "0022-0027",
bibdate = "Thu Nov 24 14:07:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcr.sagepub.com;
http://jcr.sagepub.com/content/51/1/58.abstract;
http://www.jstor.org/journals/00220027.html",
abstract = "In the spirit of Lewis Richardson's original study of
the statistics of deadly conflicts, we study the
frequency and severity of terrorist attacks worldwide
since 1968. We show that these events are uniformly
characterized by the phenomenon of ``scale
invariance,'' that is, the frequency scales as an
inverse power of the severity, $ P(x) \approx x{-
\alpha } $. We find that this property is a robust
feature of terrorism, persisting when we control for
economic development of the target country, the type of
weapon used, and even for short time scales. Further,
we show that the center of the distribution oscillates
slightly with a period of roughly 13 years, that there
exist significant temporal correlations in the
frequency of severe events, and that current models of
event incidence cannot account for these variations or
the scale invariance property of global terrorism.
Finally, we describe a simple toy model for the
generation of these statistics and briefly discuss its
implications.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Conflict Resolution",
}
@Article{Clauset:2007:PLDa,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-law distributions in empirical data",
journal = "ArXiv Physics e-prints",
day = "7",
month = jun,
year = "2007",
bibdate = "Thu Feb 28 08:52:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "arXiv:0706.1062.",
URL = "http://arxiv.org/abs/0706.1062v1",
acknowledgement = ack-nhfb,
pagecount = "27",
}
@Article{Clauset:2007:PLDb,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-law distributions in empirical data",
journal = "ArXiv Physics e-prints",
day = "2",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1137/070710111",
bibdate = "Thu Feb 28 08:52:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "arXiv:0706.1062.",
URL = "http://arxiv.org/abs/0706.1062v1",
acknowledgement = ack-nhfb,
pagecount = "43",
}
@Article{Decker:2007:GPC,
author = "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E.
Moses",
title = "Global Patterns of City Size Distributions and Their
Fundamental Drivers",
journal = j-PLOS-ONE,
volume = "2",
number = "9",
pages = "e934",
month = sep,
year = "2007",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0000934",
ISSN = "1932-6203",
bibdate = "Wed Feb 27 06:29:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000934",
abstract = "Urban areas and their voracious appetites are
increasingly dominating the flows of energy and
materials around the globe. Understanding the size
distribution and dynamics of urban areas is vital if we
are to manage their growth and mitigate their negative
impacts on global ecosystems. For over 50 years, city
size distributions have been assumed to universally
follow a power function, and many theories have been
put forth to explain what has become known as Zipf's
law (the instance where the exponent of the power
function equals unity). Most previous studies, however,
only include the largest cities that comprise the tail
of the distribution. Here we show that national,
regional and continental city size distributions,
whether based on census data or inferred from cluster
areas of remotely-sensed nighttime lights, are in fact
lognormally distributed through the majority of cities
and only approach power functions for the largest
cities in the distribution tails. To explore generating
processes, we use a simple model incorporating only two
basic human dynamics, migration and reproduction, that
nonetheless generates distributions very similar to
those found empirically. Our results suggest that
macroscopic patterns of human settlements may be far
more constrained by fundamental ecological principles
than more fine-scale socioeconomic factors.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
keywords = "Zipf's Law",
pagecount = "6",
}
@Article{Diekmann:2007:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
journal = j-J-APPL-STAT,
volume = "34",
number = "3--4",
pages = "321--329",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664760601004940",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRnumber = "2380543",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by `Benford's law'. Recently, a test against
this distribution was used to identify fraudulent
accounting data. This test is based on the supposition
that first, second, third, and other digits in real
data follow the Benford distribution while the digits
in fabricated data do not. Is it possible to apply
Benford tests to detect fabricated or falsified
scientific data as well as fraudulent financial data?
We approached this question in two ways. First, we
examined the use of the Benford distribution as a
standard by checking the frequencies of the nine
possible first and ten possible second digits in
published statistical estimates. Second, we conducted
experiments in which subjects were asked to fabricate
statistical estimates (regression coefficients). The
digits in these experimental data were scrutinized for
possible deviations from the Benford distribution.
There were two main findings. First, both digits of the
published regression coefficients were approximately
Benford distributed or at least followed a pattern of
monotonic decline. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. Surprisingly, first digits of faked
data also exhibited a pattern of monotonic decline,
while second, third, and fourth digits were distributed
less in accordance with Benford's law. At least in the
case of regression coefficients, there were indications
that checks for digit-preference anomalies should focus
less on the first (i.e., leftmost) and more on later
digits.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; data fabrication; digital analysis;
distribution of digits from regression coefficients;
first digit law; Zipf's Law",
}
@Article{Dumbgen:2007:EBA,
author = "L. D{\"u}mbgen and C. Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = "ArXiv e-prints",
month = may,
year = "2007",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0705.4488",
keywords = "Mathematics - Probability, 60E15, 60F99",
primaryclass = "math.PR",
}
@Article{Egghe:2007:UHL,
author = "Leo Egghe",
title = "Untangling {Herdan's Law} and {Heaps' Law}:
Mathematical and informetric arguments",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "58",
number = "5",
pages = "702--709",
month = mar,
year = "2007",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20524",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:40 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
keywords = "Heaps' law in information retrieval; Herdan's law in
linguistics",
onlinedate = "2 Feb 2007",
}
@InProceedings{Fu:2007:GBL,
author = "D. Fu and Y. Q. Shi and W. Su",
editor = "Edward J. {Delp III} and Ping Wah Wong",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "A generalized {Benford}'s law for {JPEG} coefficients
and its applications in image forensics",
volume = "6505",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = feb,
year = "2007",
DOI = "https://doi.org/10.1117/12.704723",
ISSN = "0277-786X (print), 1996-756X (electronic)",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
acknowledgement = ack-nhfb,
}
@InProceedings{Gava:2007:IQF,
author = "Alexandre Majola Gava and Luiz {Roque de Souza
Vitiello, Jr.}",
booktitle = "{EnANPAD 2007: XXXI Encontro da ANPAD. Rio de Janeiro
/ RJ-22 a 26 de setembro de 2007}",
title = "Inflation, Quarterly Financial Statements and Fraud:
{Benford's Law} and the {Brazilian} Case",
publisher = "????",
address = "????",
pages = "1--13",
year = "2007",
bibdate = "Thu Oct 13 07:36:53 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.anpad.org.br/diversos/trabalhos/EnANPAD/enanpad_2007/CONT/2007_CONA819.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Giles:2007:BLN,
author = "D. E. Giles",
title = "{Benford's Law} and naturally occurring prices in
certain {eBay} auctions",
journal = j-APPL-ECON-LETT,
volume = "14",
number = "3",
pages = "157--161",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1080/13504850500425667",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Wed Nov 16 09:49:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/toc/rael20/current",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
journal-URL = "http://www.tandfonline.com/loi/rael20",
keywords = "Benford's Law; Fibonacci sequences; Lucas sequences",
}
@Article{Grendar:2007:ENP,
author = "Marian Grendar and George Judge and Laura Schechter",
title = "An empirical non-parametric likelihood family of
data-based {Benford}-like distributions",
journal = j-PHYSICA-A,
volume = "380",
number = "0",
pages = "429--438",
day = "1",
month = jul,
year = "2007",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2007.02.062",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
http://www.sciencedirect.com/science/article/pii/S0378437107001963",
abstract = "A mathematical expression known as Benford's law
provides an example of an unexpected relationship among
randomly selected sequences of first significant digits
(FSDs). Newcomb [Note on the frequency of use of the
different digits in natural numbers, Am. J. Math. 4
(1881) 39 40], and later Benford [The law of anomalous
numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551 572],
conjectured that {FSDs} would exhibit a weakly
monotonic decreasing distribution and proposed a
frequency proportional to the logarithmic rule.
Unfortunately, the Benford {FSD} function does not hold
for a wide range of scale-invariant multiplicative
data. To confront this problem we use
information-theoretic methods to develop a data-based
family of alternative Benford-like exponential
distributions that provide null hypotheses for testing
purposes. Two data sets are used to illustrate the
performance of generalized Benford-like
distributions.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Empirical likelihood; First significant
digit phenomenon; Information-theoretic method;
Minimum-divergence distance measure; Relative
frequencies",
}
@Article{Guo:2007:DIM,
author = "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
and Xiaodong Zhang",
title = "Does {Internet} media traffic really follow
{Zipf}-like distribution?",
journal = j-SIGMETRICS,
volume = "35",
number = "1",
pages = "359--360",
month = jun,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1145/1254882.1254929",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:42:48 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "It is commonly agreed that Web traffic follows the
Zipf-like distribution, which is an analytical
foundation for improving Web access performance by
client-server based proxy caching systems on the
Internet. However, some recent studies have observed
non-Zipf-like distributions of Internet media traffic
in different content delivery systems. Due to the
variety of media delivery systems and the diversity of
media content, existing studies on media traffic are
largely workload specific, and the observed access
patterns are often different from or even conflict with
each other. For Web media systems, study [3] reports
that the access pattern of streaming media is Zipf-like
in a university campus network, while study [2] finds
that it is not Zipf-like in an enterprise media
server.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "media; stretched exponential; Zipf-like",
}
@Article{Gupta:2007:IMS,
author = "Arjun K. Gupta and Saralees Nadarajah",
title = "Information matrices for some bivariate {Pareto}
distributions",
journal = j-APPL-MATH-COMP,
volume = "184",
number = "2",
pages = "1069--1079",
day = "15",
month = jan,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:01 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Hand:2007:DDD,
author = "David Hand",
title = "Deception and Dishonesty with Data: Fraud in Science",
journal = j-SIGNIF,
volume = "4",
number = "1",
pages = "22--25",
month = mar,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1740-9713.2007.00215.x",
ISSN = "1740-9705 (print), 1740-9713 (electronic)",
ISSN-L = "1740-9705",
bibdate = "Thu Nov 17 19:17:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/significance.bib",
acknowledgement = ack-nhfb,
ajournal = "Signif.",
fjournal = "Significance",
journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713",
onlinedate = "02 March 2007",
}
@Article{Hasumi:2007:ITS,
author = "Tomohiro Hasumi",
title = "Interoccurrence time statistics in the two-dimensional
{Burridge--Knopoff} earthquake model",
journal = j-PHYS-REV-E,
volume = "76",
number = "??",
pages = "026117",
day = "29",
month = aug,
year = "2007",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.76.026117",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.026117",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf--Mandelbrot law",
}
@TechReport{Hungerbuhler:2007:BGF,
author = "Norbert H{\"u}ngerb{\"u}hler",
title = "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
die Mathematik Steuers{\"u}ndern das F{\"u}rchten
lehrt} [{Benford's Law} on leading digits. Mathematics
teaches tax evaders to fear]",
type = "Report",
institution = "EducETH",
address = "Z{\"u}rich, Switzerland",
pages = "24",
day = "2",
month = mar,
year = "2007",
bibdate = "Fri Nov 18 12:02:21 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
acknowledgement = ack-nhfb,
language = "German",
lastaccess = "18 November 2011",
remark = "This report has several nice figures, including
photographs of Newcomb, Benford, and worn pages of log
tables, and an amazing plot of the agreement of
200,125,088 mathematical constants with Benford's
Law.",
}
@Article{Kumar:2007:DDD,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
title = "Detecting the dubious digits: {Benford}'s law in
forensic accounting",
journal = j-SIGNIF,
volume = "4",
number = "2",
pages = "81--83",
month = jun,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1740-9713.2007.00234.x",
ISSN = "1740-9705 (print), 1740-9713 (electronic)",
ISSN-L = "1740-9705",
MRnumber = "2380610",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/significance.bib",
acknowledgement = ack-nhfb,
ajournal = "Signif.",
fjournal = "Significance",
journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713",
onlinedate = "07 June 2007",
}
@Article{Loetscher:2007:ENS,
author = "T. Loetscher and P. Brugger",
title = "Exploring Number Space by Random Digit Generation",
journal = "Experimental Brain Research",
volume = "180",
number = "4",
pages = "655--665",
month = jul,
year = "2007",
CODEN = "EXBRAP",
DOI = "https://doi.org/10.1007/s00221-007-0889-0",
ISSN = "0014-4819 (print), 1432-1106 (electronic)",
ISSN-L = "0014-4819",
bibdate = "Sat Sep 10 13:10:08 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s00221-007-0889-0",
acknowledgement = ack-nhfb,
ajournal = "Exp. Brain Res.",
journal-URL = "http://link.springer.com/journal/221",
keywords = "Benford's Law",
}
@InProceedings{Lu:2007:UFD,
author = "Fletcher Lu",
booktitle = "{Knowledge Discovery in Databases: PKDD 2007}",
title = "Uncovering Fraud in Direct Marketing Data with a Fraud
Auditing Case Builder",
publisher = pub-SV,
address = pub-SV:adr,
pages = "540--547",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-74976-9_56",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-540-74976-9_56",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Mansury:2007:EZL,
author = "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
title = "The emergence of {Zipf's Law} in a system of cities:
an agent-based simulation approach",
journal = j-J-ECON-DYN-CONTROL,
volume = "31",
number = "7",
pages = "2438--2460",
day = "15",
month = jul,
year = "2007",
CODEN = "JEDCDH",
DOI = "https://doi.org/10.1016/j.jedc.2006.08.002",
ISSN = "0165-1889 (print), 1879-1743 (electronic)",
ISSN-L = "0165-1889",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165188906001527",
ZMnumber = "1163.91504",
abstract = "This paper develops a spatial agent-based model to
generate a system of cities that exhibits the
statistical properties of the Zipf's Law. The numerical
results suggest that the combination of bounded
rationality and maximum heterogeneity of agents can
produce a generic power-law relationship in the size
distribution of cities, but does not always generate
the Zipf's Law. We found sufficient conditions on the
probability distribution of spatial reach to generate
the Zipf's Law associated with unit power coefficient.
Our model also indicates that the Zipf's Law breaks
down unless the extent of agglomeration economies
overwhelms the negative disagglomerating forces.",
acknowledgement = ack-nhfb,
classmath = "91B72 (Spatial models)",
fjournal = "Journal of Economic Dynamics and Control",
keywords = "complex systems; power laws; spatial agent based
models; Zipf's Law",
}
@Article{Maslov:2007:PTZ,
author = "V. P. Maslov",
title = "Phase transitions of the zeroth kind and the
quantization of the {Zipf} law",
journal = j-TEORET-MATH-FIZ,
volume = "150",
number = "1",
pages = "118--142",
year = "2007",
CODEN = "TMFZAL",
DOI = "https://doi.org/10.1007/s11232-007-0008-1",
ISSN = "0564-6162",
ISSN-L = "0564-6162",
MRclass = "82B26 (82B03)",
MRnumber = "2325869 (2008g:82037)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
journal-URL = "http://link.springer.com/journal/11232",
}
@InProceedings{Mebane:2007:SD,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2007 Summer Meeting of the Political Methodology
Society, Pennsylvania State University, July 18--21,
2007}",
title = "Statistics for Digits",
publisher = "????",
address = "????",
pages = "1--21",
day = "2",
month = jul,
year = "2007",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:03:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm07.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Morris:2007:MRT,
author = "Steven A. Morris and Michel L. Goldstein",
title = "Manifestation of research teams in journal literature:
a growth model of papers, authors, collaboration,
coauthorship, weak ties, and {Lotka's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "58",
number = "12",
pages = "1764--1782",
month = oct,
year = "2007",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.20661",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:37 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "24 Aug 2007",
}
@Article{Nadarajah:2007:CPG,
author = "Saralees Nadarajah and Samuel Kotz",
title = "On the convolution of {Pareto} and gamma
distributions",
journal = j-COMP-NET-AMSTERDAM,
volume = "51",
number = "12",
pages = "3650--3654",
day = "22",
month = aug,
year = "2007",
CODEN = "????",
ISSN = "1389-1286 (print), 1872-7069 (electronic)",
ISSN-L = "1389-1286",
bibdate = "Sat Apr 2 08:42:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/13891286",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks",
journal-URL = "http://www.sciencedirect.com/science/journal/13891286",
}
@Article{Nicolaisen:2007:PPB,
author = "Jeppe Nicolaisen and Birger Hj{\o}rland",
title = "Practical potentials of {Bradford}'s law: a critical
examination of the received view",
journal = j-J-DOC,
volume = "63",
number = "3",
pages = "359--377",
month = "????",
year = "2007",
CODEN = "JDOCAS",
DOI = "https://doi.org/10.1108/00220410710743298",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 11:58:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{Nigrini:2007:BLA,
author = "Mark J. Nigrini and Steven J. Miller",
title = "{Benford's Law} Applied to Hydrology Data --- Results
and Relevance to Other Geophysical Data",
journal = j-MATH-GEOL,
volume = "39",
number = "5",
pages = "469--490",
month = jul,
year = "2007",
CODEN = "MATGED",
DOI = "https://doi.org/10.1007/s11004-007-9109-5",
ISSN = "0882-8121 (print), 1573-8868 (electronic)",
ISSN-L = "0882-8121",
bibdate = "Sun Feb 17 13:35:42 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11004-007-9109-5;
http://www.springerlink.com/content/m2274ng70435u3x6/",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Geology",
}
@Article{Nye:2007:PEN,
author = "J. Nye and C. Moul",
title = "The Political Economy of Numbers: On the Application
of {Benford's Law} to International Macroeconomic
Statistics",
journal = "{B. E.} Journal of Macroeconomics",
volume = "7",
number = "1",
pages = "??--??",
month = "????",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.2202/1935-1690.1449",
ISSN = "1935-1690",
ISSN-L = "1935-1690",
bibdate = "Tue Nov 22 20:48:42 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bepress.com/bejm/vol7/iss1/art17",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "Berkeley Electronic Press Journal of Macroeconomics",
}
@Article{Oteo:2007:DPE,
author = "J. A. Oteo and J. Ros",
title = "Double precision errors in the logistic map:
Statistical study and dynamical interpretation",
journal = j-PHYS-REV-E,
volume = "76",
pages = "036214",
month = sep,
year = "2007",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.76.036214",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:35:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036214",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
issue = "3",
journal-URL = "http://pre.aps.org/browse",
pagecount = "8",
remark = "From the abstract: ``a comparison with Benford?s law
for the distribution of the leading digit of
compilation of numbers is discussed.''",
}
@Article{Paech:2007:ZLN,
author = "Kerstin Paech and Wolfgang Bauer and Scott Pratt",
title = "{Zipf}'s law in nuclear multifragmentation and
percolation theory",
journal = j-PHYS-REV-C,
volume = "76",
number = "??",
pages = "054603",
day = "15",
month = nov,
year = "2007",
CODEN = "PRVCAN",
DOI = "https://doi.org/10.1103/PhysRevC.76.054603",
ISSN = "0556-2813 (print), 1089-490X, 1538-4497",
ISSN-L = "0556-2813",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevC.76.054603",
acknowledgement = ack-nhfb,
fjournal = "Physical Review C (Nuclear Physics)",
journal-URL = "http://prc.aps.org/browse",
keywords = "Zipf's Law",
}
@InProceedings{Perez-Gonzalez:2007:GBL,
author = "F. P{\'e}rez-Gonz{\'a}lez and G. L. Heileman and C. T.
Abdallah",
booktitle = "2007 European Control Conference (ECC)",
title = "A generalization of {Benford's Law} and its
application to images",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3613--3619",
month = jul,
year = "2007",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation methods; Benford's law; Benford's law
generalization; Convolution; DCT; discrete cosine
transform domain; discrete cosine transforms; Discrete
cosine transforms; first significant digit; forensics;
Fourier expansion; Fourier series; hidden message;
Histograms; image forensics; Image forensics; image
forensics; modular logarithmic domain; probability;
probability density function; Random variables;
watermarking",
}
@InProceedings{Perin:2007:CNA,
author = "Stephen P{\'e}rin",
booktitle = "Constructal Theory of Social Dynamics",
title = "The Constructal Nature of the Air Traffic System",
publisher = pub-SV,
address = pub-SV:adr,
pages = "119--145",
year = "2007",
DOI = "https://doi.org/10.1007/978-0-387-47681-0_6",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/chapter/10.1007/978-0-387-47681-0_6",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Simons:2007:SIP,
author = "John L. Simons",
title = "A simple (inductive) proof for the non-existence of
2-cycles of the $ 3 x + 1 $ problem",
journal = j-J-NUMBER-THEORY,
volume = "123",
number = "1",
pages = "10--17",
month = mar,
year = "2007",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2006.05.011",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X06001223",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
keywords = "Benford's Law",
}
@Book{Tijms:2007:UPC,
author = "H. C. Tijms",
title = "Understanding probability: chance rules in everyday
life",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "x + 442",
year = "2007",
ISBN = "0-511-34626-3 (e-book), 0-511-35003-1 (e-book),
0-521-70172-4 (paperback)",
ISBN-13 = "978-0-511-34626-2 (e-book), 978-0-511-35003-0
(e-book), 978-0-521-70172-3 (paperback)",
LCCN = "QA273 .T48 2007",
bibdate = "Mon Feb 18 06:48:08 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Probabilities; Mathematical analysis; Chance;
Mathematics; Probability and Statistics; General;
Waarschijnlijkheidstheorie;
Wahrscheinlichkeitsverteilung",
tableofcontents = "Probability questions \\
The law of large numbers and simulation \\
Probabilities in everyday life \\
Rare events and lotteries \\
Probability and statistics \\
Chance trees and Bayes' rule \\
Foundations of probability theory \\
Conditional probability and Bayes \\
Basic rules for discrete random variables \\
Continuous random variables \\
Jointly distributed random variables \\
Multivariate normal distribution \\
Conditional distributions \\
Generating functions \\
Markov chains",
}
@Article{Torres:2007:HDN,
author = "J. Torres and S. Fern{\'a}ndez and A. Gamero and A.
Sola",
title = "How do numbers begin? (the first digit law)",
journal = j-EUR-J-PHYS,
volume = "28",
number = "3",
pages = "L17--L25",
month = may,
year = "2007",
CODEN = "EJPHD4",
DOI = "https://doi.org/10.1088/0143-0807/28/3/N04",
ISSN = "0143-0807 (print), 1361-6404 (electronic)",
ISSN-L = "0143-0807",
bibdate = "Fri Feb 15 18:37:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://iopscience.iop.org/0143-0807/28/3/N04",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Physics",
journal-URL = "http://iopscience.iop.org/0143-0807/",
keywords = "Benford's Law; Frank Benford; Simon Newcomb",
remark-1 = "From page L19: ``He [Newcomb] founded the American
Astronomical Society, and was its first president; he
was a successful scientist.''.",
remark-2 = "From page L19: ``His [Newcomb's] discovery went
unnoticed by the scientific community, in spite of the
fact that Newcomb was already a famous scientist at the
time. He continued working in physical and mathematical
astronomy, receiving honours for his career --- a
crater of Mars takes his name --- but he was also
responsible for a famous funny mistake: he tried to
demonstrate that an object heavier than air could not
fly, just months before the Wright brothers' first
one-man aeroplane flew in 1903. Far from retracting,
Newcomb said that an aeroplane for two or more people
could not fly, so aeroplanes would not be worthwhile
pursuing [3, 4]. He died in 1909, without even
remembering the matter of the first significant digit
law.''",
remark-3 = "From page L19: ``Frank Benford, a physicist working at
General Electric (who was the inventor of the electric
light pointer), \ldots{}''.",
}
@Article{Wells:2007:QPV,
author = "K. Wells and J. Chiverton and M. Partridge and M.
Barry and H. Kadhem and B. Ott",
title = "Quantifying the Partial Volume Effect in {PET} Using
{Benford's Law}",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "54",
number = "5",
pages = "1616--1625",
month = oct,
year = "2007",
CODEN = "IRNSAM",
DOI = "https://doi.org/10.1109/TNS.2007.903182",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
}
@Article{Yeh:2007:SMD,
author = "Hsiaw-Chan Yeh",
title = "Some multivariate discrete time series models for
dependent multivariate {Zipf} counts",
journal = "Bulletin of the Institute of Mathematics. Academia
Sinica. New Series",
volume = "2",
number = "1",
pages = "29--53",
year = "2007",
CODEN = "????",
ISSN = "0304-9825",
ISSN-L = "0304-9825",
MRclass = "62M10 (62H20)",
MRnumber = "2294107",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Acad. Sin. (N.S.)",
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica. New Series",
}
@Article{Aerts:2008:CDD,
author = "Walter Aerts and Geert {Van Campenhout} and Tom {Van
Caneghem}",
title = "Clustering in dividends: Do managers rely on cognitive
reference points?",
journal = "Journal of Economic Psychology",
volume = "29",
number = "3",
pages = "276--284",
year = "2008",
DOI = "https://doi.org/10.1016/j.joep.2007.10.003",
ISSN = "0167-4870 (print), 1872-7719 (electronic)",
ISSN-L = "0167-4870",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167487007000864",
abstract = "Prior studies (see e.g. [Rosch, E. (1975). Cognitive
reference points. Cognitive Psychology, {\bf 7},
532--547]) indicate that multiples of ten serve as
cognitive reference points with a view to perceiving
and evaluating numbers. In order to explore whether
managers set dividends per share (henceforth DPS) at or
just above a cognitive reference point, we perform a
digital analysis on {US} firms' {DPS} for the period
1995--2004. That is, based on the theory of cognitive
reference points, {DPS} of \$2.00 will be viewed as
being abnormally larger than {DPS} of \$1.99, whereas
the actual difference only amounts to a marginal
\$0.01. Results presented in this paper indicate that
managers fall back on cognitive reference points when
they set DPS, which shows in significantly more (fewer)
zeroes (large digits) in the second-from-the-left
position of {DPS} than would normally be expected.
Overall, results presented in this paper tally with
prior findings on odd-ending prices and price
clustering documented in related disciplines.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Cognitive psychology; Management",
}
@Article{Aono:2008:ISO,
author = "June Y. Aono and Liming Guan",
title = "The impact of {Sarbanes--Oxley} act on cosmetic
earnings management",
journal = "Research in Accounting Regulation",
volume = "20",
number = "0",
pages = "205--215",
month = oct,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1052-0457(07)00212-3",
ISSN = "1052-0457 (print), 2467-9895 (electronic)",
ISSN-L = "1052-0457",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
abstract = "This study examines the mitigating effect of
Sarbanes--Oxley Act on cosmetic earnings management,
referred by Kinnunen and Koskela (2003) as earnings
manipulative behavior to round earnings such that they
result in an upward bias. This behavior reports income
numbers to achieve key cognitive reference points
represented by $ N \times $ 10k. Using Benford's Law,
our analysis compares the distribution of second digits
in reported annual net income for publicly listed {US}
companies between a 2-year periods before and after the
year 2002 when Sarbanes--Oxley Act went into effect.
Our empirical results suggest that, in the 2-year
period prior to the Act, there was evidence of cosmetic
earnings management. However, such behavior in
manipulating net income has noticeably decreased in the
period after the Act. This finding is consistent with
the notion that Sarbanes--Oxley Act has a deterring
impact on corporate America's manipulative behavior to
report earnings that achieve certain key reference
points.",
acknowledgement = ack-nhfb,
fjournal = "Research in Accounting Regulation",
keywords = "Benford's Law",
}
@Article{Batty:2008:PSS,
author = "Michael Batty",
title = "Perspective: The Size, Scale, and Shape of Cities",
journal = j-SCIENCE,
volume = "318",
number = "5864",
pages = "769--771",
day = "8",
month = feb,
year = "2008",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.1151419",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Feb 27 06:02:28 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/319/5864/769.abstract",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "200 tallest buildings in world; US cities of one
million (or more) population; Zipf's law",
}
@Article{Berger:2008:SDI,
author = "Arno Berger and Theodore P. Hill and Kent E.
Morrison",
title = "Scale-Distortion Inequalities for Mantissas of Finite
Data Sets",
journal = j-J-THEOR-PROBAB,
volume = "21",
number = "1",
pages = "97--117",
month = mar,
year = "2008",
CODEN = "JTPREO",
DOI = "https://doi.org/10.1007/s10959-007-0112-z",
ISSN = "0894-9840 (print), 1572-9230 (electronic)",
ISSN-L = "0894-9840",
bibdate = "Thu Aug 28 19:04:16 MDT 2014",
bibsource = "http://link.springer.com/journal/10959;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0894-9840&volume=21&issue=1;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib",
URL = "http://link.springer.com/article/10.1007/s10959-007-0112-z",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Probability",
journal-URL = "http://link.springer.com/journal/10959",
}
@Article{Bhattacharya:2008:FAB,
author = "S. Bhattacharya and K. Kumar",
title = "Forensic Accounting and {Benford's Law} [In the
Spotlight]",
journal = j-IEEE-SIGNAL-PROCESS-MAG,
volume = "25",
number = "2",
pages = "152--150",
month = mar,
year = "2008",
CODEN = "ISPRE6",
DOI = "https://doi.org/10.1109/MSP.2007.914724",
ISSN = "1053-5888 (print), 1558-0792 (electronic)",
ISSN-L = "1053-5888",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
acknowledgement = ack-nhfb,
fjournal = "IEEE signal processing magazine",
}
@Article{Brown:2008:CSP,
author = "Philip Brown and Jason Mitchell",
title = "Culture and stock price clustering: Evidence from {The
Peoples' Republic of China}",
journal = "Pacific-Basin Finance Journal",
volume = "16",
number = "1 2",
pages = "95--120",
year = "2008",
DOI = "https://doi.org/10.1016/j.pacfin.2007.04.005",
ISSN = "0927-538X (print), 1879-0585 (electronic)",
ISSN-L = "0927-538X",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Behavioral Finance in Asia",
URL = "http://www.sciencedirect.com/science/article/pii/S0927538X0700025X",
abstract = "Price clustering is the tendency of prices to be
observed more frequently at some numbers than others.
It results from human bias and from haziness or
imprecise beliefs about underlying value. To many
Chinese, the number 8 is attractive because it is
considered lucky, while 4 is unlucky and to be avoided.
We conduct a tightly controlled experiment to determine
whether a culturally heuristic number preference
exists, by studying trading on the Shanghai and
Shenzhen stock exchanges, which historically have been
relatively segmented along cultural lines. Our results
are extremely clear. For much of our sample period
(1994 2002), the prices of A-shares (mostly held by
Chinese organisations or individuals) traded on the
Shanghai stock exchange were more than twice as likely
to end in 8, than 4. Similarly, for A-shares traded on
the Shenzhen stock exchange a preference for 8 was
found. Preference for 8 on both exchanges was initially
very strong, but has weakened somewhat over time. It is
observed in opening, high and low as well as closing
prices, reinforcing its pervasiveness. Overall, the
cultural preference manifest in the prices of A-shares
is widespread in both markets and its presence is
accentuated once other factors that influence price
clustering are taken into account. The preference for 8
was much weaker for B-shares, which largely have been
held by foreigners.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Feng shui; Number preferences; Shanghai
and Shenzhen stock exchanges; Stock price clustering",
}
@Article{Chakravorty:2008:TAE,
author = "Douglas N. Hales and V. Sridharan and Abirami
Radhakrishnan and Satya S. Chakravorty and Samia M.
Siha",
title = "Testing the accuracy of employee-reported data: An
inexpensive alternative approach to traditional
methods",
journal = j-EUR-J-OPER-RES,
volume = "189",
number = "3",
pages = "583--593",
day = "16",
month = sep,
year = "2008",
CODEN = "EJORDT",
DOI = "https://doi.org/10.1016/j.ejor.2006.09.092",
ISSN = "0377-2217 (print), 1872-6860 (electronic)",
ISSN-L = "0377-2217",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Operational Research",
journal-URL = "http://www.sciencedirect.com/science/journal/03772217",
keywords = "Benford's Law",
xxauthor = "S. Chakravorty and Samia M. Siha",
}
@Article{Costas:2008:NCC,
author = "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
Javier Toro and Antonio Flores-Moya",
title = "The number of cells in colonies of the cyanobacterium
{{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
law",
journal = j-AQUAT-BOT,
volume = "89",
number = "3",
pages = "341--343",
month = oct,
year = "2008",
CODEN = "AQBODS",
DOI = "https://doi.org/10.1016/j.aquabot.2008.03.011",
ISSN = "0304-3770 (print), 1879-1522 (electronic)",
ISSN-L = "0304-3770",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
abstract = "Nowadays, numerous power- or scaling-laws are
encountered in many fields of biology: an example is
Benford's law. According to this law, the first
significant digit of any given series of numbers is
figure 1 more often than figure 2, which in turn
appears more often than 3, and so on. Here we show that
number of cells per colony in the cyanobacterium
Microcystis aeruginosa (F. T. K{\"u}tzing), randomly
isolated from different reservoirs and lakes from
Andalusia (S Spain), was very variable (with figures
differing up to five orders of magnitude). However, the
distribution of the number of cells per colony
satisfies Benford's law. This situation could be much
more general in colonial cyanobacteria.",
acknowledgement = ack-nhfb,
fjournal = "Aquatic Botany",
keywords = "Benford's Law; Colony; Microcystis aeruginosa",
}
@Article{Depken:2008:BZB,
author = "Craig A. {Depken II}",
title = "{Benford}, {Zipf} and the blogosphere",
journal = j-APPL-ECON-LETT,
volume = "15",
number = "9",
pages = "689--692",
month = "????",
year = "2008",
DOI = "https://doi.org/10.1080/13504850600735270",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:18:33 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
journal-URL = "http://www.tandfonline.com/loi/rael20",
onlinedate = "04 Jul 2008",
}
@Article{Dumbgen:2008:EBA,
author = "Lutz D{\"u}mbgen and Christoph Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "99--112",
year = "2008",
CODEN = "????",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E15 (60F99)",
MRnumber = "2386066 (2009b:60056)",
MRreviewer = "Pieter C. Allaart",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://arxiv.org/abs/0705.4488;
http://weber.math.washington.edu/~ejpecp/ECP/index.php",
abstract = "Benford's law states that for many random variables $
X > 0 $ its leading digit $ D = D(X) $ satisfies
approximately the equation $ P(D = d) = \log_{10}(1 + 1
/ d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon
follows from another, maybe more intuitive fact,
applied to $ Y \coloneq \log_{10}(X) $: For many real
random variables $Y$, the remainder $ U \coloneq Y -
\floor (Y) $ is approximately uniformly distributed on
$ [0, 1) $. The present paper provides new explicit
bounds for the latter approximation in terms of the
total variation of the density of $Y$ or some
derivative of it. These bounds are an interesting
alternative to traditional Fourier methods which yield
mostly qualitative results. As a by-product we obtain
explicit bounds for the approximation error in
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Gauvrit:2008:PLB,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Pourquoi la loi de {Benford} n'est pas
myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
not mysterious]",
journal = "Math{\'e}matiques et Sciences Humaines = Mathematics
and Social Sciences",
volume = "46",
number = "182",
pages = "7--15",
year = "2008",
CODEN = "????",
ISSN = "0987-6936 (print), 1950-6821 (electronic)",
ISSN-L = "0987-6936",
MRclass = "62A01 (91E10)",
MRnumber = "2433183 (2009f:62008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Sci. Hum. Math. Soc. Sci.",
fjournal = "Math{\'e}matiques et Sciences Humaines= Mathematics
and Social Sciences",
language = "French",
}
@Article{Grandison:2008:BPK,
author = "S. Grandison and R. J. Morris",
title = "Biological Pathway Kinetic Rate Constants Are
Scale-Invariant",
journal = j-BIOINFORMATICS,
volume = "24",
number = "6",
pages = "741--743",
month = "????",
year = "2008",
DOI = "https://doi.org/10.1093/bioinformatics/btn041",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Sat Sep 10 11:56:57 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/18238786",
acknowledgement = ack-nhfb,
fjournal = "Bioinformatics",
journal-URL = "http://bioinformatics.oxfordjournals.org/",
keywords = "Benford's Law",
}
@Article{Hales:2008:TAE,
author = "Douglas N. Hales and V. Sridharan and Abirami
Radhakrishnan and Satya S. Chakravorty and Samia M.
Siha",
title = "Testing the accuracy of employee-reported data: An
inexpensive alternative approach to traditional
methods",
journal = j-EUR-J-OPER-RES,
volume = "189",
number = "3",
pages = "583--593",
year = "2008",
CODEN = "EJORDT",
DOI = "https://doi.org/10.1016/j.ejor.2006.09.092",
ISSN = "0377-2217 (print), 1872-6860 (electronic)",
ISSN-L = "0377-2217",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
abstract = "Although Information Technology (IT) solutions improve
the collection and validation of operational data,
Operations Managers must often rely on self-reported
data from workers to make decisions. The problem with
this data is that they are subject to intentional
manipulation, thus reducing their suitability for
decision-making. A method of identifying manipulated
data, digital analysis, addresses this problem at low
cost. In this paper, we demonstrate how one uses this
method in real-world companies to validate
self-reported data from line workers. The results of
our study suggest that digital analysis estimates the
accuracy of employee reported data in operations
management, within limited contexts. These findings
lead to improved operating performance by providing a
tool for practitioners to exclude inaccurate
information.",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Operational Research",
journal-URL = "http://www.sciencedirect.com/science/journal/03772217",
keywords = "Benford's Law; Digital analysis; Fraud detection;
Operations management; Plastics industry",
}
@Article{Hayes:2008:LED,
author = "S. J. Hayes",
title = "Letter to the {Editor}: Does Terminal Digit Preference
Occur in Pathology?",
journal = j-J-CLIN-PATHOL,
volume = "61",
number = "8",
pages = "975--976",
month = "????",
year = "2008",
CODEN = "JCPAAK",
DOI = "https://doi.org/10.1136/jcp.2008.057851",
ISSN = "0021-9746 (print), 1472-4146 (electronic)",
ISSN-L = "0021-9746",
bibdate = "Sat Sep 10 12:01:29 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcp.bmj.com/content/61/8/975.2",
acknowledgement = ack-nhfb,
fjournal = "Journal of Clinical Pathology",
journal-URL = "http://jcp.bmj.com/content/by/year",
keywords = "Benford's Law",
}
@Article{Hayes:2008:TDP,
author = "S. J. Hayes",
title = "Terminal Digit Preference Occurs in Pathology
Reporting Irrespective of Patient Management
Implication",
journal = j-J-CLIN-PATHOL,
volume = "61",
number = "9",
pages = "1071--1072",
month = "????",
year = "2008",
CODEN = "JCPAAK",
DOI = "https://doi.org/10.1136/jcp.2008.059543",
ISSN = "0021-9746 (print), 1472-4146 (electronic)",
ISSN-L = "0021-9746",
bibdate = "Sat Sep 10 12:05:19 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcp.bmj.com/content/61/9/1071.extract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Clinical Pathology",
keywords = "Benford's Law",
}
@Article{Hefeeda:2008:TMP,
author = "Mohamed Hefeeda and Osama Saleh",
title = "Traffic modeling and proportional partial caching for
peer-to-peer systems",
journal = j-IEEE-TRANS-NETWORKING,
volume = "16",
number = "6",
pages = "1447--1460",
month = dec,
year = "2008",
CODEN = "IEANEP",
DOI = "https://doi.org/10.1109/TNET.2008.918081",
ISSN = "1063-6692 (print), 1558-2566 (electronic)",
ISSN-L = "1063-6692",
bibdate = "Fri Mar 6 16:31:04 MST 2009",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
abstract = "Peer-to-peer (P2P) file sharing systems generate a
major portion of the Internet traffic, and this portion
is expected to increase in the future. We explore the
potential of deploying proxy caches in different
Autonomous Systems (ASes) with the goal of reducing the
cost incurred by Internet service providers and
alleviating the load on the Internet backbone. We
conduct an eight-month measurement study to analyze the
P2P traffic characteristics that are relevant to
caching, such as object popularity, popularity
dynamics, and object size. Our study shows that the
popularity of P2P objects can be modeled by a
Mandelbrot-Zipf distribution, and that several
workloads exist in P2P traffic. Guided by our findings,
we develop a novel caching algorithm for P2P traffic
that is based on object segmentation, and proportional
partial admission and eviction of objects. Our
trace-based simulations show that with a relatively
small cache size, a byte hit rate of up to 35\% can be
achieved by our algorithm, which is close to the byte
hit rate achieved by an off-line optimal algorithm with
complete knowledge of future requests. Our results also
show that our algorithm achieves a byte hit rate that
is at least 40\% more, and at most triple, the byte hit
rate of the common web caching algorithms. Furthermore,
our algorithm is robust in face of aborted downloads,
which is a common case in P2P systems.",
acknowledgement = ack-nhfb,
fjournal = "IEEE\slash ACM Transactions on Networking",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771",
keywords = "internet measurement; network protocols; peer-to-peer
systems; traffic analysis; traffic modeling",
}
@Article{Huang:2008:IZL,
author = "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
Jing-Shiuan Hua",
title = "An investigation of {Zipf's Law} for fraud detection
{(DSS\# 06-10-1826R(2))}",
journal = j-DEC-SUPP-SYS,
volume = "46",
number = "1",
pages = "70--83",
month = dec,
year = "2008",
CODEN = "DSSYDK",
DOI = "https://doi.org/10.1016/j.dss.2008.05.003",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
abstract = "Fraud risk is higher than ever before. Unfortunately,
many auditors lack the expertise to deal with the
related risks. The objectives of this research are to
develop an innovative fraud detection mechanism on the
basis of Zipf's Law. The purpose of this technique is
to assist auditors in reviewing the overwhelming
volumes of datasets and identifying any potential fraud
records. The authors conducted Quasi-experiment
research on the KDDCUP'99 benchmark intrusion detection
dataset to verify the performance of the proposed
mechanism. The simulation experimental results
demonstrate that Zipf Analysis can assist auditors to
locate the source of suspicion and further enhance the
resulting audit processes.",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law; Fraud detection; Misclassification cost
matrix; Quasi-experiment research; Zipf's Law",
}
@Article{Humenberger:2008:EBB,
author = "H. Humenberger",
title = "{Eine elementarmathematische Begr{\"u}ndung des
Benford-Gesetzes}. ({German}) [{An} elementary
mathematical derivation of the {Benford Law}]",
journal = "Der Mathematikunterricht",
volume = "54",
number = "??",
pages = "24--34",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "0025-5807",
ISSN-L = "0025-5807",
bibdate = "Fri Nov 18 11:59:44 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Ipeirotis:2008:CAH,
author = "Panagiotis G. Ipeirotis and Luis Gravano",
title = "Classification-aware hidden-web text database
selection",
journal = j-TOIS,
volume = "26",
number = "2",
pages = "6:1--6:??",
month = mar,
year = "2008",
CODEN = "ATISET",
DOI = "https://doi.org/10.1145/1344411.1344412",
ISSN = "1046-8188",
ISSN-L = "0734-2047",
bibdate = "Thu Jun 12 16:52:34 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/tois/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Many valuable text databases on the web have
noncrawlable contents that are ``hidden'' behind search
interfaces. Metasearchers are helpful tools for
searching over multiple such ``hidden-web'' text
databases at once through a unified query interface. An
important step in the metasearching process is database
selection, or determining which databases are the most
relevant for a given user query. The state-of-the-art
database selection techniques rely on statistical
summaries of the database contents, generally including
the database vocabulary and associated word
frequencies. Unfortunately, hidden-web text databases
typically do not export such summaries, so previous
research has developed algorithms for constructing
approximate content summaries from document samples
extracted from the databases via querying. We present a
novel ``focused-probing'' sampling algorithm that
detects the topics covered in a database and adaptively
extracts documents that are representative of the topic
coverage of the database. Our algorithm is the first to
construct content summaries that include the
frequencies of the words in the database.
Unfortunately, Zipf's law practically guarantees that
for any relatively large database, content summaries
built from moderately sized document samples will fail
to cover many low-frequency words; in turn, incomplete
content summaries might negatively affect the database
selection process, especially for short queries with
infrequent words. To enhance the sparse document
samples and improve the database selection decisions,
we exploit the fact that topically similar databases
tend to have similar vocabularies, so samples extracted
from databases with a similar topical focus can
complement each other. We have developed two database
selection algorithms that exploit this observation. The
first algorithm proceeds hierarchically and selects the
best categories for a query, and then sends the query
to the appropriate databases in the chosen categories.
The second algorithm uses ``shrinkage,'' a statistical
technique for improving parameter estimation in the
face of sparse data, to enhance the database content
summaries with category-specific words. We describe how
to modify existing database selection algorithms to
adaptively decide (at runtime) whether shrinkage is
beneficial for a query. A thorough evaluation over a
variety of databases, including 315 real web databases
as well as TREC data, suggests that the proposed
sampling methods generate high-quality content
summaries and that the database selection algorithms
produce significantly more relevant database selection
decisions and overall search results than existing
algorithms.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Information Systems (TOIS)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J779",
keywords = "database selection; Distributed information retrieval;
web search",
}
@Article{Jager:2008:DAD,
author = "Hendrik Jager and Pierre Liardet",
title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs
de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
journal = "Proceedings of the Koninklijke Nederlandse Akademie
van Wetenschappen, Series A, Indagationes
mathematicae",
volume = "91",
number = "2",
pages = "181--197",
day = "20",
month = jun,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1385-7258(88)80026-X",
ISSN = "1385-7258 (print), 1878-5972 (electronic)",
ISSN-L = "1385-7258",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
acknowledgement = ack-nhfb,
fjournal = "Indagationes Mathematicae (Proceedings)",
keywords = "Benford's Law",
language = "French",
xxjournal = "Indagationes Mathematicae (Proceedings)",
}
@Article{Jang:2008:CDH,
author = "Dennis Jang and Jung Uk Kang and Alex Kruckman and Jun
Kudo and Steven J. Miller",
title = "Chains of Distributions, Hierarchical {Bayesian}
Models and {Benford's Law}",
journal = "arxiv.org",
pages = "1--15",
day = "27",
month = may,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Thu Oct 13 07:41:45 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
http://arxiv.org/abs/0805.4226",
abstract = "Kossovsky recently conjectured that the distribution
of leading digits of a chain of probability
distributions converges to Benford's law as the length
of the chain grows. We prove his conjecture in many
cases, and provide an interpretation in terms of
products of independent random variables and a central
limit theorem. An interesting consequence is that in
hierarchical Bayesian models priors tend to satisfy
Benford's Law as the number of levels of the hierarchy
increases, which allows us to develop some simple tests
(based on Benford's law) to test proposed models. We
give explicit formulas for the error terms as sums of
Mellin transforms, which converges extremely rapidly as
the number of terms in the chain grows. We may
interpret our results as showing that certain Markov
chain Monte Carlo processes are rapidly mixing to
Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
pagecount = "15",
primaryclass = "math.PR",
}
@Article{Jelenkovic:2008:CMS,
author = "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
title = "Characterizing the miss sequence of the {LRU} cache",
journal = j-SIGMETRICS,
volume = "36",
number = "2",
pages = "119--121",
month = sep,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1145/1453175.1453203",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Wed Aug 25 07:31:09 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Renewed interest in caching systems stems from their
wide-spread use for reducing the document download
latency over the Internet. Since caches are usually
organized in a hierarchical manner, it is important to
study the performance properties of tandem caches. The
first step in understanding this problem is to
characterize the miss stream from one single cache
since it represents the input to the next level cache.
In this regard, we discover that the miss stream from
one single cache is approximated well by the
superposition of a number of asymptotically independent
renewal processes. Interestingly, when this weakly
correlated miss sequence is fed into another cache,
this barely observable correlation can lead to
measurably different caching performance when compared
to the independent reference model. This result is
likely to enable the development of a rigorous analysis
of the tandem cache performance.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
journal-URL = "http://portal.acm.org/toc.cfm?id=J618",
keywords = "average-case analysis; cache fault probability;
hierarchical caching; least-recently-used caching; web
caching; Zipf's law",
}
@Article{Kafri:2008:SIS,
author = "Oded Kafri",
title = "Sociological Inequality and the {Second Law}",
journal = "ArXiv e-prints",
year = "2008",
bibdate = "Mon Nov 21 06:41:29 2011",
bibsource = "http://dblp.uni-trier.de;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0805.3206",
abstract = "There are two fair ways to distribute particles in
boxes. The first way is to divide the particles equally
between the boxes. The second way, which is calculated
here, is to score fairly the particles between the
boxes. The obtained power law distribution function
yields an uneven distribution of particles in boxes. It
is shown that the obtained distribution fits well to
sociological phenomena, such as the distribution of
votes in polls and the distribution of wealth and
Benford's law.",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:ABL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Boris Aurer and Miroslav Ba{\'c}a",
booktitle = "Proceedings of the 19th Central European Conference on
Information and Intelligent Systems (CECIS 2008)",
title = "Application of {Benford's Law} in Payment System
Auditing",
publisher = "Fakultet organizacije i informatike",
address = "Vara{\v{z}}din, Croatia",
pages = "187--193",
year = "2008",
bibdate = "Sun Nov 13 11:14:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:EBL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Mario Plenkovi{\'c}",
booktitle = "Society and Technology 2008",
title = "Evaluation of {Benford's Law}: application in stock
prices and stock turnover",
publisher = "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
address = "Zagreb, Croatia",
pages = "57--71",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Nov 13 11:18:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "International Federation of Communication Studies,
Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
Zagrebu.",
}
@Article{Linville:2008:PFN,
author = "Mark Linville",
title = "The Problem of False Negative Results in the Use of
Digit Analysis",
journal = "Journal of Applied Business Research",
volume = "24",
number = "1",
pages = "17--25",
month = "First Quarter",
year = "2008",
DOI = "https://doi.org/10.19030/jabr.v24i1.1363",
ISSN = "0892-7626 (print), 2157-8834 (electronic)",
ISSN-L = "0892-7626",
bibdate = "Thu Oct 13 07:34:30 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.cluteinstitute.com/ojs/index.php/JABR/article/view/1363",
acknowledgement = ack-nhfb,
ajournal = "J. Appl. Bus. Res.",
journal-URL = "http://journals.cluteonline.com/index.php/JABR",
keywords = "Benford's Law",
}
@Article{Liu:2008:MNS,
author = "Cheng-Shi Liu",
title = "Maximal non-symmetric entropy leads naturally to
{Zipf}'s law",
journal = j-FRACTALS,
volume = "16",
number = "1",
pages = "99--101",
year = "2008",
CODEN = "FRACEG",
DOI = "https://doi.org/10.1142/S0218348X08003788",
ISSN = "0218-348X",
ISSN-L = "0218-348X",
MRclass = "94A17 (94A15)",
MRnumber = "2399875 (2009c:94027)",
MRreviewer = "Yasuichi Horibe",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fractals. Complex Geometry, Patterns, and Scaling in
Nature and Society",
journal-URL = "http://www.worldscientific.com/loi/fractals",
}
@Article{Lolbert:2008:NEG,
author = "Tam{\'a}s Lolbert",
title = "On the non-existence of a general {Benford}'s law",
journal = j-MATH-SOC-SCI,
volume = "55",
number = "2",
pages = "103--106",
month = mar,
year = "2008",
CODEN = "MSOSDD",
DOI = "https://doi.org/10.1016/j.mathsocsci.2007.09.001",
ISSN = "0165-4896 (print), 1879-3118 (electronic)",
ISSN-L = "0165-4896",
MRclass = "60A10 (60E10)",
MRnumber = "2391902",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
abstract = "Benford's law states that in randomly collected
numbers certain digits are more often leading digits
than others. More formally: the general law states that
the mantissae follow the logarithmic distribution in
any base. Benford's law was recognized by many
mathematicians so that several possible explanations
have been derived, but several questions are still
open. Applications are widespread, for example an
auditing technique (the so-called digital analysis),
which is employed around the world by internal revenue
services to detect tax fraud, is based on this
phenomenon.\par
In this paper it will be shown that there exists no
probability measure that would obey Benford's law for
any base, but if the set of possible bases does not
exceed a given upper limit, most real-life
distributions obey, or can be transformed to obey
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Social Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/01654896",
keywords = "Benford's Law; Characteristic function; Mantissa;
Numeral base",
}
@Article{Luque:2008:FDF,
author = "Bartolo Luque and Lucas Lacasa",
title = "The first digit frequencies of primes and {Riemann}
zeta zeros tend to uniformity following a
size-dependent generalized {Benford}'s law",
journal = "ArXiv e-prints",
month = nov,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See published paper \cite {Luque:2009:FDF}.",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
http://arxiv.org/abs/0811.3302",
abstract = "Prime numbers seem to distribute among the natural
numbers with no other law than that of chance, however
its global distribution presents a quite remarkable
smoothness. Such interplay between randomness and
regularity has motivated scientists of all ages to
search for local and global patterns in this
distribution that eventually could shed light into the
ultimate nature of primes. In this work we show that a
generalization of the well known first-digit Benford's
law, which addresses the rate of appearance of a given
leading digit $d$ in data sets, describes with
astonishing precision the statistical distribution of
leading digits in the prime numbers sequence. Moreover,
a reciprocal version of this pattern also takes place
in the sequence of the nontrivial Riemann zeta zeros.
We prove that the prime number theorem is, in the last
analysis, the responsible of these patterns. Some new
relations concerning the prime numbers distribution are
also deduced, including a new approximation to the
counting function $ \pi (n) $. Furthermore, some
relations concerning the statistical conformance to
this generalized Benford's law are derived. Some
applications are finally discussed.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0811.3302",
keywords = "Mathematics - Number Theory, Mathematics -
Probability, Mathematics - Statistics",
pagecount = "20",
primaryclass = "math.NT",
}
@Article{Maillart:2008:ETZ,
author = "T. Maillart and D. Sornette and S. Spaeth and G. von
Krogh",
title = "Empirical Tests of {Zipf's Law} Mechanism in Open
Source {Linux} Distribution",
journal = j-PHYS-REV-LET,
volume = "101",
number = "21",
pages = "218701",
day = "19",
month = nov,
year = "2008",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.101.218701",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/linux.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "4",
}
@Article{Manin:2008:ZLA,
author = "Dmitrii Y. Manin",
title = "{Zipf's Law} and Avoidance of Excessive Synonymy",
journal = j-COGN-SCI,
volume = "32",
number = "7",
pages = "1075--1098",
year = "2008",
CODEN = "COGSD5",
DOI = "https://doi.org/10.1080/03640210802020003",
ISSN = "0364-0213 (print), 1551-6709 (electronic)",
ISSN-L = "0364-0213",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Cognitive Science",
keywords = "Semantics; Synonymy; Word frequency; Word meaning;
Zipf's law",
}
@Article{Mayr:2008:EBE,
author = "Philipp Mayr",
title = "An evaluation of {Bradfordizing} Effects",
journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
volume = "2",
number = "2",
pages = "21--27",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1080/09737766.2008.10700850",
ISSN = "0973-7766 (print), 2168-930X (electronic)",
ISSN-L = "0973-7766",
bibdate = "Thu Sep 10 17:47:02 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
acknowledgement = ack-nhfb,
fjournal = "Collnet Journal of Scientometrics and Information
Management",
journal-URL = "http://www.tandfonline.com/loi/tsim20",
}
@InProceedings{Mebane:2008:EFO,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{The American Electoral Process conference, Center for
the Study of Democratic Politics, Princeton University,
May 1--3, 2008}",
title = "Election Forensics: Outlier and Digit Tests in
{America} and {Russia}",
publisher = "????",
address = "????",
pages = "i + 26",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:08:23 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/aep2008.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Mebane:2008:EFSa,
author = "Walter R. {Mebane, Jr.}",
editor = "R. Michael Alvarez and Thad E. Hall and Susan D.
Hyde",
booktitle = "{The Art and Science of Studying Election Fraud:
Detection, Prevention, and Consequences}",
title = "Election Forensics: The Second-digit {Benford's Law}
Test and Recent {American Presidential} Elections",
publisher = "Brookings Institution",
address = "Washington, DC, USA",
pages = "ii + 30",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Feb 16 12:04:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Preprint dated 3 November 2006.",
URL = "http://www.umich.edu/~wmebane/fraud06.pdf",
acknowledgement = ack-nhfb,
remark = "An earlier version of this paper was presented at the
Election Fraud Conference, Salt Lake City, Utah,
September 29--30, 2006.",
}
@InCollection{Mebane:2008:EFSb,
author = "Walter R. {Mebane, Jr.}",
title = "Election forensics: the second-digit {Benford's Law}
test and recent {American} presidential elections",
crossref = "Alvarez:2008:EFD",
pages = "??--??",
year = "2008",
bibdate = "Sat Sep 10 14:25:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Miller:2008:MCL,
author = "Steven J. Miller and Mark J. Nigrini",
title = "The modulo $1$ central limit theorem and {Benford's
Law} for products",
journal = "International Journal of Algebra",
volume = "2",
number = "3",
pages = "119--130",
year = "2008",
CODEN = "????",
ISSN = "1312-8868 (print), 1314-7595 (electronic)",
ISSN-L = "1312-8868",
MRclass = "60F05 (11K06 42A10)",
MRnumber = "2417189 (2009e:60053)",
MRreviewer = "Gutti J. Babu",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.m-hikari.com/ija/ija-password-2008/ija-password1-4-2008/millerIJA1-4-2008.pdf",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Algebra",
fjournal = "International Journal of Algebra",
journal-URL = "http://www.m-hikari.com/ija/index.html",
}
@Article{Miller:2008:OSB,
author = "Steven J. Miller and Mark J. Nigrini",
title = "Order statistics and {Benford}'s law",
journal = j-INT-J-MATH-MATH-SCI,
pages = "382948:1--382948:19",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1155/2008/382948",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "62G30 (62E10)",
MRnumber = "2461421 (2010c:62168)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 382948.",
URL = "http://arxiv.org/abs/math/0601344;
https://www.hindawi.com/journals/ijmms/2008/382948/",
abstract = "Fix a base $B$ and let zeta have the standard
exponential distribution; the distribution of digits of
zeta base $B$ is known to be very close to Benford's
Law. If there exists a $C$ such that the distribution
of digits of $C$ times the elements of some set is the
same as that of zeta, we say that set exhibits shifted
exponential behavior base $B$ (with a shift of $ \log_B
C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be
independent identically distributed random variables.
If the $ X_i $'s are drawn from the uniform
distribution on $ [0, L] $, then as $ N \to \infty $
the distribution of the digits of the differences
between adjacent order statistics converges to shifted
exponential behavior (with a shift of $ \log_B L / N
\bmod 1 $ ). By differentiating the cumulative
distribution function of the logarithms modulo 1,
applying Poisson Summation and then integrating the
resulting expression, we derive rapidly converging
explicit formulas measuring the deviations from
Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$
independent random variables from any compactly
supported distribution with uniformly bounded first and
second derivatives and a second order Taylor series
expansion at each point. The distribution of digits of
any $ N^\delta $ consecutive differences {\em and\/}
all $ N - 1 $ normalized differences of the order
statistics exhibit shifted exponential behavior. We
derive conditions on the probability density which
determine whether or not the distribution of the digits
of all the un-normalized differences converges to
Benford's Law, shifted exponential behavior, or
oscillates between the two, and show that the Pareto
distribution leads to oscillating behavior.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
journal-URL = "https://www.hindawi.com/journals/ijmms/",
keywords = "Benford's Law",
pagecount = "19",
}
@Article{Mitchell:2008:TST,
author = "James G. Mitchell and Laurent Seuront",
title = "Towards a seascape topology {II}: {Zipf} analysis of
one-dimensional patterns",
journal = j-J-MAR-SYST,
volume = "69",
number = "3--4",
pages = "328--338",
month = feb,
year = "2008",
CODEN = "JMASE5",
DOI = "https://doi.org/10.1016/j.jmarsys.2006.03.026",
ISSN = "0924-7963 (print), 1879-1573 (electronic)",
ISSN-L = "0924-7963",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000632",
acknowledgement = ack-nhfb,
fjournal = "Journal of Marine Systems",
keywords = "Zipf's Law",
}
@Article{Mizuno:2008:PLE,
author = "Takayuki Mizuno and Masahiro Toriyama and Takao Terano
and Misako Takayasu",
title = "{Pareto} law of the expenditure of a person in
convenience stores",
journal = j-PHYSICA-A,
volume = "387",
number = "15",
pages = "3931--3935",
year = "2008",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2008.01.059",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B82",
MRnumber = "2586890",
bibdate = "Mon Feb 18 17:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Ni:2008:BLH,
author = "D. Ni and Z. Ren",
title = "{Benford}'s law and half-lives of unstable nuclei",
journal = j-EUR-PHYS-J-A,
volume = "38",
pages = "251--255",
month = dec,
year = "2008",
CODEN = "EPJAFV",
DOI = "https://doi.org/10.1140/epja/i2008-10680-8",
ISSN = "1434-6001 (print), 1434-601X (electronic)",
ISSN-L = "1434-6001",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal A: Hadrons and Nuclei",
journal-URL = "http://www.springerlink.com/content/1434-6001",
}
@Article{Pain:2008:BLC,
author = "Jean-Christophe Pain",
title = "{Benford}'s law and complex atomic spectra",
journal = j-PHYS-REV-E,
volume = "77",
number = "1",
pages = "012102:1--012102:3",
month = jan,
year = "2008",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.77.012102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P;
http://pre.aps.org/abstract/PRE/v77/i1/e012102",
abstract = "We found that in transition arrays of complex atomic
spectra, the strengths of electric-dipolar lines obey
Benford's law, which means that their significant
digits follow a logarithmic distribution favoring the
smallest values. This indicates that atomic processes
result from the superposition of uncorrelated
probability laws and that the occurrence of digits
reflects the constraints induced by the selection
rules. Furthermore, Benford's law can be a useful test
of theoretical spectroscopic models. Its applicability
to the statistics of electric-dipolar lines can be
understood in the framework of random matrix theory and
is consistent with the Porter-Thomas law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eid = "012102",
eprint = "0801.0946",
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Probability theory, Oscillator strengths, lifetimes,
transition moments, Other topics in the theory of the
electronic structure of atoms and molecules",
pagecount = "3",
primaryclass = "quant-ph",
}
@Article{Petek:2008:PNH,
author = "Marija Petek",
title = "Personal name headings in {COBIB}: Testing {Lotka}'s
Law",
journal = j-SCIENTOMETRICS,
volume = "75",
number = "1",
pages = "175--188",
month = apr,
year = "2008",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-007-1829-2",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:03 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
URL = "http://link.springer.com/article/10.1007/s11192-007-1829-2",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Ravikumar:2008:BND,
author = "Bala Ravikumar",
title = "The {Benford--Newcomb} Distribution and Unambiguous
Context-Free Languages",
journal = j-INT-J-FOUND-COMP-SCI,
volume = "19",
number = "3",
pages = "717--727",
month = jun,
year = "2008",
CODEN = "IFCSEN",
DOI = "https://doi.org/10.1142/S0129054108005905",
ISSN = "0129-0541 (print), 1793-6373 (electronic)",
ISSN-L = "0129-0541",
MRclass = "68Q42 (68Q25 68Q45)",
MRnumber = "2417964 (2009h:68068)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Foundations of Computer
Science (IJFCS)",
journal-URL = "http://www.worldscientific.com/loi/ijfcs",
}
@Article{Ristic:2008:GSP,
author = "Miroslav M. Risti{\'c}",
title = "A generalized semi-{Pareto} minification process",
journal = j-STAT-PAPERS,
volume = "49",
number = "2",
pages = "343--351",
month = apr,
year = "2008",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-006-0017-4",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:27 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-006-0017-4",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{Schurger:2008:EBS,
author = "Klaus Sch{\"u}rger",
title = "Extensions of {Black--Scholes} processes and
{Benford's Law}",
journal = j-STOCH-PROC-APPL,
volume = "118",
number = "7",
pages = "1219--1243",
month = jul,
year = "2008",
CODEN = "STOPB7",
DOI = "https://doi.org/10.1016/j.spa.2007.07.017",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
MRclass = "60F10 (60G44 91B02 91B28)",
MRnumber = "2428715 (2009g:60037)",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414907001391",
abstract = "Let $Z$ be a stochastic process of the form $ Z (t) =
Z (0) \exp (\mu t + X (t) - \langle X \rangle_t / 2) $
where $ Z (0) > 0 $, $ \mu $ are constants, and $X$ is
a continuous local martingale having a deterministic
quadratic variation $ \langle X \rangle $ such that $
\langle X \rangle_t \to \infty $ as $ t \to \infty $.
We show that the mantissa (base $b$) of $ Z (t)$
(denoted by $ M (b) (Z (t))$) converges weakly to
Benford's Law as $ t \to \infty $. Supposing that $X$
satisfies a certain growth condition, we obtain large
deviation results for certain functionals (including
occupation time) of ($ M^{(b)} (Z(t))$). Similar
results are obtained in the discrete-time case. The
latter are used to construct a non-parametric test for
nonnegative processes ( $ Z (t)$ ) (based on the
observation of significant digits of ( $ Z (n)$ ) ) of
the null hypothesis $ H_0 (\sigma_0)$ which says that
$Z$ is a general Black--Scholes process having a
volatility $ \sigma \geq \sigma_0 ( > 0)$. Finally it
is shown that the mantissa of Brownian motion is not
even weakly convergent.",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03044149",
keywords = "Azuma's inequality; Benford's Law; Black Scholes
processes; Brownian motion; Exponential local
martingales; Large deviations; Leading digits;
Non-parametric hypothesis testing for processes;
Occupation time; Poisson's summation formula;
Significant digits; Strong theorems; Weak theorems",
}
@Article{Semboloni:2008:HCS,
author = "F. Semboloni",
title = "Hierarchy, cities size distribution and {Zipf}'s law",
journal = j-EUR-PHYS-J-B,
volume = "63",
number = "3",
pages = "295--301",
year = "2008",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1140/epjb/e2008-00203-1",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
MRclass = "91D10 (82B99 91D25)",
MRnumber = "2421552 (2009f:91111)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "Zbl 1189.91174",
acknowledgement = ack-nhfb,
fjournal = "The European Physical Journal B. Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
}
@Article{Seuront:2008:TST,
author = "Laurent Seuront and James G. Mitchell",
title = "Towards a seascape typology. {I}. {Zipf} versus
{Pareto} laws",
journal = j-J-MAR-SYST,
volume = "69",
number = "3--4",
pages = "310--327",
month = feb,
year = "2008",
CODEN = "JMASE5",
DOI = "https://doi.org/10.1016/j.jmarsys.2006.03.025",
ISSN = "0924-7963 (print), 1879-1573 (electronic)",
ISSN-L = "0924-7963",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000620",
acknowledgement = ack-nhfb,
fjournal = "Journal of Marine Systems",
keywords = "Zipf's Law",
}
@Article{Shaki:2008:RSN,
author = "Samuel Shaki and Martin H. Fischer",
title = "Reading space into numbers --- a cross-linguistic
comparison of the {SNARC} effect",
journal = j-COGNITION,
volume = "108",
number = "2",
pages = "590--599",
month = aug,
year = "2008",
CODEN = "CGTNAU",
DOI = "https://doi.org/10.1016/j.cognition.2008.04.001",
ISSN = "0010-0277 (print), 1873-7838 (electronic)",
ISSN-L = "0010-0277",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0010027708000978",
abstract = "Small numbers are spontaneously associated with left
space and larger numbers with right space (the {SNARC}
effect), for example when classifying numbers by
parity. This effect is often attributed to reading
habits but a causal link has so far never been
documented. We report that bilingual Russian Hebrew
readers show a {SNARC} effect after reading Cyrillic
script (from left-to-right) that is significantly
reduced after reading Hebrew script (from
right-to-left). In contrast, they have similar {SNARC}
effects after listening to texts in either language.
These results support the view that spatially
directional scanning habits contribute to the spatial
association of numbers but also emphasize its
flexibility.",
acknowledgement = ack-nhfb,
fjournal = "Cognition",
keywords = "Benford's Law; Mental number line; Reading direction;
Spatial Numerical Association of Response Codes
(SNARC); {SNARC}",
}
@Article{Volchenkov:2008:SUC,
author = "D. Volchenkov and Ph. Blanchard",
title = "Scaling and universality in city space syntax: Between
{Zipf} and {Matthew}",
journal = j-PHYSICA-A,
volume = "387",
number = "10",
pages = "2353--2364",
day = "1",
month = apr,
year = "2008",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2007.11.049",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437107012630",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Vuko:2008:UBL,
author = "Tina Vuko",
title = "Using {Benford's Law} to Detect Earnings Management
Practice: the Case of Listed Companies in {Croatia}",
journal = "Global Business \& Economics Anthology",
volume = "1",
number = "??",
pages = "69--74",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "1553-1333",
ISSN-L = "1553-1333",
bibdate = "Sun Nov 13 11:10:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Watrin:2008:BLI,
author = "C. Watrin and R. Struffert and R. Ullmann",
title = "{Benford's Law}: An Instrument for Selecting Tax Audit
Targets?",
journal = "Review of Managerial Science",
volume = "2",
number = "3",
pages = "219--237",
month = nov,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11846-008-0019-9",
ISSN = "1863-6683 (print), 1863-6691 (electronic)",
ISSN-L = "1863-6683",
bibdate = "Tue Nov 22 20:58:51 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11846-008-0019-9",
acknowledgement = ack-nhfb,
}
@Article{Wu:2008:IEP,
author = "Shu-Fei Wu",
title = "Interval estimation for a {Pareto} distribution based
on a doubly type {II} censored sample",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "52",
number = "7",
pages = "3779--3788",
day = "15",
month = mar,
year = "2008",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:42:27 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947308000030",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Book{Ziliak:2008:CSS,
author = "Stephen Thomas Ziliak and Deirdre N. McCloskey",
title = "The Cult of Statistical Significance: How the Standard
Error Costs Us Jobs, Justice, and Lives",
publisher = "University of Michigan Press",
address = "Ann Arbor, MI, USA",
pages = "xxiii + 321",
year = "2008",
ISBN = "0-472-07007-X (cloth), 0-472-05007-9 (paperback)",
ISBN-13 = "978-0-472-07007-7 (cloth), 978-0-472-05007-9
(paperback)",
LCCN = "HB137 .Z55 2008",
bibdate = "Tue Dec 9 15:55:11 MST 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
series = "Economics, cognition, and society",
URL = "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html",
acknowledgement = ack-nhfb,
remark = "This book has important comments on the battles among
Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
Pearson, supplementing the discussion of those
conflicts in \cite{McGrayne:2011:TWH}.",
subject = "economics; statistical methods; statistics; social
aspects; statistical hypothesis testing",
}
@Article{Ainsworth:2009:QSR,
author = "Richard Thompson Ainsworth and Urs Hengartner",
title = "{Quebec's Sales Recording Module (SRM)}: Fighting the
{Zapper}, {Phantomware}, and Tax Fraud with
technology",
journal = "Canadian Tax Journal",
volume = "57",
number = "4",
pages = "715--761",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "0068-9823",
ISSN-L = "0068-9823",
bibdate = "Fri Mar 22 08:37:54 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
journal-URL = "https://www.ctf.ca/ctfweb",
keywords = "Benford's Law",
}
@TechReport{Alexander:2009:RUB,
author = "James C. Alexander",
title = "Remarks on the use of {Benford's Law}",
type = "Working paper",
institution = "Department of Mathematics and Cognitive Science, Case
Western Reserve University",
address = "Cleveland, OH, USA",
day = "23",
month = nov,
year = "2009",
bibdate = "Fri Mar 22 08:40:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
}
@InProceedings{Altamirano:2009:GTU,
author = "Carlo Altamirano and Alberto Robledo",
editor = "J. Zhou",
booktitle = "Complex Sciences",
title = "Generalized Thermodynamics Underlying the Laws of
{Zipf} and {Benford}",
volume = "5",
publisher = pub-SV,
address = pub-SV:adr,
pages = "2232--??",
year = "2009",
DOI = "https://doi.org/10.1007/978-3-642-02469-6_100",
ISBN = "3-642-02468-8",
ISBN-13 = "978-3-642-02468-9",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
acknowledgement = ack-nhfb,
}
@Article{Anderson:2009:CRC,
author = "Thomas Anderson",
title = "Conference reviewing considered harmful",
journal = j-OPER-SYS-REV,
volume = "43",
number = "2",
pages = "108--116",
month = apr,
year = "2009",
CODEN = "OSRED8",
DOI = "https://doi.org/10.1145/1531793.1531815",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Thu Apr 23 19:43:22 MDT 2009",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "This paper develops a model of computer systems
research to help prospective authors understand the
often obscure workings of conference program
committees. We present data to show that the
variability between reviewers is often the dominant
factor as to whether a paper is accepted. We argue that
paper merit is likely to be Zipf distributed, making it
inherently difficult for program committees to
distinguish between most papers. We use game theory to
show that with noisy reviews and Zipf merit, authors
have an incentive to submit papers too early and too
often. These factors make conference reviewing, and
systems research as a whole, less efficient and less
effective. We describe some recent changes in
conference design to address these issues, and we
suggest some further potential improvements.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
}
@TechReport{Ansari:2009:PAV,
author = "Ali Ansari",
title = "Preliminary Analysis of the Voting Figures in {Iran}'s
2009 {Presidential} Election",
type = "Report",
number = "MENAP PP 2009/01",
institution = "Chatham House and the Institute of Iranian Studies,
University of St Andrews",
address = "St Andrews, UK",
day = "21",
month = jun,
year = "2009",
bibdate = "Sat Sep 10 10:42:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.chathamhouse.org/sites/files/chathamhouse/public/Research/Middle%20East/iranelection0609.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Battersby:2009:SAH,
author = "Stephen Battersby",
title = "Statistical analyses hint at fraud in {Iranian}
election",
journal = j-NEW-SCIENTIST,
volume = "202",
number = "2714",
pages = "10--??",
day = "24",
month = jun,
year = "2009",
CODEN = "NWSCAL",
DOI = "https://doi.org/10.1016/S0262-4079(09)61682-1",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
abstract = "Mathematicians add their own concerns to claims that
vote may have been rigged",
acknowledgement = ack-nhfb,
fjournal = "The New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
xxISSN = "0262-4079, 0028-6664",
}
@TechReport{Bauer:2009:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
number = "??",
institution = "Institute of Sociology, LMU Munich",
address = "Munich, Germany",
month = "????",
year = "2009",
bibdate = "Fri Nov 18 11:46:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Beber:2009:DD,
author = "B. Beber and A. Scacco",
title = "The Devil Is in the Digits",
journal = j-WASHINGTON-POST,
volume = "??",
number = "??",
pages = "??--??",
day = "20",
month = jun,
year = "2009",
ISSN = "0190-8286",
bibdate = "Sat Sep 10 10:28:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Washington Post",
journal-URL = "http://www.washingtonpost.com/",
keywords = "Benford's Law",
remark = "Not found in online newspaper archives.",
}
@TechReport{Berger:2009:BOB,
author = "A. Berger and T. P. Hill",
title = "{Benford} Online Bibliography",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2009",
bibdate = "Sat Nov 12 16:48:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.benfordonline.net",
acknowledgement = ack-nhfb,
remark = "According to \cite{Berger:2011:BLS}, the authors'
online bibliography contains more than 600
references.",
}
@InProceedings{Berinde:2009:SOH,
author = "Radu Berinde and Graham Cormode and Piotr Indyk and
Martin J. Strauss",
title = "Space-optimal heavy hitters with strong error bounds",
crossref = "Paredaens:2009:PTE",
pages = "157--166",
year = "2009",
DOI = "https://doi.org/10.1145/1559795.1559819",
bibdate = "Thu Jul 2 14:05:34 MDT 2009",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "The problem of finding heavy hitters and approximating
the frequencies of items is at the heart of many
problems in data stream analysis. It has been observed
that several proposed solutions to this problem can
outperform their worst-case guarantees on real data.
This leads to the question of whether some stronger
bounds can be guaranteed. We answer this in the
positive by showing that a class of `counter-based
algorithms' (including the popular and very
space-efficient FREQUENT and SPACESAVING algorithms)
provide much stronger approximation guarantees than
previously known. Specifically, we show that errors in
the approximation of individual elements do not depend
on the frequencies of the most frequent elements, but
only on the frequency of the remaining `tail.' This
shows that counter-based methods are the most
space-efficient (in fact, space-optimal) algorithms
having this strong error bound.\par
This tail guarantee allows these algorithms to solve
the `sparse recovery' problem. Here, the goal is to
recover a faithful representation of the vector of
frequencies, $f$. We prove that using space $ O(k) $,
the algorithms construct an approximation $ f* $ to the
frequency vector $f$ so that the L1 error $ ||f -
f*||_1 $ is close to the best possible error $ \hbox
{min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over
all vectors with at most $k$ non-zero entries. This
improves the previously best known space bound of about
$ O(k \log n) $ for streams without element deletions
(where $n$ is the size of the domain from which stream
elements are drawn). Other consequences of the tail
guarantees are results for skewed (Zipfian) data, and
guarantees for accuracy of merging multiple summarized
streams.",
acknowledgement = ack-nhfb,
keywords = "frequency estimation; heavy hitters; streaming
algorithms",
}
@Article{Blasius:2009:ZLP,
author = "Bernd Blasius and Ralf T{\"o}njes",
title = "{Zipf's Law} in the Popularity Distribution of Chess
Openings",
journal = j-PHYS-REV-LET,
volume = "103",
number = "21",
pages = "218701",
day = "16",
month = nov,
year = "2009",
CODEN = "PRLTAO",
DOI = "https://doi.org/10.1103/PhysRevLett.103.218701",
ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
ISSN-L = "0031-9007",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701",
acknowledgement = ack-nhfb,
fjournal = "Physical Review Letters",
journal-URL = "http://prl.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "4",
}
@Article{Bradley:2009:WBL,
author = "Jonathan R. Bradley and David L. Farnsworth",
title = "What Is {Benford's Law}?",
journal = "Teaching Statistics",
volume = "31",
number = "1",
pages = "2--6",
month = jan,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1467-9639.2009.00347.x",
ISSN = "0141-982X (print), 1467-9639 (electronic)",
ISSN-L = "0141-982X",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Class activity; First significant digit; Goodness of
fit; Teaching",
onlinedate = "6 Jan 2009",
}
@InProceedings{Burns:2009:SSR,
author = "B. D. Burns",
editor = "N. Taatgen and H. van Rijn",
booktitle = "{Proceedings of the Thirty-First Annual Conference of
the Cognitive Science Society, Cognitive Science
Society, Austin, TX}",
title = "Sensitivity to Statistical Regularities: People
(Largely) Follow {Benford's Law}",
publisher = "????",
address = "????",
pages = "2872--2877",
year = "2009",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 18 11:57:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Chakravorty:2009:TBL,
author = "S. Chakravorty and V. Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: a field experiment",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "DDTOFS",
DOI = "https://doi.org/10.1016/j.ijpe.2009.06.017",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
keywords = "Benford's Law",
}
@InProceedings{Chen:2009:DDM,
author = "Wen Chen and Yun Q. Shi",
booktitle = "{Digital Watermarking}",
title = "Detection of Double {MPEG} Compression Based on First
Digit Statistics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "16--30",
year = "2009",
DOI = "https://doi.org/10.1007/978-3-642-04438-0_2",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-04438-0_2",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Chou:2009:BLN,
author = "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and
Zuozheng Wang and Huan Zheng",
title = "{Benford's Law} and Number Selection in Fixed-Odds
Numbers Game",
journal = j-J-GAMBL-STUD,
volume = "25",
number = "4",
pages = "503--521",
month = dec,
year = "2009",
CODEN = "JGSTEM",
DOI = "https://doi.org/10.1007/s10899-009-9145-9",
ISSN = "1050-5350 (print), 1573-3602 (electronic)",
ISSN-L = "1050-5350",
bibdate = "Sat Feb 16 15:35:14 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s10899-009-9145-9",
acknowledgement = ack-nhfb,
fjournal = "Journal of Gambling Studies",
}
@Article{Chuang:2009:FPS,
author = "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
title = "Feature-preserved sampling over streaming data",
journal = j-TKDD,
volume = "2",
number = "4",
pages = "15:1--15:??",
month = jan,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1460797.1460798",
ISSN = "1556-4681 (print), 1556-472X (electronic)",
ISSN-L = "1556-4681",
bibdate = "Fri Apr 24 17:59:51 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/tkdd/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this article, we explore a novel sampling model,
called {\em feature preserved sampling\/} ({\em FPS\/})
that sequentially generates a high-quality sample over
sliding windows. The sampling quality we consider
refers to the degree of consistency between the sample
proportion and the population proportion of each
attribute value in a window. Due to the time-variant
nature of real-world datasets, users are more likely to
be interested in the most recent data. However,
previous works have not been able to generate a
high-quality sample over sliding windows that precisely
preserves up-to-date population characteristics.
Motivated by this shortcoming, we have developed the
{\em FPS\/} algorithm, which has several advantages:
(1) it sequentially generates a sample from a
time-variant data source over sliding windows; (2) the
execution time of {\em FPS\/} is linear with respect to
the database size; (3) the {\em relative\/}
proportional differences between the sample proportions
and population proportions of most distinct attribute
values are guaranteed to be below a specified error
threshold, $ \epsilon $, while the {\em relative\/}
proportion differences of the remaining attribute
values are as close to $ \epsilon $ as possible, which
ensures that the generated sample is of high quality;
(4) the sample rate is close to the user specified rate
so that a high quality sampling result can be obtained
without increasing the sample size; (5) by a thorough
analytical and empirical study, we prove that {\em
FPS\/} has acceptable space overheads, especially when
the attribute values have Zipfian distributions, and
{\em FPS\/} can also excellently preserve the
population proportion of multivariate features in the
sample; and (6) {\em FPS\/} can be applied to infinite
streams and finite datasets equally, and the generated
samples can be used for various applications. Our
experiments on both real and synthetic data validate
that {\em FPS\/} can effectively obtain a high quality
sample of the desired size. In addition, while using
the sample generated by {\em FPS\/} in various mining
applications, a significant improvement in efficiency
can be achieved without compromising the model's
precision.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Knowledge Discovery from Data
(TKDD)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1054",
keywords = "sampling; Streaming mining",
}
@Article{Clauset:2009:PLDc,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-Law Distributions in Empirical Data",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "661--703",
month = "????",
year = "2009",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/070710111",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Mon May 17 17:56:49 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Dlugosz:2009:VLD,
author = "Stephan Dlugosz and Ulrich M{\"u}ller-Funk",
title = "The value of the last digit: statistical fraud
detection with digit analysis",
journal = "Advances in Data Analysis and Classification",
volume = "3",
number = "3",
pages = "281--290",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1007/s11634-009-0048-5",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11634-009-0048-5",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/11634",
keywords = "Benford's Law",
}
@Article{Docampo:2009:BLA,
author = "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
Flores-Moya",
title = "{Benford}'s law applied to aerobiological data and its
potential as a quality control tool",
journal = j-AEROBIOLOGIA,
volume = "25",
number = "4",
pages = "275--283",
month = dec,
year = "2009",
CODEN = "AROBFT",
DOI = "https://doi.org/10.1007/s10453-009-9132-8",
ISSN = "0393-5965 (print), 1573-3025 (electronic)",
ISSN-L = "0393-5965",
bibdate = "Fri Nov 25 10:47:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
acknowledgement = ack-nhfb,
fjournal = "Aerobiologia",
}
@Article{Dorfleitner:2009:PBE,
author = "Gregor Dorfleitner and Christian Klein",
title = "Psychological barriers in {European} stock markets:
Where are they?",
journal = j-GLOB-FINANCE-J,
volume = "19",
number = "3",
pages = "268--285",
month = oct,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.gfj.2008.09.001",
ISSN = "1044-0283 (print), 1873-5665 (electronic)",
ISSN-L = "1044-0283",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
abstract = "We examine four European stock indices and the prices
of eight major German stocks for indications of
psychological barriers. The frequency, (expected)
returns, intraday volatility and trading volume of
these assets are studied contingent on whether the
prices lie within a certain range around round numbers.
Our results indicate that psychological barriers do not
exist on a consistent basis. It seems that some
barriers have disappeared after these anomalies have
been published. This discovery is consistent with
current literature findings about disappearing stock
market anomalies.",
acknowledgement = ack-nhfb,
fjournal = "Global Finance Journal",
keywords = "Benford's Law; Disappearing anomalies; M-values;
Psychological barriers",
}
@Article{Egghe:2009:PRP,
author = "Leo Egghe",
title = "Performance and its relation with productivity in
{Lotkaian} systems",
journal = j-SCIENTOMETRICS,
volume = "81",
number = "2",
pages = "567--585",
month = nov,
year = "2009",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-008-2226-1",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:15 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
URL = "http://link.springer.com/article/10.1007/s11192-008-2226-1",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Fewster:2009:SEB,
author = "Rachel M. Fewster",
title = "A Simple Explanation of {Benford's Law}",
journal = j-AMER-STAT,
volume = "63",
number = "1",
pages = "26--32",
month = feb,
year = "2009",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2009.0005",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2655700",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Gauvrit:2009:LBG,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
[{General} {Benford}'s law]",
journal = "Math. Sci. Hum. Math. Soc. Sci.",
volume = "??",
number = "186",
pages = "5--15",
year = "2009",
CODEN = "????",
ISSN = "0987-6936 (print), 1950-6821 (electronic)",
ISSN-L = "0987-6936",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2562062 (2010i:62029)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://msh.revues.org/document11034.html",
acknowledgement = ack-nhfb,
fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics
and Social Sciences",
language = "French",
}
@Article{Gauvrit:2009:SRI,
author = "N. Gauvrit and J.-P. Delahaye",
title = "Scatter and regularity imply {Benford}'s law \ldots{}
and more",
journal = "ArXiv e-prints",
month = oct,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
http://arxiv.org/abs/0910.1359",
abstract = "A random variable (r.v.) $X$ is said to follow
Benford's law if $ \log (X) $ is uniform $ \bmod 1 $.
Many experimental data sets prove to follow an
approximate version of it, and so do many mathematical
series and continuous random variables. This phenomenon
received some interest, and several explanations have
been put forward. Most of them focus on specific data,
depending on strong assumptions, often linked with the
log function. Some authors hinted --- implicitly ---
that the two most important characteristics of a random
variable when it comes to Benford are regularity and
scatter. In a first part, we prove two theorems, making
up a formal version of this intuition: scattered and
regular r.v.'s do approximately follow Benford's law.
The proofs only need simple mathematical tools, making
the analysis easy. Previous explanations thus become
corollaries of a more general and simpler one. These
results suggest that Benford's law does not depend on
properties linked with the log function. We thus
propose and test a general version of the Benford's
law. The success of these tests may be viewed as an a
posteriori validation of the analysis formulated in the
first part.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0910.1359",
keywords = "Mathematics - Probability, Statistics - Methodology,
G.3",
primaryclass = "math.PR",
}
@Article{Gisin:2009:EEV,
author = "Vladimir Gisin and Andrey Markov and Igor Vinukov",
title = "Estimation of extreme values of returns using the
{Zipf--Mandelbrot} flow",
journal = j-INT-J-PURE-APPL-MATH,
volume = "50",
number = "2",
pages = "245--250",
year = "2009",
CODEN = "????",
ISSN = "1311-8080 (print), 1314-3395 (electronic)",
ISSN-L = "1314-3395",
MRclass = "60G70 (91B28 91B84)",
MRnumber = "2488836",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
journal-URL = "http://ijpam.eu/",
}
@TechReport{Gonzales-Garcia:2009:BLM,
author = "J. Gonzales-Garcia and G. Pastor",
title = "{Benford's Law} and Macroeconomic Data Quality",
type = "Working Paper",
institution = "International Monetary Fund",
address = "Washington, DC, USA",
year = "2009",
bibdate = "Tue Nov 22 18:53:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
acknowledgement = ack-nhfb,
}
@Article{Graham:2009:SFD,
author = "Scott D. J. Graham and John Hasseldine and David
Paton",
title = "Statistical fraud detection in a commercial lobster
fishery",
journal = "New Zealand Journal of Marine and Freshwater
Research",
volume = "43",
number = "1",
pages = "457--463",
year = "2009",
DOI = "https://doi.org/10.1080/00288330909510014",
bibdate = "Sat Sep 10 11:38:12 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Abstract In this study we introduce the first step
towards a statistical model for the reliability of
fisheries data. We applied Benford's Law to catch data
from the Atlantic Canadian lobster ({\em Homarus
americanus}) fishery's lobster fishery areas (LFAs) 33
and 34 and compared our results to those using
observations from the grey zone (a highly regulated
lobster fishery shared by Canada and United States) and
a fishery with a different regulatory regime (snow
crab, {\em Chionoecetes opilio}). Non conformity with
Benford's Law is often considered as an indicator of
human manipulation of accounting data. We found that
observations from the grey zone conformed to the
distribution predicted by Benford's Law, whereas
observations from snow crab and both lobster fishery
areas did not conform.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Gunnel:2009:DBL,
author = "S. G{\"u}nnel and K.-H. T{\"o}dter",
title = "Does {Benford's Law} Hold in Economic Research and
Forecasting?",
journal = j-EMPIRICA,
volume = "36",
number = "3",
pages = "273--292",
month = aug,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10663-008-9084-1",
ISSN = "0340-8744 (print), 1573-6911 (electronic)",
ISSN-L = "0340-8744",
bibdate = "Thu Nov 17 19:16:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/100261/",
abstract = "First and higher order digits in data sets of natural
and socio-economic processes often follow a
distribution called Benford's law. This phenomenon has
been used in business and scientific applications,
especially in fraud detection for financial data. In
this paper, we analyse whether Benford's law holds in
economic research and forecasting. First, we examine
the distribution of regression coefficients and
standard errors in research papers, published in
Empirica and Applied Economics Letters. Second, we
analyse forecasts of GDP growth and CPI inflation in
Germany, published in Consensus Forecasts. There are
two main findings: The relative frequencies of the
first and second digits in economic research are
broadly consistent with Benford's law. In sharp
contrast, the second digits of Consensus Forecasts
exhibit a massive excess of zeros and fives, raising
doubts on their information content.",
acknowledgement = ack-nhfb,
fjournal = "Empirica",
}
@Article{Hales:2009:TBL,
author = "Douglas N. Hales and Satya S. Chakravorty and V.
Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: A field experiment",
journal = j-INT-J-PROD-ECON,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "JPCEYE",
DOI = "https://doi.org/10.1016/j.ijpe.2009.06.017",
ISSN = "0925-5273 (print), 1873-7579 (electronic)",
ISSN-L = "0925-5273",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
abstract = "Supply chain managers must often trust data reported
from suppliers to make decisions about sourcing and
product reliability due to the costs or complexity of
implementing traditional monitoring systems. Without
some form of monitoring, these types of data are
vulnerable to manipulation, thus making their
suitability for decision-making ambiguous and creating
an opportunity for supplier opportunism. Recent
practitioner literature suggests one solution to this
problem they refer to as trust-but-verify . The purpose
of this empirical study is to scientifically examine
the feasibility and cost of implementing one
trust-but-verify method in a real-world supply chain
using a principle called Benford's Law. The results of
this two-year study suggest that the technique is
feasible and cost effective in identifying supply chain
data that have been intentionally manipulated. This
finding can allow supply chain managers to segregate
suspect data from decision-making until they can be
validated and thus mitigate supplier opportunism.",
acknowledgement = ack-nhfb,
ajournal = "Int. j. prod. econ.",
fjournal = "International Journal of Production Economics",
keywords = "Benford's Law; Digital analysis; Operations
management; Supplier opportunism; Supply chain
management",
}
@Article{Hartshorn:2009:BRB,
author = "Kevin Hartshorn",
title = "Book Review: {{\booktitle{The fabulous Fibonacci
numbers}} by Alfred Posamentier and Ingmar Lehmann}",
journal = j-J-MATH-ARTS,
volume = "3",
number = "2",
pages = "113--116",
month = "????",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1080/17513470902897569",
ISSN = "1751-3472 (print), 1751-3480 (electronic)",
ISSN-L = "1751-3480",
bibdate = "Sat Jan 07 09:43:47 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and the Arts",
journal-URL = "http://www.tandfonline.com/loi/tmaa20",
onlinedate = "05 Jun 2009",
}
@Article{Hayes:2009:CBL,
author = "S. J. Hayes",
title = "Correspondence: {Benford's Law} in Relation to
Terminal Digit Preference",
journal = j-J-CLIN-PATHOL,
volume = "62",
number = "6",
pages = "574--575",
month = "????",
year = "2009",
CODEN = "JCPAAK",
ISSN = "0021-9746 (print), 1472-4146 (electronic)",
ISSN-L = "0021-9746",
bibdate = "Sat Sep 10 12:07:02 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcp.bmj.com/content/62/6/575.2.extract",
acknowledgement = ack-nhfb,
fjournal = "Journal of Clinical Pathology",
keywords = "Benford's Law",
}
@Article{Hernando:2009:ZLF,
author = "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas
and C. Vesperinas and A. Plastino",
title = "{Zipf}'s law from a {Fisher} variational-principle",
journal = j-PHYS-LET-A,
volume = "374",
number = "1",
pages = "18--21",
day = "14",
month = dec,
year = "2009",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/j.physleta.2009.10.027",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0375960109012894",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
keywords = "Zipf's Law",
}
@InCollection{Horgan:2009:BL,
author = "Jane M. Horgan",
title = "{Benford's Law}",
crossref = "Horgan:2009:PRI",
chapter = "9.4",
pages = "142--144",
year = "2009",
bibdate = "Mon Feb 18 18:46:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hurlimann:2009:GBL,
author = "Werner H{\"u}rlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = j-INT-J-MATH-MATH-SCI,
pages = "10",
year = "2009",
CODEN = "????",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "60E05 (11B83 62E15)",
MRnumber = "2533550 (2010h:60043)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 970284.",
URL = "http://arxiv.org/abs/math/0607166",
abstract = "A simple method to derive parametric analytical
extensions of Benford's law for first digits of
numerical data is proposed. Two generalized Benford
distributions are considered, namely the two-sided
power Benford distribution and the new Pareto Benford
distribution. The fitting capabilities of these
generalized Benford distributions are illustrated and
compared at some interesting and important integer
sequences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
}
@Article{Jang:2009:CDH,
author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
Steven J. Miller",
title = "Chains of distributions, hierarchical {Bayesian}
models and {Benford's Law}",
journal = "Journal of Algebra, Number Theory: Advances and
Applications",
volume = "1",
number = "1",
pages = "37--60",
month = mar,
year = "2009",
CODEN = "????",
ISSN = "0972-5555",
ISSN-L = "0972-5555",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
primaryclass = "math.PR",
}
@Article{Janvresse:2009:BL,
author = "Elise Janvresse and Thierry de la Rue",
title = "{Benford}'s law",
journal = "Butl. Soc. Catalana Mat.",
volume = "24",
number = "1",
pages = "5--12",
year = "2009",
CODEN = "????",
ISSN = "0214-316X",
ISSN-L = "0214-316X",
MRclass = "62-01",
MRnumber = "2567485",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translated by Frederic Utzet",
acknowledgement = ack-nhfb,
fjournal = "Butllet{\'\i}n de la Societat Catalana de
Matem{\`a}tiques",
}
@Article{Jin:2009:AUR,
author = "Jang C. Jin",
title = "{Asian} University Rankings in International and
Development Economics: An Application of {Zipf's Law}",
journal = j-REV-INT-ECON,
volume = "17",
number = "1",
pages = "137--143",
year = "2009",
DOI = "https://doi.org/10.1111/j.1467-9396.2008.00790.x",
ISSN = "0965-7576 (print), 1467-9396 (electronic)",
ISSN-L = "0965-7576",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Review of International Economics",
}
@Article{Jin:2009:PME,
author = "Jang C. Jin",
title = "Publications in mathematical economics and
econometrics: ranking of {Asian} universities and an
application of {Zipf's Law}",
journal = "{Asian-Pacific} Economic Literature",
volume = "23",
number = "2",
pages = "116--122",
year = "2009",
DOI = "https://doi.org/10.1111/j.1467-8411.2009.01233.x",
ISSN = "0818-9935 (print), 1467-8411 (electronic)",
ISSN-L = "0818-9935",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411",
}
@Article{Jolissaint:2009:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. {II}. ({French})
[{Benford}'s Law, recurrence relations, and
equidistributed sequences. {II}]",
journal = j-ELEM-MATH,
volume = "64",
number = "1",
pages = "21--36",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.4171/EM/112",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2471593 (2010f:62032)",
MRreviewer = "Denys Pommeret",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Judge:2009:DPS,
author = "G. Judge and L. Schechter",
title = "Detecting Problems in Survey Data using {Benford's
Law}",
journal = j-J-HUM-RESOUR,
volume = "44",
number = "1",
pages = "1--24",
month = "Winter",
year = "2009",
CODEN = "JHREA9",
DOI = "https://doi.org/10.3368/jhr.44.1.1",
ISSN = "0022-166X (print), 1548-8004 (electronic)",
ISSN-L = "0022-166X",
bibdate = "Tue Nov 22 18:55:52 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jhr.uwpress.org/content/44/1/1.abstract;
http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Human Resources",
}
@Article{Kafri:2009:DNE,
author = "Oded Kafri",
title = "The Distributions in Nature and Entropy Principle",
journal = "ArXiv e-prints",
day = "28",
month = jul,
year = "2009",
bibdate = "Mon Nov 21 07:26:11 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0907.4852",
abstract = "The derivation of the maximum entropy distribution of
particles in boxes yields two kinds of distributions: a
``bell-like'' distribution and a long-tail
distribution. The first one is obtained when the ratio
between particles and boxes is low, and the second one
when the ratio is high. The obtained long tail
distribution yields correctly the empirical Zipf law,
Pareto's 20:80 rule and Benford's law. Therefore, it is
concluded that the long tail and the ``bell-like''
distributions are outcomes of the tendency of
statistical systems to maximize entropy.",
acknowledgement = ack-nhfb,
pagecount = "19",
}
@Article{Kafri:2009:EPD,
author = "Oded Kafri",
title = "Entropy Principle in Direct Derivation of {Benford's
Law}",
journal = "ArXiv e-prints",
month = jan,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
http://arxiv.org/abs/0901.3047",
abstract = "The uneven distribution of digits in numerical data,
known as Benford's law, was discovered in 1881. Since
then, this law has been shown to be correct in copious
numerical data relating to economics, physics and even
prime numbers. Although it attracts considerable
attention, there is no a priori probabilistic criterion
when a data set should or should not obey the law. Here
a general criterion is suggested, namely that any file
of digits in the Shannon limit (namely, having maximum
entropy) has a Benford's law distribution of digits.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0901.3047",
keywords = "Computer Science - Discrete Mathematics, Physics -
Data Analysis, Statistics and Probability",
primaryclass = "cs.DM",
}
@Article{Kim:2009:ITA,
author = "Hyo-Jeong Kim and Michael Mannino and Robert J.
Nieschwietz",
title = "Information technology acceptance in the internal
audit profession: Impact of technology features and
complexity",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "10",
number = "4",
pages = "214--228",
year = "2009",
CODEN = "IJAIA7",
DOI = "https://doi.org/10.1016/j.accinf.2009.09.001",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Ninth International Research Symposium on Accounting
Information Systems (IRSAIS)",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089509000360",
abstract = "Although various information technologies have been
studied using the technology acceptance model (TAM),
the study of acceptance of specific technology features
for professional groups employing information
technologies such as internal auditors (IA) has been
limited. To address this gap, we extended the {TAM} for
technology acceptance among {IA} professionals and
tested the model using a sample of internal auditors
provided by the Institute of Internal Auditors (IIA).
System usage, perceived usefulness, and perceived ease
of use were tested with technology features and
complexity. Through the comparison of {TAM} variables,
we found that technology features were accepted by
internal auditors in different ways. The basic features
such as database queries, ratio analysis, and audit
sampling were more accepted by internal auditors while
the advanced features such as digital analysis,
regression/ANOVA, and classification are less accepted
by internal auditors. As feature complexity increases,
perceived ease of use decreased so that system usage
decreased. Through the path analysis between {TAM}
variables, the results indicated that path magnitudes
were significantly changed by technology features and
complexity. Perceived usefulness had more influence on
feature acceptance when basic features were used, and
perceived ease of use had more impact on feature
acceptance when advanced features were used.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law; Information technology adoption;
Internal auditing; System acceptance; {IS} features",
}
@Article{Krakar:2009:ABL,
author = "Mario {\v{Z}}gela and Zdravko Krakar",
title = "Application of {Benford's Law} in Payment System
Auditing",
journal = j-J-INFO-ORG-SCI,
volume = "33",
number = "1",
pages = "39--51",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "1846-3312 (print), 1846-9418 (electronic)",
ISSN-L = "1846-3312",
bibdate = "Sun Nov 13 11:12:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf;
http://jios.foi.hr/index.php/jios/article/view/108/66;
http://jios.foi.hr/index.php/jios/issue/view/13",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informational and Organizational Sciences",
journal-URL = "http://jios.foi.hr/index.php/jios/index",
xxjournal = "Journal of Information Ethics and Organisational
Science (wrong!)",
}
@Article{Krishna:2009:DBD,
author = "Hare Krishna and Pramendra Singh Pundir",
title = "Discrete {Burr} and discrete {Pareto} distributions",
journal = j-STAT-METHODOL,
volume = "6",
number = "2",
pages = "177--188",
month = mar,
year = "2009",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:36 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S157231270800052X",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@MastersThesis{Krygier:2009:PRB,
author = "J. Krygier",
title = "Psychological Relevance of {Benford's Law}:
Sensitivity to Statistical Regularities and
Implications for Theories of Number Representation",
type = "Honours thesis",
school = "University of Sydney",
address = "Sydney, NSW, Australia",
year = "2009",
bibdate = "Sat Sep 10 12:48:34 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Lansey:2009:ISR,
author = "Jonathan C. Lansey and Bruce Bukiet",
title = "{Internet} Search Result Probabilities: {Heaps' Law}
and Word Associativity",
journal = j-J-QUANT-LINGUISTICS,
volume = "16",
number = "1",
pages = "40--66",
month = "????",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1080/09296170802514153",
ISSN = "0929-6174 (print), 1744-5035 (electronic)",
ISSN-L = "0929-6174",
bibdate = "Sat Jan 07 09:36:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
abstract = "We study the number of internet search results
returned from multi-word queries based on the number of
results returned when each word is searched for
individually. We derive a model to describe search
result values for multi-word queries using the total
number of pages indexed by Google and by applying the
Zipf power law to the words per page distribution on
the internet and Heaps' law for unique word counts.
Based on data from 351 word pairs each with exactly one
hit when searched for together, and a Zipf law
coefficient determined in other studies, we approximate
the Heaps' law coefficient for the indexed worldwide
web (about 8 billion pages) to be $ \beta = 0.52 $.
Previous studies used under 20,000 pages. We
demonstrate through examples how the model can be used
to analyse automatically the relatedness of word pairs
assigning each a value we call ``strength of
associativity''. We demonstrate the validity of our
method with word triplets and through two experiments
conducted 8 months apart. We then use our model to
compare the index sizes of competing search giants
Yahoo and Google.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
keywords = "Benford's Law; Heaps' Law; Zipf's Law",
onlinedate = "25 Feb 2009",
remark = "From page 65: ``We mention that tests we have
conducted show that internet searches for random
numbers return approximately log-normally distributed
results and sorting by first digits yields results that
follow Benford's law (1938).''",
}
@Article{Li:2009:PDD,
author = "Weihai Li and Yuan Yuan and Nenghai Yu",
title = "Passive detection of doctored {JPEG} image via block
artifact grid extraction",
journal = j-SIG-PROC,
volume = "89",
number = "9",
pages = "1821--1829",
year = "2009",
CODEN = "SPRODR",
DOI = "https://doi.org/10.1016/j.sigpro.2009.03.025",
ISSN = "0165-1684 (print), 1872-7557 (electronic)",
ISSN-L = "0165-1684",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165168409001315",
abstract = "It has been noticed that the block artifact grids
(BAG), caused by the blocking processing during {JPEG}
compression, are usually mismatched when interpolating
or concealing objects by copy paste operations. In this
paper, the {BAGs} are extracted blindly with a new
extraction algorithm, and then abnormal {BAGs} can be
detected with a marking procedure. Then the phenomenon
of grid mismatch or grid blank can be taken as a trail
of such forensics. Experimental results show that our
method can mark these trails efficiently.",
acknowledgement = ack-nhfb,
fjournal = "Signal Processing",
journal-URL = "http://www.sciencedirect.com/science/journal/01651684",
keywords = "Benford's Law; Block artifact grid; Doctored image
forensic; Grid mismatch; {JPEG} compression",
}
@Article{Lipovetsky:2009:PLD,
author = "Stan Lipovetsky",
title = "{Pareto} $ 80 / 20 $ law: derivation via random
partitioning",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "40",
number = "2",
pages = "271--277",
month = "????",
year = "2009",
CODEN = "IJMEBM",
DOI = "https://doi.org/10.1080/00207390802213609",
ISSN = "0020-739X (print), 1464-5211 (electronic)",
ISSN-L = "0020-739X",
bibdate = "Sat Jan 07 09:22:31 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
abstract = "The Pareto 80/20 Rule, also known as the Pareto
principle or law, states that a small number of causes
(20\%) is responsible for a large percentage (80\%) of
the effect. Although widely recognized as a heuristic
rule, this proportion has not been theoretically based.
The article considers derivation of this 80/20 rule and
some other standard quotients from the mean and its
interval estimation for the total value defined by the
product of two variables in the random partitioning
model.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematical Education in
Science and Technology",
onlinedate = "19 Feb 2009",
}
@Article{Luque:2009:FDF,
author = "Bartolo Luque and Lucas Lacasa",
title = "The first digit frequencies of prime numbers and
{Riemann} zeta zeros",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "465",
number = "2107",
pages = "2197--2216",
day = "8",
month = jul,
year = "2009",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2009.0126",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
bibdate = "Mon Feb 25 10:44:43 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society A: Mathematical,
Physical, \& Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
keywords = "Benford's Law",
onlinedate = "22 April 2009",
}
@Article{Mahdian:2009:UNI,
author = "Babak Mahdian and Stanislav Saic",
title = "Using noise inconsistencies for blind image
forensics",
journal = j-IMAGE-VIS-COMPUT,
volume = "27",
number = "10",
pages = "1497--1503",
year = "2009",
CODEN = "IVCODK",
DOI = "https://doi.org/10.1016/j.imavis.2009.02.001",
ISSN = "0262-8856 (print), 1872-8138 (electronic)",
ISSN-L = "0262-8856",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib",
note = "Special Section: Computer Vision Methods for Ambient
Intelligence",
URL = "http://www.sciencedirect.com/science/article/pii/S0262885609000146",
abstract = "A commonly used tool to conceal the traces of
tampering is the addition of locally random noise to
the altered image regions. The noise degradation is the
main cause of failure of many active or passive image
forgery detection methods. Typically, the amount of
noise is uniform across the entire authentic image.
Adding locally random noise may cause inconsistencies
in the image's noise. Therefore, the detection of
various noise levels in an image may signify tampering.
In this paper, we propose a novel method capable of
dividing an investigated image into various partitions
with homogeneous noise levels. In other words, we
introduce a segmentation method detecting changes in
noise level. We assume the additive white Gaussian
noise. Several examples are shown to demonstrate the
proposed method's output. An extensive quantitative
measure of the efficiency of the noise estimation part
as a function of different noise standard deviations,
region sizes and various {JPEG} compression qualities
is proposed as well.",
acknowledgement = ack-nhfb,
fjournal = "Image and Vision Computing",
keywords = "Benford's Law; Digital forgery; Image forensics; Image
segmentation; Image tampering; Noise inconsistency",
}
@Article{Mebane:2009:EFR,
author = "Walter R. {Mebane, Jr.} and K. Kalinin",
title = "Electoral Falsification in {Russia}: Complex
Diagnostics Selections 2003--2004, 2007--2008",
journal = "Russian Electoral Review",
volume = "2",
number = "??",
pages = "57--70",
month = "????",
year = "2009",
bibdate = "Sat Sep 10 14:30:23 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
language = "Russian",
}
@TechReport{Mebane:2009:NPE,
author = "Walter R. {Mebane, Jr.}",
title = "Note on the {Presidential} Election in {Iran}",
type = "Report",
number = "????",
institution = "University of Michigan",
address = "Ann Arbor, MI, USA",
month = jun,
year = "2009",
bibdate = "Sat Sep 10 14:17:31 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/rvwmebane/note29jun2009.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Meintanis:2009:UAT,
author = "Simos G. Meintanis",
title = "A unified approach of testing for discrete and
continuous {Pareto} laws",
journal = j-STAT-PAPERS,
volume = "50",
number = "3",
pages = "569--580",
month = jun,
year = "2009",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-007-0103-2",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:30 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-007-0103-2",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@TechReport{Moller:2009:MQA,
author = "M. M{\"o}ller",
title = "Measuring the Quality of Auditing Services with the
Help of {Benford's Law} -- An Empirical Analysis and
Discussion of this Methodical Approach",
type = "Report",
number = "??",
institution = "Institute for Accounting and Control, University of
Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "25",
day = "24",
month = apr,
year = "2009",
bibdate = "Tue Nov 22 20:40:12 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ssrn.com/abstract=1529307",
abstract = "The so-called Benford's Law describes regularity in
the distribution of digits of randomly selected
numbers, which states that the relative frequency of
the leading digits reduces in a systematic manner from
the digit 1 to the digit 9. This distribution
hypothesis is being discussed in recent times as an
audit instrument in order to gain insights into
possible conscious and inadvertent errors in data
records. The present paper analyses the closing
accounts of 1,373 annual financial statements of
companies listed on the German DAX and compares these
with the Benford's distribution hypothesis. It can be
seen in the process that data pertaining to financial
accounts, which have not been audited by the so-called
``Big 4'' audit firms, but by smaller external
auditors, deviate to a significant extent from the
regularity of Benford's Law, which appears to make the
use of Benford's Law suitable as a benchmark to assess
the quality of the audit.",
acknowledgement = ack-nhfb,
}
@Article{Moret:2009:GSA,
author = "M. A. Moret and V. de Senna and M. C. Santana and G.
F. Zebende",
title = "Geometric Structural Aspects of Proteins and
{Newcomb--Benford Law}",
journal = j-INT-J-MOD-PHYS-C,
volume = "20",
number = "12",
pages = "1981--1988",
month = "????",
year = "2009",
CODEN = "IJMPEO",
DOI = "https://doi.org/10.1142/S0129183109014874",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
ISSN-L = "0129-1831",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
journal-URL = "http://www.worldscientific.com/loi/ijmpc",
keywords = "Hydrophobicity, protein packing, complex systems, Time
series analysis, Systems obeying scaling laws, Binary
and multiple stars",
}
@Article{Ni:2009:BLD,
author = "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
title = "{Benford's Law} and $ \beta $-Decay Half-Lives",
journal = j-COMM-THEOR-PHYS,
volume = "51",
number = "4",
pages = "713--716",
month = apr,
year = "2009",
CODEN = "CTPHDI",
DOI = "https://doi.org/10.1088/0253-6102/51/4/25",
ISSN = "0253-6102 (print), 1572-9494 (electronic)",
ISSN-L = "0253-6102",
bibdate = "Sun Nov 13 11:01:52 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
http://stacks.iop.org/0253-6102/51/i=4/a=25",
abstract = "The experimental values of 2059 $ \beta $-decay
half-lives are systematically analyzed and
investigated. We have found that they are in
satisfactory agreement with Benford's law, which states
that the frequency of occurrence of each figure, 1--9,
as the first significant digit in a surprisingly large
number of different data sets follows a logarithmic
distribution favoring the smaller ones. Benford's
logarithmic distribution of $ \beta $-decay half-lives
can be explained in terms of Newcomb's justification of
Benford's law and empirical exponential law of $ \beta
$-decay half-lives. Moreover, we test the calculated
values of 6721 $ \beta $-decay half-lives with the aid
of Benford's law. This indicates that Benford's law is
useful for theoretical physicists to test their methods
for calculating $ \beta $-decay half-lives.",
acknowledgement = ack-nhfb,
fjournal = "Communications in theoretical physics",
}
@Article{Nigrini:2009:DDU,
author = "Mark J. Nigrini and Steven J. Miller",
title = "Data Diagnostics Using Second-Order Tests of
{Benford's Law}",
journal = j-AUDITING,
volume = "28",
number = "2",
pages = "305--324",
month = nov,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.2308/aud.2009.28.2.305",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:11:56 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v28/i2/p305/s1",
abstract = "Auditors are required to use analytical procedures to
identify the existence of unusual transactions, events,
and trends. Benford's Law gives the expected patterns
of the digits in numerical data, and has been advocated
as a test for the authenticity and reliability of
transaction level accounting data. This paper describes
a new second-order test that calculates the digit
frequencies of the differences between the ordered
(ranked) values in a data set. These digit frequencies
approximate the frequencies of Benford's Law for most
data sets. The second-order test is applied to four
sets of transactional data. The second-order test
detected errors in data downloads, rounded data, data
generated by statistical procedures, and the inaccurate
ordering of data. The test can be applied to any data
set and nonconformity usually signals an unusual issue
related to data integrity that might not have been
easily detectable using traditional analytical
procedures",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@InCollection{Nisbet:2009:CFD,
author = "Robert Nisbet and John Elder and Gary Miner",
booktitle = "Handbook of Statistical Analysis and Data Mining
Applications",
title = "Chapter 17 --- Fraud Detection",
publisher = "Academic Press",
address = "Boston",
pages = "347--361",
year = "2009",
DOI = "https://doi.org/10.1016/B978-0-12-374765-5.00017-6",
ISBN = "0-12-374765-1",
ISBN-13 = "978-0-12-374765-5",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780123747655000176",
abstract = "Fraud can be defined as a criminal activity, involving
false representations to gain an unjust advantage. It
occurs in a wide variety of forms and is ever changing
as new technologies and new economic and social systems
provide new opportunities for fraudulent activity. This
chapter introduces fraud detection, provides a simple
example of how to build a fraud model, and directs one
to additional references to broaden and deepen the
knowledge of the vast scope of fraud detection. Fraud
is a form of human response that can be modeled in ways
very similar to customer response in business. The
temporal dimension of fraud provides a rich source of
information related to fraud. The occurrence of a fraud
event at a given time may be highly related to the
pattern of events that happened in the past. These
historical data are the most important source of
attributes needed to sufficiently define the fraud
signature in the data set. Fraud modeling requires the
construction of reference objects based on
relationships that are drawn in the past between
various conditions and the incidence of fraud. The
basic approach to fraud detection with an analytical
model is to identify possible predictors of fraud
associated with known fraudsters and their actions in
the past. The most powerful fraud models are built on
historical data.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Rajabpour:2009:SRC,
author = "M. A. Rajabpour and S. M. {Vaez Allaei}",
title = "Scaling relations for contour lines of rough
surfaces",
journal = j-PHYS-REV-E,
volume = "80",
number = "1",
pages = "011115",
day = "13",
month = jul,
year = "2009",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.80.011115",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.80.011115",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
}
@Article{Ramanana-Rahary:2009:APR,
author = "Suzy Ramanana-Rahary and Michel Zitt and Ronald
Rousseau",
title = "Aggregation properties of relative impact and other
classical indicators: Convexity issues and the
{Yule--Simpson} paradox",
journal = j-SCIENTOMETRICS,
volume = "79",
number = "2",
pages = "311--327",
month = may,
year = "2009",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-009-0420-4",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:11 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
URL = "http://link.springer.com/article/10.1007/s11192-009-0420-4",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Romero-Rochin:2009:DBL,
author = "V. Romero-Rochin",
title = "A derivation of {Benford's Law} \ldots{} and a
vindication of {Newcomb}",
journal = "ArXiv e-prints",
month = sep,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R;
http://arxiv.org/abs/0909.3822",
abstract = "We show how Benford's Law (BL) for first, second,
\ldots{}, digits, emerges from the distribution of
digits of numbers of the type $ a^R $, with $a$ any
real positive number and $R$ a set of real numbers
uniformly distributed in an interval $ [P \log_a(10),
(P + 1) \log_a(10)) $ for any integer $P$. The result
is shown to be number base and scale invariant. A rule
based on the mantissas of the logarithms allows for a
determination of whether a set of numbers obeys BL or
not. We show that BL applies to numbers obtained from
the {\em multiplication\/} or {\em division\/} of
numbers drawn from any distribution. We also argue that
(most of) the real-life sets that obey BL are because
they are obtained from such basic arithmetic
operations. We exhibit that all these arguments were
discussed in the original paper by Simon Newcomb in
1881, where he presented Benford's Law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0909.3822",
keywords = "Mathematics - Probability, Mathematics - History and
Overview",
pagecount = "12",
primaryclass = "math.PR",
}
@Article{Roukema:2009:BLA,
author = "Boudewijn F. Roukema",
title = "{Benford's Law} anomalies in the 2009 {Iranian}
presidential election",
journal = "ArXiv e-prints",
day = "16",
month = jun,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R;
http://arxiv.org/abs/0906.2789",
abstract = "The vote count first digit frequencies of the 2009
Iranian presidential election are analysed assuming
proportionality of candidates' votes to the total vote
per voting area. This method is closely related to
Benford's Law. A highly significant ($ p \approx 0.0007
$ ) excess of vote counts for candidate $K$ that start
with the digit 7 is found (41 observed, 21.2--22
expected). Using this property as a selection criterion
leads to the following coincidences. (i) Among the six
most populous voting areas, this criterion selects
those three that have greater proportions of votes for
A than the other three. The probability that the two
sub-groups are drawn from the same distribution is $ p
\approx 0.1 $. (ii) $K$'s vote counts for these same
three voting areas all have the same second digit. The
probability of this is $ p \approx 0.01 $. (iii) Most
(75\%) of the vote counts for $K$ in voting areas with
70 to 79 votes for $K$ are odd, and every even number
occurs exactly once. The probability of the latter is $
p \approx 0.0005 $. Interpreting the big city effect
(i) +( ii) as an overestimate of the true vote, assumed
to be roughly 50\% to match other data, while retaining
constant total vote numbers and increasing votes for
the other three candidates in proportion to their
average voting percentages, would imply that the
difference between A's and M's vote totals would drop
by about one million votes. These results do not
exclude other anomalies.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0906.2789",
keywords = "Statistics - Applications",
primaryclass = "stat.AP",
remark = "It appears the title changed over six updates to this
paper to the one in the final journal version
\cite{Roukema:2014:FDA}.",
xxtitle = "A first-digit anomaly in the 2009 {Iranian}
{Presidential} election",
}
@Article{Sambridge:2009:ABL,
author = "M. Sambridge and H. Tkalcic and A. Jackson",
title = "On the applicability of {Benford's Law} in the
Geosciences",
journal = "AGU Fall Meeting Abstracts",
pages = "A1756--??",
month = dec,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:32:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S",
acknowledgement = ack-nhfb,
keywords = "[1294] GEODESY AND GRAVITY / Instruments and
techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM /
Instruments and techniques, [3294] MATHEMATICAL
GEOPHYSICS / Instruments and techniques, [7299]
SEISMOLOGY / General or miscellaneous",
}
@Article{Shao:2009:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First digit distribution of hadron full width",
journal = j-MOD-PHYS-LETT-A,
volume = "24",
number = "40",
pages = "3275--3282",
month = "????",
year = "2009",
CODEN = "MPLAEQ",
DOI = "https://doi.org/10.1142/S0217732309031223",
ISSN = "0217-7323 (print), 1793-6632 (electronic)",
ISSN-L = "0217-7323",
bibdate = "Mon Nov 14 16:26:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e., $ 1, 2,
\ldots {}, 9 $, of numbers from many real world sources
is not uniformly distributed, but instead favors
smaller ones according to a logarithmic distribution.
We investigate, for the first time, the first digit
distribution of the full widths of mesons and baryons
in the well defined science domain of particle physics
systematically, and find that they agree excellently
with the Benford distribution. We also discuss several
general properties of Benford's law, i.e., the law is
scale-invariant, base-invariant, and power-invariant.
This means that the lifetimes of hadrons follow also
Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1004.3077",
fjournal = "Modern Physics Letters A (MPLA)",
journal-URL = "http://www.worldscientific.com/loi/mpla",
primaryclass = "hep-ph",
}
@Article{Shi:2009:FDL,
author = "Yun Q. Shi",
title = "{First Digit Law} and Its Application to Digital
Forensics",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5450",
pages = "448--453",
year = "2009",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-04438-0_37",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:32:48 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04438-0_37",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-04438-0",
book-URL = "http://www.springerlink.com/content/978-3-642-04438-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Speed:2009:YWP,
author = "T. Speed",
title = "You want proof?",
journal = j-BULL-INST-MATH-STAT,
volume = "38",
number = "??",
pages = "11--??",
month = "????",
year = "2009",
CODEN = "SMBCVA",
ISSN = "0146-3942",
ISSN-L = "0146-3942",
bibdate = "Wed Nov 16 07:00:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bulletin.imstat.org/archive/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin --- Institute of Mathematical Statistics",
keywords = "Benford's Law",
remark = "As of 16 November 2011, volume 38 is not yet online at
the publisher Web site, although there are (broken)
links for volumes 31 (2002) to date.",
}
@Article{Stosic:2009:CSM,
author = "Borko D. Stosi{\'c} and Tatijana Stosi{\'c}",
title = "Comment on {``Ising model on the scale-free network
with a Cayley-tree-like structure''}",
journal = j-PHYS-REV-E,
volume = "79",
number = apr,
pages = "048101",
day = "24",
month = apr,
year = "2009",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.79.048101",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.79.048101",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "2",
}
@Misc{Tao:2009:BLZ,
author = "Terrence Tao",
title = "{Benford}'s law, {Zipf}'s law, and the {Pareto}
distribution",
howpublished = "Web document.",
year = "2009",
bibdate = "Mon Nov 14 16:59:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/",
acknowledgement = ack-nhfb,
}
@Article{Todter:2009:BLI,
author = "Karl-Heinz T{\"o}dter",
title = "{Benford's Law} as an Indicator of Fraud in
Economics",
journal = j-GER-ECON-REV,
volume = "10",
number = "3",
pages = "339--351",
month = aug,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1468-0475.2009.00475.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
onlinedate = "16 Jun 2009",
}
@Article{Villasenor-Alva:2009:BGF,
author = "Jos{\'e} A. Villase{\~n}or-Alva and Elizabeth
Gonz{\'a}lez-Estrada",
title = "A bootstrap goodness of fit test for the generalized
{Pareto} distribution",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "53",
number = "11",
pages = "3835--3841",
day = "1",
month = sep,
year = "2009",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:42:33 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947309001406",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@InProceedings{Wang:2009:UBL,
author = "J. Wang and B. H. Cha and S. H. Cho and C. C. J. Kuo",
editor = "{IEEE}",
booktitle = "2009 IEEE International Conference on Multimedia and
Expo",
title = "Understanding {Benford's Law} and its vulnerability in
image forensics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1568--1571",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1109/ICME.2009.5202811",
ISSN = "1945-7871",
bibdate = "Sat Sep 10 11:29:36 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Application software; Authentication; Benford law;
Benford's law; Digital images; forensic science;
Forensics; Gaussian processes; generalized Benford's
law; generalized Gaussian function; generalized
Laplacian function; histogram manipulation; histogram
manipulation attack; Histograms; image authentication;
image coding; image forensics; Image processing;
Laplace equations; message authentication; probability;
Probability density function; probability density
function; random processes; random variable; Random
variables; Signal processing",
}
@Article{Xie:2009:FAS,
author = "Tao Xie and Yao Sun",
title = "A file assignment strategy independent of workload
characteristic assumptions",
journal = j-TOS,
volume = "5",
number = "3",
pages = "10:1--10:??",
month = nov,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1629075.1629079",
ISSN = "1553-3077 (print), 1553-3093 (electronic)",
ISSN-L = "1553-3077",
bibdate = "Tue Mar 16 15:33:57 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tos/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tos.bib",
abstract = "The problem of statically assigning nonpartitioned
files in a parallel I/O system has been extensively
investigated. A basic workload characteristic
assumption of most existing solutions to the problem is
that there exists a strong inverse correlation between
file access frequency and file size. In other words,
the most popular files are typically small in size,
while the large files are relatively unpopular. Recent
studies on the characteristics of Web proxy traces
suggested, however, the correlation, if any, is so weak
that it can be ignored. Hence, the following two
questions arise naturally. First, can existing
algorithms still perform well when the workload
assumption does not hold? Second, if not, can one
develop a new file assignment strategy that is immune
to the workload assumption? To answer these questions,
we first evaluate the performance of three well-known
file assignment algorithms with and without the
workload assumption, respectively. Next, we develop a
novel static nonpartitioned file assignment strategy
for parallel I/O systems, called static round-robin
(SOR), which is immune to the workload assumption.
Comprehensive experimental results show that SOR
consistently improves the performance in terms of mean
response time over the existing schemes.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Storage",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J960",
keywords = "File assignment; load balancing; parallel I/O;
workload characteristics; Zipfian distribution",
}
@Article{Zhang:2009:ZDT,
author = "Jianhua Zhang and Qinghua Chen and Yougui Wang",
title = "{Zipf} distribution in top {Chinese} firms and an
economic explanation",
journal = j-PHYSICA-A,
volume = "388",
number = "10",
pages = "2020--2024",
day = "15",
month = may,
year = "2009",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2009.01.027",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437109000806",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@InProceedings{Zhao:2009:IFU,
author = "Xi Zhao and A. T. S. Ho and Y. Q. Shi",
booktitle = "2009 16th International Conference on Digital Signal
Processing",
title = "Image forensics using generalised {Benford's Law} for
accurate detection of unknown {JPEG} compression in
watermarked images",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--8",
month = jul,
year = "2009",
DOI = "https://doi.org/10.1109/ICDSP.2009.5201261",
ISSN = "1546-1874",
bibdate = "Sat Sep 10 11:42:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Authentication; average QF correct detection rate;
data compression; DCT; Digital images; Forensics;
generalised Benford law; Generalised Benford's Law;
Image Authentication; Image coding; image coding; image
forensics technique; Image storage; JPEG Compression;
message authentication; object detection; Physics
computing; Q factor; Q-factor; quality factors;
Semi-fragile Watermarking; semifragile watermarking;
Signal processing algorithms; Transform coding; unknown
JPEG compression detection; watermarked images;
Watermarking; watermarking",
}
@Article{Abourbih:2010:SSD,
author = "Jonathan A. Abourbih and Luke Blaney and Alan Bundy
and Fiona McNeill",
title = "A Single-Significant-Digit Calculus for Semi-Automated
Guesstimation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6173",
pages = "354--368",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-14203-1_31",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:43:23 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-14203-1",
book-URL = "http://www.springerlink.com/content/978-3-642-14203-1",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Afify:2010:EEP,
author = "W. M. Afify",
title = "On estimation of the exponentiated {Pareto}
distribution under different sample schemes",
journal = j-STAT-METHODOL,
volume = "7",
number = "2",
pages = "77--83",
month = mar,
year = "2010",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:41 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312709000653",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Misc{Alagoz:2010:MDB,
author = "Ali Alag{\"o}z and Mustafa Ay",
title = "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital
Analiz. ({Turkish}) [{Benford Law}-Based Digital
Analysis of Accounting Oversight]",
pages = "17",
day = "8",
month = jan,
year = "2010",
bibdate = "Mon Feb 18 09:19:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf",
acknowledgement = ack-nhfb,
language = "Turkish",
}
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When Can One Test an Explanation? {Compare} and
Contrast {Benford's Law} and the Fuzzy {CLT}",
journal = j-AMER-STAT,
volume = "64",
number = "3",
pages = "221--227",
month = aug,
year = "2010",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2010.09098",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2757166",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Altamirano:2010:PTS,
author = "Carlo Altamirano and Alberto Robledo",
title = "Possible thermodynamic structure underlying the laws
of {Zipf} and {Benford}",
journal = "ArXiv e-prints",
day = "10",
month = aug,
year = "2010",
bibdate = "Mon Nov 21 07:12:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1008.1614",
abstract = "We show that the laws of Zipf and Benford, obeyed by
scores of numerical data generated by many and diverse
kinds of natural phenomena and human activity are
related to the focal expression of a generalized
thermodynamic structure. This structure is obtained
from a deformed type of statistical mechanics that
arises when configurational phase space is incompletely
visited in a severe way. Specifically, the restriction
is that the accessible fraction of this space has
fractal properties. The focal expression is an
(incomplete) Legendre transform between two entropy (or
Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of
Benford's law. The inverse functional of this
expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for
small and large rank. Remarkably, we find that the
entire problem is analogous to the transition to chaos
via intermittency exhibited by low-dimensional
nonlinear maps. Our results also explain the generic
form of the degree distribution of scale-free
networks.",
acknowledgement = ack-nhfb,
remark = "To be published in European Physical Journal B.",
}
@Article{Anderson:2010:BLC,
author = "Theresa Anderson and Larry Rolen and Ruth Stoehr",
title = "{Benford's} Law For Coefficients of Modular Forms and
Partition Functions",
journal = "ArXiv e-prints",
day = "3",
month = sep,
year = "2010",
bibdate = "Mon Nov 21 07:10:51 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1009.0780",
abstract = "Here we prove that Benford's law holds for
coefficients of an infinite class of modular forms.
Expanding the work of Bringmann and Ono on exact
formulas for harmonic Maass forms, we derive the
necessary asymptotics. This implies that the
unrestricted partition function $ p(n) $, as well as
other natural partition functions, satisfy Benford's
law.",
acknowledgement = ack-nhfb,
pagecount = "10",
}
@Article{Bachmann:2010:APC,
author = "Val{\'e}rie Bachmann and Martin H. Fischer and
Hans-Peter Landolt and Peter Brugger",
title = "Asymmetric prefrontal cortex functions predict
asymmetries in number space",
journal = j-BRAIN-COGN,
volume = "74",
number = "3",
pages = "306--311",
month = dec,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.bandc.2010.08.011",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; small-number bias (SNB); Spatial
Numerical Association of Response Codes (SNARC)
effect",
}
@Article{Balanzario:2010:SCB,
author = "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
title = "Sufficient conditions for {Benford's Law}",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "23--24",
pages = "1713--1719",
day = "1--15",
month = dec,
year = "2010",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2010.07.014",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "62E10 (62E17)",
MRnumber = "2734233 (2011i:62019)",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
abstract = "We present two sufficient conditions for an absolutely
continuous random variable to obey Benford's Law for
the distribution of the first significant digit. These
two sufficient conditions suggest that Benford's Law
will not often be observed in everyday sets of
numerical data. On the other hand, we recall that there
are two processes by way of which a random variable can
come close to following Benford's Law. The first of
these is the multiplication of independent random
variables and the second is the exponentiation of a
random variable to a large power. Our working tool is
the Poisson sum formula of Fourier analysis. Like the
central limit theorem, Benford's Law has an asymptotic
nature.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; First significant digit",
}
@Article{Balaz:2010:BLD,
author = "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
title = "{Benford}'s law and distribution functions of
sequences in $ (0, 1) $",
journal = j-MATH-NOTES-ACAD-SCI-USSR,
volume = "88",
number = "3--4",
pages = "449--463",
month = oct,
year = "2010",
CODEN = "MTHNB2",
DOI = "https://doi.org/10.1134/S0001434610090178",
ISSN = "0001-4346 (print), 1573-8876 (electronic)",
ISSN-L = "0001-4346",
bibdate = "Fri Nov 25 10:52:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1134/S0001434610090178",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Notes of the {Academy of Sciences of the
USSR = Matematicheskie Zametki}",
}
@Article{Balazh:2010:BLD,
author = "V. Balazh and K. Nagasaka and O. Shtraukh",
title = "{Benford}'s law and distribution functions of
sequences in {$ (0, 1) $}",
journal = j-MAT-ZAMETKI,
volume = "88",
number = "4",
pages = "485--501",
year = "2010",
DOI = "https://doi.org/10.1134/S0001434610090178",
ISSN = "0025-567X",
ISSN-L = "0025-567X",
MRclass = "11K06 (60E05)",
MRnumber = "2882211",
MRreviewer = "Michael Drmota",
bibdate = "Thu Feb 14 07:02:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
journal-URL = "http://link.springer.com/journal/11006",
}
@TechReport{Bauer:2010:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
institution = "Institute of Sociology,
Ludwig-Maximilians-Universit{\"a}t",
address = "M{\"u}nchen, Germany",
pages = "????",
year = "2010",
bibdate = "Tue Nov 22 21:15:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Beber:2010:WNS,
author = "Bernd Beber and Alexandria Scacco",
title = "What the Numbers Say: a Digit-Based Test for Election
Fraud",
journal = j-POLIT-ANAL,
volume = "20",
number = "2",
pages = "211--234",
month = "Spring",
year = "2010",
DOI = "https://doi.org/10.1093/pan/mps003",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Mon Feb 18 17:29:42 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pan.oxfordjournals.org/content/20/2/211.abstract",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
keywords = "Benford's Law",
}
@TechReport{Berger:2010:FFFa,
author = "A. Berger and T. P. Hill",
title = "Fundamental Flaws in {Feller}'s Classical Derivation
of {Benford's Law}",
type = "Preprint",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
pages = "8",
year = "2010",
bibdate = "Mon Feb 18 17:31:57 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf",
abstract = "Feller's classic text \booktitle{An Introduction to
Probability Theory and its Applications}
\cite{Feller:1968:IPT} contains a derivation of the
well known significant-digit law called Benford's law.
More specifically, Feller gives a sufficient condition
(`large spread') for a random variable $X$ to be
approximately Benford distributed, that is, for $
\log_{10} X $ to be approximately uniformly distributed
modulo one. This note shows that the large-spread
derivation, which continues to be widely cited and
used, contains serious basic errors. Concrete examples
and a new inequality clearly demonstrate that large
spread (or large spread on a logarithmic scale) does
not imply that a random variable is approximately
Benford distributed, for any reasonable definition of
`spread' or measure of dispersion.",
acknowledgement = ack-nhfb,
}
@Article{Berger:2010:FFFb,
author = "Arno Berger and Theodore P. Hill",
title = "Fundamental Flaws in {Feller}'s Classical Derivation
of {Benford's Law}",
journal = "ArXiv e-prints",
month = may,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:23:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
http://arxiv.org/abs/1005.2598",
abstract = "Feller's classic text \booktitle{An Introduction to
Probability Theory and its Applications}
\cite{Feller:1968:IPT} contains a derivation of the
well known significant-digit law called Benford's law.
More specifically, Feller gives a sufficient condition
(`large spread') for a random variable $X$ to be
approximately Benford distributed, that is, for $
\log_{10}X $ to be approximately uniformly distributed
modulo one. This note shows that the large-spread
derivation, which continues to be widely cited and
used, contains serious basic errors. Concrete examples
and a new inequality clearly demonstrate that large
spread (or large spread on a logarithmic scale) does
not imply that a random variable is approximately
Benford distributed, for any reasonable definition of
`spread' or measure of dispersion",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.2598",
keywords = "Mathematics - Probability, Mathematics - Statistics,
62Axx",
primaryclass = "math.PR",
}
@TechReport{Berger:2010:LSD,
author = "A. Berger",
title = "Large Spread Does Not Imply {Benford's Law}",
type = "Preprint",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2010",
bibdate = "Sat Nov 12 16:46:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.ualberta.ca/~aberger/Publications.html",
acknowledgement = ack-nhfb,
}
@Article{Block:2010:GEB,
author = "Henry W. Block and Thomas H. Savits",
title = "A General Example for {Benford} Data",
journal = j-AMER-STAT,
volume = "64",
number = "4",
pages = "335--339",
month = nov,
year = "2010",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2010.09169",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2758565",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Benford's Law deals, among other things, with the
proportion of numbers whose first significant digit is
a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
significant digit $1$) in a variety of datasets. In
these datasets, which arise in various compendiums or
as mixtures of various sets of numbers, the proportion
of numbers with first significant digit one is $ 0.3010
$ which is much higher than the commonsense value of $
1 / 9 $. The reasons for this occurrence have been
elusive. Mathematical attempts to explain this
phenomenon have been relatively fruitless. Methods
involving probability have been somewhat more
successful. In this article we give some simple reasons
for this occurrence and also give an example of a
general mixture of distributions which exactly
satisfies this Law. Various other examples and
counterexamples are also given.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Bonache:2010:DFL,
author = "A. B. Bonache and K. Moris and J. Maurice",
title = "{D}{\'e}tection de fraudes et loi de {Benford}:
Quelques risques associ{\'e}s. ({French}) [{Fraud}
detection and {Benford}'s law: Some risks]",
journal = "Revue Fran{\c{c}}aise de Comptabilit{\'e}",
volume = "??",
number = "431",
pages = "24--27",
month = apr,
year = "2010",
CODEN = "????",
DOI = "????",
ISSN = "0484-8764",
ISSN-L = "0484-8764",
bibdate = "Mon Feb 18 17:33:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "????",
acknowledgement = ack-nhfb,
journal-URL = "http://www.experts-comptables.fr/csoec/Publications/RFC",
language = "French",
}
@InCollection{Brahler:2010:EMS,
author = "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena
Emke",
booktitle = "{Ilmenauer Schriften zur Betriebswirtschaftslehre}.
({German}) [{Illmenauer} writings on economics]",
title = "{Der Einsatz mathematisch-statistischer Methoden in
der digitalen Betriebspr{\"u}fung}. ({German}) [{The}
use of mathematical and statistical methods in the
digital audit]",
volume = "4/2010",
publisher = "Verlag proWiWi e.V.",
address = "Ilmenau, Germany",
pages = "48",
month = apr,
year = "2010",
ISBN = "3-940882-23-2",
ISBN-13 = "978-3-940882-23-3",
ISSN = "1866-2145 (print), 2192-4643 (electronic)",
LCCN = "????",
bibdate = "Mon Feb 18 17:35:58 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Bravo-Marquez:2010:HLM,
author = "Felipe Bravo-Marquez and Gaston L'Huillier and
Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez",
title = "Hypergeometric Language Model and {Zipf}-Like Scoring
Function for {Web} Document Similarity Retrieval",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6393",
pages = "303--308",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-16321-0_32",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:49:42 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-16321-0",
book-URL = "http://www.springerlink.com/content/978-3-642-16321-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Burns:2010:PL,
author = "John Burns",
title = "Probably likely",
journal = j-NEW-SCIENTIST,
volume = "208",
number = "2786",
pages = "32-",
year = "2010",
CODEN = "NWSCAL",
DOI = "https://doi.org/10.1016/S0262-4079(10)62810-2",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407910628102",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
}
@Article{Cartlidge:2010:NNO,
author = "Edwin Cartlidge",
title = "In nature, number one dominates",
journal = "Institute of Physics, Environmental Research Letters",
volume = "??",
number = "??",
pages = "??--??",
day = "25",
month = oct,
year = "2010",
DOI = "????",
bibdate = "Mon Feb 18 17:38:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://environmentalresearchweb.org/cws/article/news/44124",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Cifarelli:2010:GSP,
author = "D. Michele Cifarelli and R. P. Gupta and K.
Jayakumar",
title = "On generalized semi-{Pareto} and semi-{Burr}
distributions and random coefficient minification
processes",
journal = j-STAT-PAPERS,
volume = "51",
number = "1",
pages = "193--208",
month = jan,
year = "2010",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-008-0132-5",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:31 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-008-0132-5",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Misc{Conway:2010:CFM,
author = "D. Conway",
title = "{Benford's Law} Tests for {Wikileaks} Data",
howpublished = "Zero Intelligence Agents website.",
day = "1",
month = aug,
year = "2010",
bibdate = "Mon Feb 18 17:39:45 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.drewconway.com/zia/?p=2234",
acknowledgement = ack-nhfb,
}
@InCollection{Corazza:2010:CFM,
author = "Marco Corazza and Andrea Ellero and Alberto Zorzi",
booktitle = "Mathematical and statistical methods for actuarial
sciences and finance",
title = "Checking financial markets via {Benford}'s law: the
{S\&P 500} case",
publisher = "Springer Italia",
address = "Milan, Italy",
pages = "93--102",
year = "2010",
DOI = "https://doi.org/10.1007/978-88-470-1481-7_10",
MRclass = "62P05",
MRnumber = "2676191",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/chapter/10.1007/978-88-470-1481-7_10",
acknowledgement = ack-nhfb,
}
@Article{Corominas-Murtra:2010:UZL,
author = "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
title = "Universality of {Zipf}'s law",
journal = j-PHYS-REV-E,
volume = "82",
number = "1",
pages = "011102",
day = "1",
month = jul,
year = "2010",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.82.011102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82B03 (62B10)",
MRnumber = "2736361 (2011j:82002)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.011102",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "9",
}
@Article{Courtland:2010:CML,
author = "Rachel Courtland",
title = "Curious mathematical law is rife in nature",
journal = j-NEW-SCIENTIST,
volume = "208",
number = "2782",
pages = "10--10",
day = "16",
month = oct,
year = "2010",
CODEN = "NWSCAL",
DOI = "https://doi.org/10.1016/S0262-4079(10)62497-9",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
abstract = "Disparate data sets produced by natural phenomena all
follow Benford's law, suggesting new ways to detect
earthquakes or scientific anomalies",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law; earthquake detection",
xxISSN = "0262-4079, 0028-6664",
}
@InCollection{Crato:2010:MB,
author = "Nuno Crato",
booktitle = "Figuring It Out: Entertaining Encounters with Everyday
Math",
title = "{Mr. Benford}",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "ix + 227",
pages = "173--178",
year = "2010",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-04833-3_41",
ISBN = "3-642-04832-3 (hardcover)",
ISBN-13 = "978-3-642-04832-6 (hardcover)",
bibdate = "Wed Aug 12 09:28:13 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04833-3_41.pdf",
abstract = "This is a book of mathematical stories, funny and
puzzling mathematical stories. They tell of villains
who try to steal secrets, heroes who encode their
messages, and mathematicians who spend years on end
searching for the best way to pile oranges. There are
also stories about highway confusions occurring when
the rules of Cartesian geometry are ignored,
small-change errors due to ignorance of ancient
paradoxes, and mistakes in calendars arising from poor
numerical approximations. This book is about the power
and beauty of mathematics. It shows mathematics in
action, explained in a way that everybody can
understand.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-04833-3",
tableofcontents = "Everyday Matters. \\
The dinner table algorithm \\
Cutting the Christmas cake \\
Oranges and computers \\
When two and two don't make four \\
Getting more intelligent every day \\
The other lane always goes faster \\
Shoelaces and neckties \\
Number puzzles \\
Tossing a coin \\
The switch \\
Eubulides, the heap and the Euro \\
The Earth is Round. \\
How GPS works \\
Gear wheels \\
February 29 \\
The Nonius scale \\
Pedro Nunes' map \\
Lighthouse geometry \\
Asteroids and least squares \\
The useful man and the genius \\
Secret Affairs. \\
Alice and Bob \\
Inviolate cybersecrets \\
Quantum cryptography \\
The FBI wavelet \\
The enigma machine \\
Art and Geometry. \\
The Vitruvian man \\
The golden number \\
The geometry of A4 paper sizes \\
The strange worlds of Escher \\
Escher and the M{\"o}bius strip \\
Picasso, Einstein and the fourth dimension \\
Pollock's fractals \\
Voronoi diagrams \\
The Platonic solids \\
Pythagorean mosquitoes \\
The most beautiful of all \\
Mathematical Objects. \\
The power of math \\
Doubts in the realm of certainty \\
When chance enhances reliability \\
The difficulty of chance \\
Conjectures and proofs \\
Mr. Benford \\
Financial fractals \\
Turing's test \\
DNA computers \\
Magical multiplication \\
Pi day \\
The best job in the world \\
Out of This World. \\
Electoral paradoxes \\
The melon paradox \\
The cupcake paradox \\
Infinity \\
Unfair games \\
Monsieur Bertrand \\
Boy or girl? \\
A puzzle for Christmas \\
Crisis time for Easter eggs",
}
@Article{Debreceny:2010:DMJ,
author = "Roger S. Debreceny and Glen L. Gray",
title = "Data mining journal entries for fraud detection: An
exploratory study",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "157--181",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "https://doi.org/10.1016/j.accinf.2010.08.001",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See discussion
\cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000540;
http://www.sciencedirect.com/science/journal/14670895",
abstract = "Fraud detection has become a critical component of
financial audits and audit standards have heightened
emphasis on journal entries as part of fraud detection.
This paper canvasses perspectives on applying data
mining techniques to journal entries. In the past, the
impediment to researching journal entry data mining is
getting access to journal entry data sets, which may
explain why the published research in this area is a
null set. For this project, we had access to journal
entry data sets for 29 different organizations. Our
initial exploratory test of the data sets had
interesting preliminary findings. (1) For all 29
entities, the distribution of first digits of journal
dollar amounts differed from that expected by Benford's
Law. (2) Regarding last digits, unlike first digits,
which are expected to have a logarithmic distribution,
the last digits would be expected to have a uniform
distribution. Our test found that the distribution was
not uniform for many of the entities. In fact, eight
entities had one number whose frequency was three times
more than expected. (3) We compared the number of
accounts related to the top five most frequently
occurring three last digit combinations. Four entities
had a very high occurrences of the most frequent three
digit combinations that involved only a small set of
accounts, one entity had a low occurrences of the most
frequent three digit combination that involved a large
set of accounts and 24 had a low occurrences of the
most frequent three digit combinations that involved a
small set of accounts. In general, the first four
entities would probably pose the highest risk of fraud
because it could indicate that the fraudster is
covering up or falsifying a particular class of
transactions. In the future, we will apply more data
mining techniques to discover other patterns and
relationships in the data sets. We also want to seed
the dataset with fraud indicators (e.g., pairs of
accounts that would not be expected in a journal entry)
and compare the sensitivity of the different data
mining techniques to find these seeded indicators.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Accounting information systems; Auditing; Benford's
Law; Data mining; Fraud; Journal entries; XBRL GL",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance.",
}
@TechReport{Deckert:2010:IBL,
author = "Joseph Deckert and Mikhail Myagkov and Peter C.
Ordeshook",
title = "The Irrelevance of {Benford's Law} for Detecting Fraud
in Elections",
type = "{CALTECH} working paper",
number = "9",
institution = "California Institute of Technology",
address = "Pasadena, CA, USA",
pages = "27",
day = "9",
month = mar,
year = "2010",
bibdate = "Mon Feb 18 17:40:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://vote.caltech.edu/drupal/node/327",
acknowledgement = ack-nhfb,
remark = "From the abstract: ``..., we argue here that Benford's
Law is essentially useless as a forensic indicator of
fraud.''",
}
@Article{Deligny:2010:RRL,
author = "H. Deligny and P. Jolissaint",
title = "Relations de r{\'e}currence lin{\'e}aires,
primitivit{\'e} et loi de {Benford}. ({French})
[{Linear} recurrence relations, primitivity, and
{Benford's Law}]",
journal = "ArXiv e-prints",
day = "23",
month = jul,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:14:51 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
http://arxiv.org/abs/1007.5349",
abstract = "We prove that many sequences of positive numbers $
(a_n) $ defined by finite linear difference equations $
a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0
a_n $ with suitable nonnegative reals coefficients $
c_i $ satisfy Benford's Law on the first digit in many
bases $ b > 2 $. Our techniques rely on
Perron--Frobenius theory via the companion matrix of
the characteristic polynomial of the defining
equation.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1007.5349",
keywords = "Mathematics - Dynamical Systems, Mathematics - Rings
and Algebras, 11A99",
language = "French",
primaryclass = "math.DS",
}
@Article{Diekmann:2010:BLF,
author = "Andreas Diekmann and Ben Jann",
title = "{Benford's Law} and Fraud Detection: Facts and
Legends",
journal = j-GER-ECON-REV,
volume = "11",
number = "3",
pages = "397--401",
month = aug,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1468-0475.2010.00510.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
keywords = "Benford's law; false negative; false positive; fraud
detection; regression coefficients",
onlinedate = "6 Apr 2010",
}
@Article{Dixit:2010:EEP,
author = "U. J. Dixit and M. Jabbari Nooghabi",
title = "Efficient estimation in the {Pareto} distribution",
journal = j-STAT-METHODOL,
volume = "7",
number = "6",
pages = "687--691",
month = nov,
year = "2010",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:44 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312710000419",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Article{Egghe:2010:BCN,
author = "Leo Egghe",
title = "Brief Communication: A new short proof of {Naranan}'s
theorem, explaining {Lotka's Law} and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "61",
number = "12",
pages = "2581--2583",
month = dec,
year = "2010",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.21431",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:42:58 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "27 Sep 2010",
}
@Article{Egghe:2010:CSS,
author = "L. Egghe",
title = "Characteristic scores and scales in a {Lotkaian}
framework",
journal = j-SCIENTOMETRICS,
volume = "83",
number = "2",
pages = "455--462",
month = may,
year = "2010",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-009-0009-y",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:20 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-009-0009-y",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Egghe:2010:NSP,
author = "Leo Egghe",
title = "A new short proof of {Naranan}'s theorem, explaining
{Lotka's Law} and {Zipf's Law}",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "61",
number = "12",
pages = "2581--2583",
year = "2010",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.21431",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}
@Article{Farkas:2010:SUN,
author = "Janos Farkas and Gy{\"o}rgy Gyurky",
title = "The significance of using the {Newcomb--Benford} law
as a test of nuclear half-life calculations",
journal = j-ACTA-PHYS-POL-B,
volume = "41",
number = "6",
pages = "1213--1221",
year = "2010",
CODEN = "APOBBB",
ISSN = "0587-4254 (print), 1509-5770 (electronic)",
ISSN-L = "0587-4254",
bibdate = "Mon Nov 14 16:21:42 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
http://arxiv.org/abs/1006.3615",
abstract = "Half-life number sequences collected from nuclear data
charts are found to obey the Newcomb--Benford law.
Based on this fact, it has been suggested recently,
that this law should be used to test the quality of
nuclear decay models. In this paper we briefly recall
how, when and why the Newcomb--Benford law can be
observed in a set of numbers with a given probability
distribution. We investigate the special case of
nuclear half-lives, and show that the law provides no
additional clue in understanding decay half-lives.
Thus, it can play no significant role in testing
nuclear decay theories.",
acknowledgement = ack-nhfb,
ajournal = "Acta Phys. Pol. B",
ajournal-2 = "Acta Phys. Polon. B",
archiveprefix = "arXiv",
eprint = "1006.3615",
fjournal = "Acta Physica Polonica B",
journal-URL = "http://www.actaphys.uj.edu.pl/pl/acta_physica_polonica_b",
primaryclass = "math-ph",
}
@Article{Ferrer-i-Cancho:2010:RTD,
author = "Ramon Ferrer-i-Cancho and Brita Elvev{\aa}g",
title = "Random Texts Do Not Exhibit the Real {Zipf's Law}-Like
Rank Distribution",
journal = j-PLOS-ONE,
volume = "5",
number = "3",
pages = "e9411:1--e9411:10",
month = mar,
year = "2010",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0009411",
ISSN = "1932-6203",
bibdate = "Wed Aug 12 08:54:42 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009411",
abstract = "Zipf's law states that the relationship between the
frequency of a word in a text and its rank (the most
frequent word has rank 1, the 2nd most frequent word
has rank 2, \ldots{}) is approximately linear when
plotted on a double logarithmic scale. It has been
argued that the law is not a relevant or useful
property of language because simple random texts ---
constructed by concatenating random characters
including blanks behaving as word delimiters ---
exhibit a Zipf's law-like word rank distribution.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{Fischer:2010:HCS,
author = "Martin H. Fischer and Richard A. Mills and Samuel
Shaki",
title = "How to cook a {SNARC}: Number placement in text
rapidly changes spatial-numerical associations",
journal = j-BRAIN-COGN,
volume = "72",
number = "3",
pages = "333--336",
month = apr,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.bandc.2009.10.010",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
abstract = "Most theoreticians believe that reading habits explain
why Western adults associate small numbers with left
space and large numbers with right space (the {SNARC}
effect). We challenge this belief by documenting, in
both English and Hebrew, that {SNARC} changes during
reading: small and large numbers in our texts appeared
near the left or right ends of the lines, positioned
either spatially congruent or incongruent with reading
habits. In English, the congruent group showed reliable
{SNARC} before and after reading and the incongruent
group's {SNARC} was significantly reduced. In Hebrew
the incongruent reading condition even induced a
reverse SNARC. These results show that {SNARC} is a
fleeting aspect of number representation that captures
multiple spatial associations.",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; Number line; Numerical cognition;
Reading; Spatial Numerical Association of Response
Codes (SNARC); Spatial numerical associations; {SNARC}
effect",
}
@Article{Formann:2010:NBL,
author = "Anton K. Formann",
title = "The {Newcomb--Benford Law} in Its Relation to Some
Common Distributions",
journal = j-PLOS-ONE,
volume = "5",
number = "5",
pages = "e10541:1--e10541:13",
month = may,
year = "2010",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0010541",
ISSN = "1932-6203",
ISSN-L = "1932-6203",
bibdate = "Mon Nov 14 18:19:09 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
abstract = "An often reported, but nevertheless persistently
striking observation, formalized as the Newcomb-Benford
law (NBL), is that the frequencies with which the
leading digits of numbers occur in a large variety of
data are far away from being uniform. Most spectacular
seems to be the fact that in many data the leading
digit 1 occurs in nearly one third of all cases.
Explanations for this uneven distribution of the
leading digits were, among others, scale- and
base-invariance. Little attention, however, found the
interrelation between the distribution of the
significant digits and the distribution of the observed
variable. It is shown here by simulation that long
right-tailed distributions of a random variable are
compatible with the NBL, and that for distributions of
the ratio of two random variables the fit generally
improves. Distributions not putting most mass on small
values of the random variable (e.g. symmetric
distributions) fail to fit. Hence, the validity of the
NBL needs the predominance of small values and, when
thinking of real-world data, a majority of small
entities. Analyses of data on stock prices, the areas
and numbers of inhabitants of countries, and the
starting page numbers of papers from a bibliography
sustain this conclusion. In all, these findings may
help to understand the mechanisms behind the NBL and
the conditions needed for its validity. That this law
is not only of scientific interest per se, but that, in
addition, it has also substantial implications can be
seen from those fields where it was suggested to be put
into practice. These fields reach from the detection of
irregularities in data (e.g. economic fraud) to
optimizing the architecture of computers regarding
number representation, storage, and round-off errors.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{Genolini:2010:EIP,
author = "Christophe Genolini and Tarak Driss",
title = "Eveiller l'int{\'e}r{\^e}t pour la statistique par
l'exemple. ({French}) [{Raising} interest in statistics
by example]",
journal = "Statistique et Enseignement",
volume = "1",
number = "2",
pages = "49--57",
month = "????",
year = "2010",
CODEN = "????",
DOI = "????",
ISSN = "2108-6745",
ISSN-L = "2108-6745",
bibdate = "Mon Feb 18 17:43:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16",
acknowledgement = ack-nhfb,
journal-URL = "http://www.statistique-et-enseignement.fr/",
keywords = "Benford's Law",
language = "French",
}
@Article{Giuliano:2010:UPI,
author = "Rita Giuliano and {\'E}lise Janvresse",
title = "A unifying probabilistic interpretation of {Benford}'s
law",
journal = "Uniform Distribution Theory",
volume = "5",
number = "2",
pages = "169--182",
year = "2010",
CODEN = "????",
ISSN = "1336-913X",
ISSN-L = "1336-913X",
MRclass = "60J10 (11K99 60A99)",
MRnumber = "2781415",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Unif. Distrib. Theory",
fjournal = "Uniform Distribution Theory",
}
@InProceedings{Gonzalez-Jimenez:2010:BLN,
author = "D. Gonzalez-Jimenez and E. Argones-Rua and F.
Perez-Gonzalez and J. L. Alba-Castro",
editor = "IEEE",
booktitle = "IEEE International Conference on Image Processing",
title = "{Benford's Law} for Natural and Synthetic Images",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1245--1248",
year = "2010",
bibdate = "Sat Sep 10 11:34:53 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "Not found in IEEE Xplore database??",
}
@Article{Grabski:2010:DDM,
author = "Severin Grabski",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "182--185",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "https://doi.org/10.1016/j.accinf.2010.07.008",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance",
}
@Article{Herron:2010:EPO,
author = "Erik S. Herron",
title = "The effect of passive observation methods on
{Azerbaijan}'s 2008 presidential election and 2009
referendum",
journal = j-ELECT-STUDIES,
volume = "29",
number = "3",
pages = "417--424",
year = "2010",
DOI = "https://doi.org/10.1016/j.electstud.2010.03.013",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Special Symposium: Voters and Coalition Governments",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379410000259",
abstract = "Election observation is used by domestic and
international groups to assess election quality and
deter fraud. However, a limited amount of research has
assessed its effectiveness. This article adds to the
literature by analyzing how a passive monitoring tool
affected the process and outcome of voting in two
elections in Azerbaijan. The analysis shows that the
placement of webcams in polling stations is
consistently associated with lower reported turnout and
inconsistently associated with lower regime support.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Azerbaijan; Benford's Law; Election observation;
Fraud",
}
@Article{Hickman:2010:DAC,
author = "Matthew Hickman and Stephen Rice",
title = "Digital Analysis of Crime Statistics: Does Crime
Conform to {Benford's Law}?",
journal = j-J-QUANT-CRIMINOL,
volume = "26",
number = "3",
pages = "333--349",
month = sep,
year = "2010",
CODEN = "JQCRE6",
DOI = "https://doi.org/10.1007/s10940-010-9094-6",
ISSN = "0748-4518 (print), 1573-7799 (electronic)",
ISSN-L = "0748-4518",
bibdate = "Fri Nov 25 10:30:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Criminology",
keywords = "Benford distribution; Benford's law; Crime data; Crime
statistics; Data errors; Digital analysis; Fabricated
data; First digit; Fraud detection; Uniform crime
reports",
}
@MastersThesis{Jasak:2010:BZR,
author = "Zoran Jasak",
title = "Benfordov zakon i reinforcement u{\v{c}}enje.
({Bosnian}) [{Benford's Law} and reinforcement
learning]",
type = "{Magistarski Rad} ({M.Sc.} Thesis)",
school = "Prirodno-Matematicki Fakultet, Odsjek za matematiku,
Ju Univerzitet u Tuzla",
address = "Tuzla, Bosnia and Herzegovina",
pages = "124",
month = dec,
year = "2010",
bibdate = "Mon Feb 18 17:48:33 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf",
acknowledgement = ack-nhfb,
keywords = "action; Adaptive Benford's method; Adaptivna
Benfordova metoda; akcija; Benford's law; Benfordov
zakon; confidence intervals; contamination level;
intervali povjerenja; koli{\v{c}}nik; nivo
kontaminacije; Q learning; Q u{\v{c}}enje; quotient;
reinforcement learning; reinforcement u{\v{c}}enje;
Sarsa; stanje; state",
language = "Bosnian",
}
@Article{Jiang:2010:NMS,
author = "Weina Jiang and Anthony T. S. Ho and Helen Treharne
and Yun Q. Shi",
title = "A Novel Multi-size Block {Benford's Law} Scheme for
Printer Identification",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6297",
pages = "643--652",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-15702-8_59",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Jan 21 17:47:23 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-15702-8",
book-URL = "http://www.springerlink.com/content/978-3-642-15702-8",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kaynar:2010:FSM,
author = "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
title = "Finite-state {Markov} Chains obey {Benford's Law}",
journal = "ArXiv e-prints",
day = "2",
month = mar,
year = "2010",
CODEN = "????",
ISSN = "????",
MRclass = "60J22, 11K06, 15B51",
bibdate = "Tue Nov 15 06:30:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
http://arxiv.org/abs/1003.0562",
abstract = "A sequence of real numbers ($ x_n$) is Benford if the
significands, i.e. the fraction parts in the
floating-point representation of ($ x_n$) are
distributed logarithmically. Similarly, a discrete-time
irreducible and aperiodic finite-state Markov chain
with probability transition matrix $P$ and limiting
matrix $ P*$ is Benford if every component of both
sequences of matrices $ (P^n - P*)$ and $ (P^{n + 1} -
P^n)$ is Benford or eventually zero. Using recent tools
that established Benford behavior both for Newton's
method and for finite-dimensional linear maps, via the
classical theories of uniform distribution modulo $1$
and Perron-Frobenius, this paper derives a simple
sufficient condition (nonresonant) guaranteeing that
$P$, or the Markov chain associated with it, is
Benford. This result in turn is used to show that
almost all Markov chains are Benford, in the sense that
if the transition probabilities are chosen
independently and continuously, then the resulting
Markov chain is Benford with probability one. Concrete
examples illustrate the various cases that arise, and
the theory is complemented with several simulations and
potential applications.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1003.0562",
keywords = "Mathematics - Probability",
primaryclass = "math.PR",
}
@Article{Kibria:2010:PTE,
author = "B. M. Golam Kibria and A. K. Md. E. Saleh",
title = "Preliminary test estimation of the parameters of
exponential and {Pareto} distributions for censored
samples",
journal = j-STAT-PAPERS,
volume = "51",
number = "4",
pages = "757--773",
month = dec,
year = "2010",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-008-0163-y",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:33 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-008-0163-y",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{Klar:2010:ZLL,
author = "B. Klar and P. R. Parthasarathy and N. Henze",
title = "{Zipf} and {Lerch} limit of birth and death
processes",
journal = j-PROB-ENG-INFO-SCI,
volume = "24",
number = "1",
pages = "129--144",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1017/S0269964809990179",
ISSN = "0269-9648 (print), 1469-8951 (electronic)",
ISSN-L = "0269-9648",
MRclass = "60J27 (91F20)",
MRnumber = "2575846 (2010m:60254)",
bibdate = "Sat Mar 23 12:53:04 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Probab. Engrg. Inform. Sci.",
fjournal = "Probability in the Engineering and Informational
Sciences",
keywords = "Zipf's Law",
}
@Article{Kriel:2010:DDM,
author = "Eckhardt Kriel",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "186--188",
month = sep,
year = "2010",
CODEN = "IJAIA7",
DOI = "https://doi.org/10.1016/j.accinf.2010.07.009",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
remark = "2009 Research Symposium on Information Integrity \&
Information Systems Assurance.",
}
@Book{Lagarias:2010:UCP,
editor = "Jeffrey C. Lagarias",
title = "The ultimate challenge: the $ 3 x + 1 $ problem",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xiv + 344",
year = "2010",
ISBN = "0-8218-4940-9",
ISBN-13 = "978-0-8218-4940-8",
LCCN = "QA292 .U48 2010",
MRclass = "11B83; 37A45; 11B37; 68Q99",
bibdate = "Sat Sep 10 13:02:05 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The $ 3 x + 1 $ problem, or Collatz problem, concerns
the following seemingly innocent arithmetic procedure
applied to integers: If an integer $x$ is odd then
``multiply by three and add one'', while if it is even
then ``divide by two''. The $ 3 x + 1$ problem asks
whether, starting from any positive integer, repeating
this procedure over and over will eventually reach the
number 1. Despite its simple appearance, this problem
is unsolved. Generalizations of the problem are known
to be undecidable, and the problem itself is believed
to be extraordinarily difficult. This book reports on
what is known on this problem. It consists of a
collection of papers, which can be read independently
of each other. The book begins with two introductory
papers, one giving an overview and current status, and
the second giving history and basic results on the
problem. These are followed by three survey papers on
the problem, relating it to number theory and dynamical
systems, to Markov chains and ergodic theory, and to
logic and the theory of computation. The next paper
presents results on probabilistic models for behavior
of the iteration. This is followed by a paper giving
the latest computational results on the problem, which
verify its truth for $ x < 5.4 \cdot 10^{18}$. The book
also reprints six early papers on the problem and
related questions, by L. Collatz, J. H. Conway, H. S.
M. Coxeter, C. J. Everett, and R. K. Guy, each with
editorial commentary. The book concludes with an
annotated bibliography of work on the problem up to the
year 2000.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Sequences (Mathematics); Polynomials; Harmonic
analysis; Number theory -- Sequences and sets --
Special sequences and polynomials.; Dynamical systems
and ergodic theory -- Ergodic theory -- Relations with
number theory and harmonic analysis.; Number theory --
Sequences and sets -- Recurrences.; Computer science --
Theory of computing -- None of the above, but in this
section.",
tableofcontents = "The $ 3 x + 1 $ problem: an overview \\
The $ 3 x + 1 $ problem and its generalizations /
Jeffrey C. Lagarias \\
Survey papers \\
A $ 3 x + 1 $ survey: number theory and dynamical
systems / Marc Chamberland \\
Generalized $ 3 x + 1 $ mappings: Markov chains and
ergodic theory / K. R. Matthews \\
Generalized $ 3 x + 1 $ functions and the theory of
computation / Pascal Michel and Maurice Margenstern \\
Stochastic modelling and computation papers \\
Stochastic models for the $ 3 x + 1 $ and $ 5 x + 1$
problems and related problems / Alex V. Kontorovich and
Jeffrey C. Lagarias \\
Empirical verification of the $ 3 x + 1 $ and related
conjectures / Tom{\'a}s Oliveira E Silva \\
Reprinted early papers \\
Cyclic sequences and frieze patterns (The fourth Felix
Behrend Memorial Lecture) / H. S. M. Coxeter \\
Unpredictable iterations / J. H. Conway \\
Iteration of the number-theoretic function: $f(2n) =
n$, $f(2n + 1) = 3n + 2$ / C. J. Everett \\
Don't try to solve these problems! / Richard K. Guy \\
On the motivation and origin of the $(3n + 1)$-problem
/ Lothar Collatz \\
FRACTRAN: a simple universal programming language for
arithmetic / J. H. Conway \\
The $ 3 x + 1 $ problem: an annotated bibliography
(1963--1999) / Jeffrey C. Lagarias",
}
@Article{Lee:2010:SAR,
author = "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
title = "{Stigler}'s approach to recovering the distribution of
first significant digits in natural data sets",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "2",
pages = "82--88",
day = "15",
month = jan,
year = "2010",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2009.09.015",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
abstract = "Benford's Law can be seen as one of the many first
significant digit (FSD) distributions in a family of
monotonically decreasing distributions. We examine the
interrelationship between Benford and other
monotonically decreasing distributions such as those
arising from Stigler, Zipf, and the power laws. We
examine the theoretical basis of the Stigler
distribution and extend his reasoning by incorporating
{FSD} first-moment information into
information-theoretic methods. We present
information-theoretic methods as a way to describe,
connect, and unify these related distributions and
thereby extend the reach of Benford's Law and {FSD}
research more generally.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law",
}
@Article{Liu:2010:CIE,
author = "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
title = "Comments on {``An integrated efficient solution for
computing frequent and top-$k$ elements in data
streams''}",
journal = j-TODS,
volume = "35",
number = "2",
pages = "15:1--15:??",
month = apr,
year = "2010",
CODEN = "ATDSD3",
DOI = "https://doi.org/10.1145/1735886.1735894",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Wed Apr 28 13:44:08 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Metwally:2006:IES}.",
abstract = "We investigate a well-known algorithm, {\em
Space-Saving\/} [Metwally et al. 2006], which has been
proven efficient and effective at mining frequent
elements in data streams. We discovered an error in one
of the theorems in Metwally et al. [2006]. Experiments
are conducted to illustrate the error.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Database Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777",
keywords = "approximate queries; data streams; frequent elements;
top-$k$ elements; Zipfian distributions",
}
@Article{Lu:2010:BLP,
author = "Ocean Fan Lu and David E. Giles",
title = "{Benford's Law} and psychological barriers in certain
{eBay} auctions",
journal = j-APPL-ECON-LETT,
volume = "17",
number = "10",
pages = "1005--1008",
month = "????",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1080/13504850802631814",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:10:23 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
abstract = "Using generalizations of Benford's Law we test for the
absence of psychological barriers at various price
levels in eBay auctions for professional football
tickets. Our empirical results indicate that this
hypothesis cannot be rejected.",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
journal-URL = "http://www.tandfonline.com/loi/rael20",
onlinedate = "16 Jun 2009",
}
@Article{Mahdian:2010:BBM,
author = "Babak Mahdian and Stanislav Saic",
title = "A bibliography on blind methods for identifying image
forgery",
journal = j-SIGNAL-PROCESS-IMAGE-COMMUN,
volume = "25",
number = "6",
pages = "389--399",
month = jul,
year = "2010",
CODEN = "SPICEF",
DOI = "https://doi.org/10.1016/j.image.2010.05.003",
ISSN = "0923-5965 (print), 1879-2677 (electronic)",
ISSN-L = "0923-5965",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
abstract = "Verifying the integrity of digital images and
detecting the traces of tampering without using any
protecting pre-extracted or pre-embedded information
have become an important and hot research field. The
popularity of this field and the rapid growth in papers
published during the last years have put considerable
need on creating a complete bibliography addressing
published papers in this area. In this paper, an
extensive list of blind methods for detecting image
forgery is presented. By the word blind we refer to
those methods that use only the image function. An
attempt has been made to make this paper complete by
listing most of the existing references and by
providing a detailed classification group.",
acknowledgement = ack-nhfb,
fjournal = "Signal Processing: Image Communication",
keywords = "Benford's Law; Blind forgery detection; Digital
forgery; Image forensics; Image tampering; Multimedia
security",
}
@Article{Manoochehrnia:2010:BLA,
author = "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
W. Schulz and G. Diendorfer",
title = "{Benford's Law} and Its Application to Lightning
Data",
journal = j-IEEE-TRANS-ELECTROMAGN-COMPAT,
volume = "52",
number = "4",
pages = "956--961",
month = nov,
year = "2010",
CODEN = "IEMCAE",
DOI = "https://doi.org/10.1109/TEMC.2010.2067218",
ISSN = "0018-9375 (print), 1558-187X (electronic)",
ISSN-L = "0018-9375",
bibdate = "Mon Nov 21 22:24:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electromagnetic Compatibility",
}
@InProceedings{Mebane:2010:EFR,
author = "Walter R. {Mebane, Jr.} and K. Kalinin",
editor = "????",
booktitle = "{Proceedings of the 2010 Annual Meeting of the Midwest
Political Science Association, Chicago, IL, April
22--25, 2010}",
title = "Electoral Fraud in {Russia}: Vote Counts Analysis
Using Second-Digit Mean Tests",
publisher = "????",
address = "????",
pages = "??--??",
year = "2010",
bibdate = "Sat Sep 10 14:32:06 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InProceedings{Mebane:2010:EFSa,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{Proceedings of the 2010 Annual Meeting of the Midwest
Political Science Association, Chicago, IL, April
22--25, 2010}",
title = "Election Fraud or Strategic Voting?",
publisher = "????",
address = "????",
pages = "??--??",
year = "2010",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Sat Sep 10 14:19:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InProceedings{Mebane:2010:EFSb,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{2010 Summer Meeting of the Political Methodology
Society, University of Iowa, July 22--24, 2010}",
title = "Election Fraud or Strategic Voting? {Can} Second-digit
Tests Tell the Difference?",
publisher = "????",
address = "????",
pages = "1--49",
year = "2010",
ISBN = "????",
ISBN-13 = "????",
bibdate = "Sat Feb 16 11:56:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/pm10.pdf",
acknowledgement = ack-nhfb,
}
@Article{Mebane:2010:FPE,
author = "Walter R. {Mebane, Jr.}",
title = "Fraud in the {2009 Presidential Election} in {Iran}?",
journal = j-CHANCE,
volume = "23",
number = "1",
pages = "6--15",
month = mar,
year = "2010",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1007/s00144-010-0003-4",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Mon Feb 18 17:50:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/0337v415563q0753/abstract/",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
xxnote = "Publisher archive at
\path=http://amstat.tandfonline.com/loi/ucha20= is
missing volumes 18 (2005)--24 (2011). Those volumes are
available at
\path=http://link.springer.com/journal/144=",
}
@TechReport{Mebane:2010:MSD,
author = "Walter R. {Mebane, Jr.}",
title = "Memo on second-digit tests done on precinct counts for
{Democratic Senate} primary in {South Carolina}, 2010",
type = "Report",
institution = "University of Michigan",
address = "Ann Arbor, MI, USA",
day = "12",
month = jun,
year = "2010",
bibdate = "Sat Feb 16 12:06:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf",
acknowledgement = ack-nhfb,
}
@Article{Morrison:2010:MG,
author = "Kent E. Morrison",
title = "The Multiplication Game",
journal = j-MATH-MAG,
volume = "83",
number = "??",
pages = "100--110",
month = apr,
year = "2010",
CODEN = "MAMGA8",
DOI = "????",
ISSN = "0025-570X",
ISSN-L = "0025-570X",
bibdate = "Mon Feb 18 17:51:50 2013",
bibsource = "http://www.maa.org/pubs/mag_apr10_toc.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
keywords = "Benford's Law",
}
@Book{Newbold:2010:SBE,
author = "Paul Newbold and William L. Carlson and Betty Thorne",
title = "Statistics for Business and Economics",
publisher = "Pearson",
address = "Boston, MA, USA",
edition = "Seventh",
pages = "986 + 16",
year = "2010",
ISBN = "0-13-507248-4",
ISBN-13 = "978-0-13-507248-6",
LCCN = "QA276.18 .N49 2010",
bibdate = "Fri Mar 22 09:03:48 MDT 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@Book{Nillsen:2010:RRD,
author = "Rodney Victor Nillsen",
title = "Randomness and recurrence in dynamical systems: a real
analysis approach",
volume = "31",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "xviii + 357",
year = "2010",
ISBN = "0-88385-043-5",
ISBN-13 = "978-0-88385-043-5",
LCCN = "QA614.8 .N55 2010",
bibdate = "Mon Feb 18 17:53:28 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "The Carus mathematical monographs",
acknowledgement = ack-nhfb,
subject = "Differentiable dynamical systems; Measure theory",
tableofcontents = "Background ideas and knowledge \\
Irrational numbers and dynamical systems \\
Probability and randomness \\
Recurrence \\
Averaging in time and space",
}
@Article{Novikov:2010:APB,
author = "V. P. Novikov",
title = "Aspectual Principle, {Benford's Law} and {Russell's
Paradox}",
journal = "ArXiv e-prints",
month = dec,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:11:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N;
http://arxiv.org/abs/1012.5537",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1012.5537",
keywords = "Mathematics - Classical Analysis and ODEs",
pagecount = "5",
primaryclass = "math.CA",
}
@Book{Oleksy:2010:DMB,
author = "Marius Oleksy",
title = "{Data Mining und Benford's Law als
Controllinginstrumente}. ({German}) [{Data} Mining and
{Benford's Law} as controlling instruments]",
volume = "45",
publisher = "Europ{\"a}ischer Hochschulverlag",
address = "Bremen, Germany",
pages = "181 (est.)",
year = "2010",
ISBN = "3-86741-405-X",
ISBN-13 = "978-3-86741-405-0",
LCCN = "????",
bibdate = "Mon Feb 18 17:54:59 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "{Wismarer Schriften zu Management und Recht}",
URL = "http://www.amazon.de/Data-Mining-Benfords-Law-Controllinginstrumente/dp/386741405X",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Orita:2010:UBL,
author = "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and
Kazuki Ohno",
title = "Use of {Benford's Law} in drug discovery data",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "15",
number = "9--10",
pages = "328--331",
month = may,
year = "2010",
CODEN = "DDTOFS",
DOI = "https://doi.org/10.1016/j.drudis.2010.03.003",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1359644610000796",
abstract = "Benford's law states that the distribution of the
first digit of many data sets is not uniform. The first
digit of any random number will be 1 almost 30\% of the
time, and larger digits occur as the first digit with
lower and lower frequency, to the point where 9 occurs
as a first digit only 5\% of the time. Here, we
demonstrate that several data sets in the field of drug
discovery follow Benford's distribution, whereas
doctored data do not. Our findings indicate the
applicability of Benford's law in assessing data
quality in the field of drug discovery. We also propose
a useful index of evaluating data quality based on
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
keywords = "Benford's Law",
}
@Misc{Pan:2010:EJC,
author = "Da Pan and Lijing Shao and Bo-Qiang Ma",
title = "{Benford's Law} in Statistical Physics",
howpublished = "Wolfram Online Demonstrations Projects.",
year = "2010",
bibdate = "Mon Feb 18 18:00:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://demonstrations.wolfram.com/BenfordsLawInStatisticalPhysics/",
acknowledgement = ack-nhfb,
}
@Article{Peng:2010:SFW,
author = "Fei Peng and Re-Si Guo and Chang-Tsun Li and Min
Long",
title = "A semi-fragile watermarking algorithm for
authenticating {$2$D} {CAD} engineering graphics based
on log-polar transformation",
journal = j-COMPUT-AIDED-DES,
volume = "42",
number = "12",
pages = "1207--1216",
year = "2010",
CODEN = "CAIDA5",
DOI = "https://doi.org/10.1016/j.cad.2010.08.004",
ISSN = "0010-4485 (print), 1879-2685 (electronic)",
ISSN-L = "0010-4485",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010448510001491",
abstract = "Copyright violation and illegal manipulation of
digital data have been acute challenges for many
sectors since the very same set of enabling techniques
for generating and processing digital data started to
emerge. Although traditional protective methods, such
as encryption and digital signatures, have been in use
for decades, their inability to provide protection
after decryption and locating tampering has prompted
the development of digital watermarking. In this paper,
a semi-fragile watermarking algorithm for
authenticating 2D {CAD} engineering graphics based on
log-polar coordinate mapping is proposed. Firstly, the
vertices are divided into groups, and for each group,
the vertices for carrying a watermark are mapped to the
log-polar coordinate system. Then the watermark is
embedded in the mantissa of the real-valued log-polar
coordinates via bit substitution. Theoretical analysis
and experimental results show that the proposed
algorithm is not only robust against incidental global
operations such as rotation, translation and scaling,
but can also detect and locate malicious attacks such
as entity modification and entity addition/deletion.",
acknowledgement = ack-nhfb,
fjournal = "Computer-Aided Design",
journal-URL = "http://www.sciencedirect.com/science/journal/00104485",
keywords = "Benford's Law; Content authentication; Data hiding;
Engineering graphics; Integrity verification;
Semi-fragile watermarking",
}
@Article{Peng:2010:ZLC,
author = "Guohua Peng",
title = "{Zipf}'s law for {Chinese} cities: {Rolling} sample
regressions",
journal = j-PHYSICA-A,
volume = "389",
number = "18",
pages = "3804--3813",
day = "15",
month = sep,
year = "2010",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2010.05.004",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037843711000381X",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Perc:2010:ZLL,
author = "Matja{\v{z}} Perc",
title = "{Zipf}'s law and log-normal distributions in measures
of scientific output across fields and institutions: 40
years of {Slovenia's} research as an example",
journal = j-J-INFORMETRICS,
volume = "4",
number = "3",
pages = "358--364",
day = "1",
month = jul,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.joi.2010.03.001",
ISSN = "1751-1577 (print), 1875-5879 (electronic)",
ISSN-L = "1751-1577",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1751157710000234",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informetrics",
journal-URL = "http://www.sciencedirect.com/science/journal/17511577",
keywords = "Zipf's Law",
}
@Book{Posch:2010:ZNB,
author = "Peter N. Posch",
title = "{Ziffernanalyse mit dem Newcomb--Benford Gesetz in
Theorie und Praxis}. ({German}) [{Digit} analysis with
the {Newcomb--Benford} law in theory and practice]",
publisher = "Verlag Europ{\"a}ische Wirtschaft",
address = "Munich, Germany",
edition = "Second",
pages = "105 (est.)",
year = "2010",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Feb 18 18:01:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Qadir:2010:EJC,
author = "G. Qadir and X. Zhao and A. T. S. Ho",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "Estimating {JPEG2000} compression for image forensics
using {Benford's Law}",
volume = "7723",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = apr,
year = "2010",
DOI = "https://doi.org/10.1117/12.855085",
bibdate = "Mon Nov 14 18:25:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q",
acknowledgement = ack-nhfb,
}
@Article{Raqab:2010:PPD,
author = "Mohammad Z. Raqab and A. Asgharzadeh and R.
Valiollahi",
title = "Prediction for {Pareto} distribution based on
progressively {Type-II} censored samples",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "54",
number = "7",
pages = "1732--1743",
day = "1",
month = jul,
year = "2010",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:00 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947310000563",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Rezayan:2010:SRG,
author = "Hani Rezayan and Mahmoud Reza Delavar and Andrew
Ulrich Frank and A. Mansouri",
title = "Spatial rules that generate urban patterns: Emergence
of the power law in the distribution of axial line
length",
journal = "International Journal of Applied Earth Observation and
Geoinformation",
volume = "12",
number = "5",
pages = "317--330",
year = "2010",
DOI = "https://doi.org/10.1016/j.jag.2010.04.003",
ISSN = "0303-2434",
ISSN-L = "0303-2434",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0303243410000413",
abstract = "This paper studies emergence/generation of power law
in rank-order distribution of axial line length, which
is a global pattern observed in real cities, due to
interaction of a set of seven simple spatial rules at a
local scale. These rules and their interactions form a
model expected to simulate the morphological structure
of free spaces in unplanned organic pedestrian small
cities. Effects of each of the seven rules are
discussed through repeated simulations of eight
possible combinations of the rules, using a bottom-up
process. The results show that the rules generate
environments with statistically stable rank-order
distribution of axial line length that follows the
power law. It means that the axial maps of the
simulated environments have a scale-free hierarchical
structure such that their distributions lean toward
short axial lines. It also represents dominance of
local spatial structure, as the model renders a faster
rate of growth at a local scale while allowing a steady
growth at a global scale.",
acknowledgement = ack-nhfb,
keywords = "Axial line; Axial map; Axial representation; Benford's
Law; Emergence; Power law",
}
@Article{Rousseau:2010:AFO,
author = "Christiane Rousseau",
title = "Apprendre {\`a} frauder ou {\`a} d{\'e}tecter les
fraudes. ({French}) [{Learning} to defraud or to detect
fraud]",
journal = "Accrom$\alpha$th",
volume = "5",
pages = "2--7",
month = "{\'E}t{\'e}--automne",
year = "2010",
ISSN = "1911-0197",
bibdate = "Mon Feb 18 18:07:49 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://accromath.uqam.ca/contents/pdf/Benford.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://www.accromath.ca/",
language = "French",
}
@Book{Saichev:2010:TZL,
author = "Alexander Saichev and Yannick Malevergne and Didier
Sornette",
title = "Theory of {Zipf}'s law and beyond",
volume = "632",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 171",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-02946-2",
ISBN = "3-642-02945-0",
ISBN-13 = "978-3-642-02945-5",
MRclass = "91-02 (91B70 91B82)",
MRnumber = "2569206 (2011b:91008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Economics and Mathematical Systems",
ZMnumber = "Zbl 1189.91009",
acknowledgement = ack-nhfb,
}
@Article{Saldana-Zepeda:2010:GFT,
author = "Dayna P. Salda{\~n}a-Zepeda and Humberto
Vaquera-Huerta and Barry C. Arnold",
title = "A goodness of fit test for the {Pareto} distribution
in the presence of Type {II} censoring, based on the
cumulative hazard function",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "54",
number = "4",
pages = "833--842",
day = "1",
month = apr,
year = "2010",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:42:57 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947309004071",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Sambridge:2010:BLN,
author = "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A.
Jackson",
title = "{Benford}'s law in the natural sciences",
journal = "Geophysical Research Letters",
volume = "37",
number = "22",
pages = "L22301--L22306",
month = "????",
year = "2010",
CODEN = "GPRLAJ",
DOI = "https://doi.org/10.1029/2010GL044830",
ISSN = "0094-8276 (print), 1944-8007 (electronic)",
ISSN-L = "0094-8276",
bibdate = "Sun Nov 13 11:03:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S;
http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml",
abstract = "More than 100 years ago it was predicted that the
distribution of first digits of real world observations
would not be uniform, but instead follow a trend where
measurements with lower first digit (1, 2, \ldots {})
occur more frequently than those with higher first
digits (\ldots {}, 8, 9). This result has long been
known but regarded largely as a mathematical curiosity
and received little attention in the natural sciences.
Here we show that the first digit rule is likely to be
a widespread phenomenon and may provide new ways to
detect anomalous signals in data. We test 15 sets of
modern observations drawn from the fields of physics,
astronomy, geophysics, chemistry, engineering and
mathematics, and show that Benford's law holds for them
all. These include geophysical observables such as the
length of time between geomagnetic reversals, depths of
earthquakes, models of Earth's gravity, geomagnetic and
seismic structure. In addition we find it also holds
for other natural science observables such as the
rotation frequencies of pulsars; green-house gas
emissions, the masses of exoplanets as well as numbers
of infectious diseases reported to the World Health
Organization. The wide range of areas where it is
manifested opens up new possibilities for exploitation.
An illustration is given of how seismic energy from an
earthquake can be detected from just the first digit
distribution of displacement counts on a seismometer,
i.e., without actually looking at the details of a
seismogram at all. This led to the first ever detection
of an earthquake using first digit information alone.",
acknowledgement = ack-nhfb,
ajournal = "Geophys. Res. Lett.",
fjournal = "Geophysical research letters",
keywords = "earthquakes; large data sets; observational
seismology; statistics",
}
@TechReport{Schraepler:2010:BLI,
author = "J{\"o}rg-Peter Schraepler",
title = "{Benford's Law} as an instrument for fraud detection
in surveys using the data of the {Socio-Economic Panel
(SOEP)}",
type = "{SOEP} paper",
number = "273",
institution = "Socio-Economic Panel, Deutsches Institut f{\"u}r
Wirtschaftsforschung",
address = "Berlin, Germany",
pages = "ii + 56",
day = "2",
month = mar,
year = "2010",
ISSN = "1864-6689",
ISSN-L = "1864-6689",
bibdate = "Mon Feb 18 18:10:18 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf",
acknowledgement = ack-nhfb,
}
@Article{Shao:2010:EMD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "Empirical Mantissa Distributions of Pulsars",
journal = j-ASTROPART-PHYS,
volume = "33",
number = "4",
pages = "255--262",
month = may,
year = "2010",
CODEN = "APHYEE",
DOI = "https://doi.org/10.1016/j.astropartphys.2010.02.003",
ISSN = "0927-6505 (print), 1873-2852 (electronic)",
ISSN-L = "0927-6505",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.1702;
http://www.sciencedirect.com/science/article/pii/S0927650510000447",
abstract = "The occurrence of digits one through nine as the
leftmost nonzero digit of numbers from real world
sources is often not uniformly distributed, but
instead, is distributed according to a logarithmic law,
known as Benford's Law. Here, we investigate
systematically the mantissa distributions of some
pulsar quantities, and find that for most quantities
their first digits conform to this law. However, the
barycentric period shows significant deviation from the
usual distribution, but satisfies a generalized
Benford's Law roughly. Therefore pulsars can serve as
an ideal assemblage to study the first digit
distributions of real world data, and the observations
can be used to constrain theoretical models of pulsar
behavior.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.1702",
fjournal = "Astroparticle Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/09276505",
keywords = "Benford's Law; First digit law; Mantissa distribution;
Pulsar",
primaryclass = "astro-ph.IM",
}
@Article{Shao:2010:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First Digit Distribution of Hadron Full Width",
journal = "ArXiv e-prints",
day = "19",
month = apr,
year = "2010",
bibdate = "Mon Nov 21 07:21:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1004.3077",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e., $ 1, 2,
\ldots {}, 9 $, of numbers from many real world sources
is not uniformly distributed, but instead favors
smaller ones according to a logarithmic distribution.
We investigate, for the first time, the first digit
distribution of the full widths of mesons and baryons
in the well defined science domain of particle physics
systematically, and find that they agree excellently
with the Benford distribution. We also discuss several
general properties of Benford's law, i.e., the law is
scale-invariant, base-invariant, and power-invariant.
This means that the lifetimes of hadrons follow also
Benford's law.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Shao:2010:FDLa,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First-Digit Law in Nonextensive Statistics",
journal = "ArXiv e-prints",
year = "2010",
bibdate = "Mon Nov 21 07:09:52 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1010.2699",
abstract = "Nonextensive statistics, characterized by a
nonextensive parameter $q$, is a promising and
practically useful generalization of the Boltzmann
statistics to describe power-law behaviors from
physical and social observations. We here explore the
unevenness of the first digit distribution of
nonextensive statistics analytically and numerically.
We find that the first-digit distribution follows
Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the
temperature. The fluctuation decreases when $q$
increases, and the result converges to Benford's law
exactly as $q$ approaches 2. The relevant regularities
between nonextensive statistics and Benford's law are
also presented and discussed.",
acknowledgement = ack-nhfb,
}
@Article{Shao:2010:FDLb,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First-digit law in nonextensive statistics",
journal = j-PHYS-REV-E,
volume = "82",
number = "4",
pages = "041110",
month = oct,
year = "2010",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.82.041110",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Mon Feb 18 18:11:37 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.041110;
http://pre.aps.org/abstract/PRE/v82/i4/e041110",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
}
@Article{Shao:2010:SDL,
author = "Lijing Shao and Bo-Qiang Ma",
title = "The significant digit law in statistical physics",
journal = j-PHYSICA-A,
volume = "389",
number = "16",
pages = "3109--3116",
month = may,
year = "2010",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2010.04.021",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82B03",
MRnumber = "2652860 (2011d:82007)",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.0660;
http://inspirehep.net/record/855898;
http://inspirehep.net/record/873155;
http://www.sciencedirect.com/science/article/pii/S0378437110003596",
abstract = "The occurrence of the nonzero leftmost digit, i.e., $
1, 2, \ldots {}, 9 $, of numbers from many real world
sources is not uniformly distributed as one might
naively expect, but instead, the nature favors smaller
ones according to a logarithmic distribution, named
Benford's Law. We investigate three kinds of widely
used physical statistics, i.e., the Boltzmann--Gibbs
(BG) distribution, the Fermi--Dirac (FD) distribution,
and the Bose--Einstein (BE) distribution, and find that
the BG and FD distributions both fluctuate slightly in
a periodic manner around Benford's distribution with
respect to the temperature of the system, while the BE
distribution conforms to it exactly whatever the
temperature is. Thus Benford's Law seems to present a
general pattern for physical statistics and might be
even more fundamental and profound in nature.
Furthermore, various elegant properties of Benford's
Law, especially the mantissa distribution of data sets,
are discussed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; First digit law; Mantissa distribution;
Statistical physics",
}
@Article{Shebaro:2010:LTC,
author = "Bilal Shebaro and Fernando Perez-Gonzalez and Jedidiah
R. Crandall",
title = "Leaving timing-channel fingerprints in hidden service
log files",
journal = "Digital Investigation",
volume = "7, Supplement",
number = "0",
pages = "S104--S113",
year = "2010",
DOI = "https://doi.org/10.1016/j.diin.2010.05.013",
ISSN = "1742-2876 (print), 1873-202X (electronic)",
ISSN-L = "1742-2876",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The Proceedings of the Tenth Annual {DFRWS}
Conference",
URL = "http://www.sciencedirect.com/science/article/pii/S174228761000040X",
abstract = "Hidden services are anonymously hosted services that
can be accessed over an anonymity network, such as Tor.
While most hidden services are legitimate, some host
illegal content. There has been a fair amount of
research on locating hidden services, but an open
problem is to develop a general method to prove that a
physical machine, once confiscated, was in fact the
machine that had been hosting the illegal content. In
this paper we assume that the hidden service logs
requests with some timestamp, and give experimental
results for leaving an identifiable fingerprint in this
log file as a timing channel that can be recovered from
the timestamps. In 60 min, we are able to leave a
36-bit fingerprint that can be reliably recovered. The
main challenges are the packet delays caused by the
anonymity network that requests are sent over and the
existing traffic in the log from the actual clients
accessing the service. We give data to characterize
these noise sources and then describe an implementation
of timing-channel fingerprinting for an Apache web
server based hidden service on the Tor network, where
the fingerprint is an additive channel that is
superencoded with a Reed Solomon code for reliable
recovery. Finally, we discuss the inherent tradeoffs
and possible approaches to making the fingerprint more
stealthy.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Fingerprints; Hidden services;
Timestamps; Timing channel; Tor network",
}
@InProceedings{Shengmin:2010:DSC,
author = "Z. Shengmin and W. Wenchao",
editor = "{IEEE}",
booktitle = "{2010 International Conference on Management and
Service Science (MASS), 24--26 Aug. 2010, Wuhan,
China}",
title = "Does [sic] {Chinese} Stock Indices Agree with
{Benford's Law}?",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--3",
year = "2010",
DOI = "https://doi.org/10.1109/ICMSS.2010.5575999",
ISBN = "1-4244-5325-9, 1-4244-5326-7",
ISBN-13 = "978-1-4244-5325-2, 978-1-4244-5326-9",
LCCN = "????",
bibdate = "Mon Feb 18 18:12:46 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Singleton:2010:FAF,
author = "Tommie Singleton and Aaron J. Singleton",
title = "Fraud auditing and forensic accounting",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Fourth",
pages = "xiv + 317",
year = "2010",
ISBN = "0-470-56413-X",
ISBN-13 = "978-0-470-56413-4",
LCCN = "HV8079.W47 B65 2010",
bibdate = "Tue Nov 22 10:31:33 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley corporate F and A",
URL = "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html",
abstract = "Completely revised and updated, Fraud Auditing and
Forensic Accounting, Fourth Edition reveals how to
develop an investigative eye toward both internal and
external fraud and provides crucial information on how
to deal with it when discovered. With new chapters on
the physiological aspects of the fraudster and on fraud
response, as well as new material on non-financial
aspects of fraud investigation, body language,
discourse analysis, and interviewing techniques, this
authoritative, timely book equips auditors,
investigators, corporate attorneys, and accountants to
identify the signs of financial fraud and successfully
investigate it",
acknowledgement = ack-nhfb,
remark = "Derived from third edition (2006). This book does not
discuss Benford's Law, but may be helpful background
for application of that law to the detection of
fraud.",
subject = "White collar crime investigation; United States;
Forensic accounting; Fraud investigation",
tableofcontents = "Background of Fraud Auditing and Forensic
Accounting \\
Fraud Principles \\
Fraud Schemes \\
Red Flags \\
Fraud Risk Assessment \\
Fraud Prevention \\
Fraud Detection \\
Fraud Response \\
Computer Crime \\
Fraud and the Accounting Information System \\
Gathering Evidence \\
Cyber Forensics \\
Obtaining and Evaluating Nonfinancial Evidence in a
Fraud Examination \\
General Criteria and Standards for Establishing an
Expert Witness's Qualifications \\
The Legal Role and Qualifications of an Expert Witness
\\
Effective Tactics and Procedures for the Expert Witness
in Court \\
Fraud and the Public Accounting Profession",
}
@Article{Stalcup:2010:BLH,
author = "Ken Stalcup",
title = "{Benford's Law}: How a Simple Misconception can Trip
up a Fraudster and How a Savvy {CFE} Can Spot It",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2010",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 07:57:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=203",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
}
@Article{Strzalka:2010:SPB,
author = "Dominik Strza{\l}ka",
title = "On some properties of {Benford}'s law",
journal = "Journal of the {Korean Mathematical Society}",
volume = "47",
number = "5",
pages = "1055--1075",
year = "2010",
CODEN = "JKMSDG",
DOI = "https://doi.org/10.4134/JKMS.2010.47.5.1055",
ISSN = "0304-9914",
ISSN-L = "0304-9914",
MRclass = "11A63",
MRnumber = "2723008",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "J. {Korean Math. Soc.}",
fjournal = "Journal of the {Korean Mathematical Society}",
}
@Article{Sudhier:2010:BLS,
author = "K. G. Sudhier",
title = "{Bradford's law} of Scattering Revisited: A study
based on the References in Doctoral theses in the area
of Physics",
journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
volume = "4",
number = "2",
pages = "35--47",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1080/09737766.2010.10700891",
ISSN = "0973-7766 (print), 2168-930X (electronic)",
ISSN-L = "0973-7766",
bibdate = "Thu Sep 10 17:47:06 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
acknowledgement = ack-nhfb,
fjournal = "Collnet Journal of Scientometrics and Information
Management",
journal-URL = "http://www.tandfonline.com/loi/tsim20",
}
@Article{Suh:2010:CAB,
author = "Ikseon Suh and T. Christopher Headrick",
title = "A comparative analysis of the bootstrap versus
traditional statistical procedures applied to digital
analysis based on {Benford's Law}",
journal = "Journal of Forensic and Investigative Accounting",
volume = "2",
number = "2",
pages = "144--175",
month = jul # "\slash " # dec,
year = "2010",
CODEN = "????",
DOI = "????",
ISSN = "2165-3755",
bibdate = "Mon Feb 18 18:16:07 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epublications.marquette.edu/account_fac/31;
http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/FullText/2010v2n2a7.pdf;
http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/v2n2.htm",
acknowledgement = ack-nhfb,
journal-URL = "http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/articles.htm",
}
@Article{Szewczak:2010:LTR,
author = "Zbigniew S. Szewczak",
title = "A limit theorem for random sums modulo $1$",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "9--10",
pages = "747--751",
month = may,
year = "2010",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2010.01.005",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
abstract = "Residues of partial sums in a class of dependent
random variables, including functionals of uniformly
recurrent Markov chains, are in the domain of
attraction of the uniform distribution. These types of
limit theorems arise for example in the multiplication
of floating-point numbers.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law",
}
@Article{Uzer:2010:MTC,
author = "Ali Uzer",
title = "Multiplicative type complex calculus as an alternative
to the classical calculus",
journal = j-COMPUT-MATH-APPL,
volume = "60",
number = "10",
pages = "2725--2737",
month = nov,
year = "2010",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/j.camwa.2010.08.089",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Feb 14 05:56:39 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122110006747",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the paper: ``\ldots{} an important work of
Benford that was published 70 years ago implies many
physical quantities in the nature are of exponentially
varying type.''.",
}
@Misc{Wagon:2010:BLD,
author = "S. Wagon",
title = "{Benford's Law} and Data Spread",
year = "2010",
bibdate = "Sat Nov 12 16:59:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Web site.",
URL = "http://demonstrations.wolfram.com/BenfordsLawAndDataSpread",
acknowledgement = ack-nhfb,
}
@Article{Zhao:2010:IFU,
author = "Xi Zhao and Anthony Tung Shuen Ho and Yun Q. Shi",
title = "Image Forensics Using Generalised {Benford's Law} for
Improving Image Authentication Detection Rates in
Semi-Fragile Watermarking",
journal = "International Journal of Digital Crime and Forensics",
volume = "2",
number = "2",
pages = "1--20",
month = "????",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.4018/jdcf.2010040101",
ISSN = "1941-6210 (print), 1941-6229 (electronic)",
ISSN-L = "1941-6210",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/ijdcf/ijdcf2.html#ZhaoHS10",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Digit. Crime Forensics",
dblp-key = "journals/ijdcf/ZhaoHS10",
dblp-mdate = "2020-08-12",
fjournal = "International Journal of Digital Crime and Forensics",
journal-URL = "https://www.igi-global.com/gateway/journal/1112",
}
@Article{Abrantes-Metz:2011:TLR,
author = "R. M. Abrantes-Metz and S. B. Villas-Boas and G.
Judge",
title = "Tracking the {Libor} rate",
journal = j-APPL-ECON-LETT,
volume = "18",
number = "10",
pages = "893--899",
month = "????",
year = "2011",
DOI = "https://doi.org/10.1080/13504851.2010.515197",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Mon Feb 18 18:17:20 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
journal-URL = "http://www.tandfonline.com/loi/rael20",
keywords = "Benford's Second-Digit Law",
remark = "From the abstract: ``Libor rates depart significantly
from the expected Benford reference distribution. This
raises potential concerns relative to the unbiased
nature of the signals coming from the 16 banks from
which the Libor is computed and the usefulness of the
Libor as a major economic indicator.''",
}
@Article{Adamic:2011:CSU,
author = "Lada Adamic",
title = "Complex systems: Unzipping {Zipf}'s law",
journal = j-NATURE,
volume = "474",
number = "7350",
pages = "164--165",
day = "8",
month = jun,
year = "2011",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/474164a",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Nov 15 09:29:15 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
onlinedate = "09 June 2011",
}
@Article{Altamirano:2011:PTS,
author = "C. Altamirano and A. Robledo",
title = "Possible thermodynamic structure underlying the laws
of {Zipf} and {Benford}",
journal = j-EUR-PHYS-J-B,
volume = "81",
number = "3",
pages = "345--351",
month = jun,
year = "2011",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1140/epjb/e2011-10968-5",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Mon Nov 14 17:53:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011EPJB...81..345A",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1008.1614",
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
primaryclass = "cond-mat.stat-mech",
}
@Article{Anderson:2011:BLC,
author = "Theresa C. Anderson and Larry Rolen and Ruth Stoehr",
title = "{Benford}'s law for coefficients of modular forms and
partition functions",
journal = j-PROC-AM-MATH-SOC,
volume = "139",
number = "5",
pages = "1533--1541",
year = "2011",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-2010-10577-4",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "11F12 (11F20 11P83)",
MRnumber = "2763743",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Andrew:2011:OBM,
author = "Alex M. Andrew",
title = "Obituary: {Beno{\^\i}t Mandelbrot: 20 November
1924--14 October 2010}",
journal = "Kybernetes",
volume = "40",
number = "1--2",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "KBNTA3",
ISSN = "0368-492X (print), 1758-7883 (electronic)",
ISSN-L = "0368-492X",
bibdate = "Fri Nov 25 07:32:54 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://en.wikipedia.org/wiki/ernst_von_glasersfeld;
http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf;
http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825;
http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary;
http://www.math.yale.edu/mandelbrot/;
http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2011:BLH,
author = "Anonymous",
title = "{Benford's Law} --- How mathematics can detect
fraud!",
howpublished = "Web video lecture (10m47s).",
day = "9",
month = apr,
year = "2011",
bibdate = "Fri Oct 09 06:40:54 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.youtube.com/watch?v=vIsDjbhbADY",
acknowledgement = ack-nhfb,
xxauthor = "Brady Haran",
}
@Article{Archambault:2011:EMA,
author = "J. Archambault and M. Archambault",
title = "Earnings management among firms during the pre-{SEC}
era: a {Benford}'s law analysis",
journal = j-ACCOUNT-HIST-J,
volume = "38",
number = "2",
pages = "145--170",
month = "????",
year = "2011",
ISSN = "0148-4184",
ISSN-L = "0148-4184",
bibdate = "Mon Feb 18 11:32:23 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Accounting Historians Journal",
journal-URL = "http://www.jstor.org/action/showPublication?journalCode=accohistjour;
http://www.aahhq.org/",
remark = "JSTOR has a 3-year moving wall, so this article is not
yet in that archive; the publisher's Web site is poor,
and I cannot find the article there.",
}
@Article{Baek:2011:ZLU,
author = "Seung Ki Baek and Sebastian Bernhardsson and Petter
Minnhagen",
title = "{Zipf}'s law unzipped",
journal = j-NEW-J-PHYS,
volume = "13",
number = "4",
pages = "043004",
month = "????",
year = "2011",
CODEN = "NJOPFM",
DOI = "https://doi.org/10.1088/1367-2630/13/4/043004",
ISSN = "1367-2630",
ISSN-L = "1367-2630",
bibdate = "Tue Nov 15 09:32:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://iopscience.iop.org/1367-2630/13/4/043004",
abstract = "Why does Zipf's law give a good description of data
from seemingly completely unrelated phenomena? Here it
is argued that the reason is that they can all be
described as outcomes of a ubiquitous random group
division: the elements can be citizens of a country and
the groups family names, or the elements can be all the
words making up a novel and the groups the unique
words, or the elements could be inhabitants and the
groups the cities in a country and so on. A random
group formation (RGF) is presented from which a
Bayesian estimate is obtained based on minimal
information: it provides the best prediction for the
number of groups with $k$ elements, given the total
number of elements, groups and the number of elements
in the largest group. For each specification of these
three values, the RGF predicts a unique group
distribution $ N(k) \propto \exp ( - b k) / k^\gamma $,
where the power-law index $ \gamma $ is a unique
function of the same three values. The universality of
the result is made possible by the fact that no
system-specific assumptions are made about the
mechanism responsible for the group division. The
direct relation between $ \gamma $ and the total number
of elements, groups and the number of elements in the
largest group is calculated. The predictive power of
the RGF model is demonstrated by direct comparison with
data from a variety of systems. It is shown that $
\gamma $ usually takes values in the interval $ 1 \leq
\gamma \leq 2 $ and that the value for a given
phenomenon depends in a systematic way on the total
size of the dataset. The results are put in the context
of earlier discussions on Zipf's and Gibrat's laws, $
N(k) \propto k^{-2} $ and the connection between growth
models and RGF is elucidated.",
acknowledgement = ack-nhfb,
fjournal = "New Journal of Physics",
journal-URL = "http://iopscience.iop.org/1367-2630",
pagecount = "21",
}
@Misc{Barnes:2011:LCS,
author = "K. Barnes",
title = "Letter to {China Shen Zhou Mining and Resources (AMEX:
SHZ)} current shareholders and potential investors from
{Absaroka Capital}",
howpublished = "Absaroka Capital Management, LLP, Wyoming, USA.",
year = "2011",
bibdate = "Fri Mar 22 08:42:58 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Barrale:2011:SID,
author = "Tom Barrale and R. Hendel and Michael Sluys",
booktitle = "{Proceedings of the 14th international conference on
Fibonacci numbers and their applications, Morelia,
Mexico, July 5--9, 2010}",
title = "Sequences of the initial digits of {Fibonacci}
numbers",
publisher = "Sociedad Matem\'atica Mexicana",
address = "M{\'e}xico, DF, M{\'e}xico",
pages = "25--42",
year = "2011",
ISBN = "607-02-2543-0 (paperback)",
ISBN-13 = "978-607-02-2543-7 (paperback)",
MRnumber = "11B37 11B39",
bibdate = "Sat Sep 10 10:27:11 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "1287.11017",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Fibonacci numbers",
}
@Article{Bauer:2011:DDF,
author = "Johannes Bauer and Jochen Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford?s
Law} on Regression Tables",
journal = "Journal of Economics and Statistics (Jahrb{\"u}cher
f{\"u}r National{\"o}konomie und Statistik)",
volume = "231",
number = "5--6",
pages = "733--748",
month = nov,
year = "2011",
DOI = "????",
bibdate = "Mon Feb 18 18:18:45 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html",
acknowledgement = ack-nhfb,
journal-URL = "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/",
}
@Article{Bawden:2011:BMS,
author = "David Bawden",
title = "{Beno{\^\i}t Mandelbrot} and the self-similarity of
information",
journal = j-J-DOC,
volume = "67",
number = "2",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "JDOCAS",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:40:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
journal-URL = "http://www.emeraldinsight.com/loi/jd",
}
@Article{Becker:2011:BLC,
author = "T. Becker and A. Greaves-Tunnell and Steven J. Miller
and R. Ronan and F. W. Strauch",
title = "{Benford's Law} and Continuous Dependent Random
Variables",
journal = "ArXiv e-prints",
month = nov,
year = "2011",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 17:50:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B;
http://arxiv.org/abs/1111.0568",
abstract = "Many systems exhibit a digit bias. For example, the
first digit base 10 of the Fibonacci numbers, or of $
2^n $, equals 1 not 10\% or 11\% of the time, as one
would expect if all digits were equally likely, but
about 30\% of the time. This phenomenon, known as
Benford's Law, has many applications, ranging from
detecting tax fraud for the IRS to analyzing round-off
errors in computer science.\par
The central question is determining which data sets
follow Benford's law. Inspired by natural processes
such as particle decay, our work examines models for
the decomposition of conserved quantities. We prove
that in many instances the distribution of lengths of
the resulting pieces converges to Benford behavior as
the number of divisions grow. The main difficulty is
that the resulting random variables are dependent,
which we handle by a careful analysis of the
dependencies and tools from Fourier analysis to obtain
quantified convergence rates.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1111.0568",
keywords = "Mathematics - Probability, 11K06, 60A10 (primary),
60E10 (secondary)",
primaryclass = "math.PR",
}
@Article{Berger:2011:BLS,
author = "Arno Berger and Theodore P. Hill",
title = "{Benford}'s law strikes back: no simple explanation in
sight for mathematical gem",
journal = j-MATH-INTEL,
volume = "33",
number = "1",
pages = "85--91",
month = mar,
year = "2011",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/s00283-010-9182-3",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "62A99 (60E05)",
MRnumber = "2774458",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See letter \cite{Hill:2011:LEB}.",
URL = "http://link.springer.com/article/10.1007/s00283-010-9182-3",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
}
@Article{Berger:2011:BTB,
author = "Arno Berger and Theodore P. Hill",
title = "A basic theory of {Benford's Law}",
journal = j-PROBAB-SURV,
volume = "8",
number = "??",
pages = "1--126",
month = "????",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/11-PS175",
ISSN = "1549-5787",
ISSN-L = "1549-5787",
MRclass = "37A45 (11K06 60-02 60F15 60G57 62E10)",
MRnumber = "2846899 (2012h:37015)",
MRreviewer = "Steven Joel Miller",
bibdate = "Tue Nov 15 11:07:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/probabsurv.bib",
URL = "http://projecteuclid.org/euclid.ps/1311860830",
abstract = "Drawing from a large, diverse body of work, this
survey presents a comprehensive and unified
introduction to the mathematics underlying the
prevalent logarithmic distribution of significant
digits and significands, often referred to as {\em
Benford's Law\/} (BL) or, in a special case, as the
{\em First Digit Law}. The invariance properties that
characterize BL are developed in detail. Special
attention is given to the emergence of BL in a wide
variety of deterministic and random processes. Though
mainly expository in nature, the article also provides
strengthened versions of, and simplified proofs for,
many key results in the literature. Numerous intriguing
problems for future research arise naturally.",
acknowledgement = ack-nhfb,
fjournal = "Probability Surveys",
journal-URL = "http://projecteuclid.org/all/euclid.ps",
keywords = "base-invariance; Benford's Law; difference equation;
mixture of distributions; random probability measure;
scale-invariance; shadowing; significant digits;
sum-invariance; uniform distribution mod 1",
}
@Article{Berger:2011:FSM,
author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and
Ad Ridder",
title = "Finite-state {Markov} Chains Obey {Benford's Law}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "32",
number = "3",
pages = "665--684",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/100789890",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15B51 (11J71 60J22 65C40)",
MRnumber = "2825319 (2012h:15058)",
MRreviewer = "E. Seneta",
bibdate = "Wed Aug 24 11:18:18 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1;
https://dblp.org/db/journals/siammax/siammax32.html#BergerHKR11",
acknowledgement = ack-nhfb,
dblp-key = "journals/siammax/BergerHKR11",
dblp-mdate = "2020-05-26",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "July 21, 2011",
}
@Article{Berger:2011:SDP,
author = "Arno Berger",
title = "Some dynamical properties of {Benford} sequences",
journal = j-J-DIFFERENCE-EQU-APPL,
volume = "17",
number = "2",
pages = "137--159",
year = "2011",
CODEN = "JDEAEA",
DOI = "https://doi.org/10.1080/10236198.2010.549012",
ISSN = "1023-6198 (print), 1563-5120 (electronic)",
ISSN-L = "1023-6198",
MRclass = "37A45 (11K06 37Bxx)",
MRnumber = "2783341",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012",
acknowledgement = ack-nhfb,
ajournal = "J. Difference Equ. Appl.",
fjournal = "Journal of Difference Equations and Applications",
journal-URL = "http://www.informaworld.com/1023-6198",
}
@Article{Bernhardsson:2011:PPM,
author = "Sebastian Bernhardsson and Seung Ki Baek and Petter
Minnhagen",
title = "A paradoxical property of the monkey book",
journal = j-J-STAT-MECH-THEORY-EXP,
volume = "2011",
number = "??",
pages = "P07013",
month = jul,
year = "2011",
CODEN = "JSMTC6",
DOI = "https://doi.org/10.1088/1742-5468/2011/07/P07013",
ISSN = "1742-5468",
ISSN-L = "1742-5468",
bibdate = "Mon Nov 21 21:57:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1103.2681;
http://iopscience.iop.org/1742-5468/2011/07/P07013/",
abstract = "A `monkey book' is a book consisting of a random
sequence of letters and blanks, where a group of
letters surrounded by two blanks is defined as a word.
We compare the statistics of the word distribution for
a monkey book to real books. It is shown that the word
distribution statistics for the monkey book is
different and quite distinct from a typical real book.
In particular, the monkey book obeys Heaps' power law
to an extraordinarily good approximation, in contrast
to the word distributions for real books, which deviate
from Heaps' law in a characteristic way. This
discrepancy is traced to the different properties of a
`spiked' distribution and its smooth envelope. The
somewhat counter-intuitive conclusion is that a `monkey
book' obeys Heaps' power law precisely because its
word-frequency distribution is not a smooth power law,
contrary to the expectation based on simple
mathematical arguments that if one is a power law, so
is the other.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Mechanics: Theory and
Experiment",
journal-URL = "http://iopscience.iop.org/1742-5468/",
keywords = "Heaps' Law",
}
@Article{Bhattacharya:2011:ABA,
author = "Sukanto Bhattacharya and Dongming Xu and Kuldeep
Kumar",
title = "An {ANN}-based auditor decision support system using
{Benford}'s law",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "3",
pages = "576--584",
month = feb,
year = "2011",
CODEN = "DSSYDK",
DOI = "https://doi.org/10.1016/j.dss.2010.08.011",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "On quantitative methods for detection of financial
fraud",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001351",
abstract = "While there is a growing professional interest on the
application of Benford's law and digit analysis in
financial fraud detection, there has been relatively
little academic research to demonstrate its efficacy as
a decision support tool in the context of an analytical
review procedure pertaining to a financial audit. We
conduct a numerical study using a genetically optimized
artificial neural network. Building on an earlier work
by others of a similar nature, we assess the benefits
of Benford's law as a useful classifier in segregating
naturally occurring (i.e. non-concocted) numbers from
those that are made up. Alongside the frequency of the
first and second significant digits and their mean and
standard deviation, a posited set of non-digit input
variables categorized as information theoretic,
distance-based and goodness-of-fit measures, help to
minimize the critical classification errors that can
lead to an audit failure. We come up with the optimal
network structure for every instance corresponding to a
$ 3 \times 3 $ Manipulation Involvement matrix that is
drawn to depict the different combinations of the level
of sophistication in data manipulation by the
perpetrators of a financial fraud and also the extent
of collusive involvement.",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "ANNs; ARPs; Auditor decision support system; Benford's
law; Benford's Law; Benford's law; Benford's Law;
Genetic optimization; {ANNs}; {ARPs}",
}
@Article{Bose:2011:QMD,
author = "Indranil Bose and Selwyn Piramuthu and Michael J.
Shaw",
title = "Quantitative methods for Detection of Financial
Fraud",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "3",
pages = "557--558",
month = feb,
year = "2011",
CODEN = "DSSYDK",
DOI = "https://doi.org/10.1016/j.dss.2010.08.005",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "On quantitative methods for detection of financial
fraud",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001296",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law",
}
@InCollection{Brahler:2011:BGS,
author = "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph
Jakobi",
editor = "????",
booktitle = "Ilmenauer Schriften zur Betriebswirtschaftslehre",
title = "{Das Benfordsche Gesetz und seine Anwendbarkeit bei
der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}.
({German}) [{The} {Benford} law and its applicability
in the digital examination of logbooks]",
volume = "3/2011",
publisher = "Verlag proWiWi e.V.",
address = "Ilmenau, Germany",
pages = "??--??",
month = mar,
year = "2011",
ISBN = "3-940882-28-3",
ISBN-13 = "978-3-940882-28-8",
ISSN = "1866-2145 (print), 2192-4643 (electronic)",
LCCN = "????",
bibdate = "Mon Feb 18 18:21:29 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Breunig:2011:SEI,
author = "Christian Breunig and Achim Goerres",
title = "Searching for electoral irregularities in an
established democracy: Applying {Benford's Law} tests
to {Bundestag} elections in {Unified Germany}",
journal = j-ELECT-STUDIES,
volume = "30",
number = "3",
pages = "534--545",
month = sep,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.electstud.2011.03.005",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "Special Symposium on the Politics of Economic Crisis",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379411000370",
abstract = "This article investigates electoral irregularities in
the 1990 to 2005 Bundestag elections of unified
Germany. Drawing on the Second Digit Benford Law (2BL)
by Mebane (2006), the analysis consists of comparing
the observed frequencies of numerals of candidate votes
and party votes at the precinct level against the
expected frequencies according to Benford's Law. Four
central findings stand out. First, there is no evidence
for systematic fraud or mismanagement with regard to
candidate votes from districts where fraud would be
most instrumental. Second, at the state level
(Bundesland), there are 51 violations in 190 tests of
the party list votes. Third, East German states are not
more prone to violations than Western ones. This
finding refutes the notion that the East's more recent
transition to democracy poses problems in electoral
management. Fourth, a strong variation in patterns of
violation across Bundesl{\"a}nder exists: states with
dominant party control are more likely to display
irregularities. The article concludes by hypothesizing
and exploring the notion that partisan composition of
nominees involved in the counting may produce a higher
likelihood of violation and be a cause of L{\"a}nder
variation. This may especially be the case when a party
dominates in a Bundesland or opponents to the former
socialist regime party are involved in the counting.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Benford's Law; Bundestag; Fraud; Germany",
}
@TechReport{Bul:2011:BGG,
author = "K. Bul",
title = "{Das Benford'sche Gesetz}. ({German}) [{Benford's
Law}]",
type = "Working paper",
institution = "Max-von-Laue-gymnasium",
address = "Koblenz, Germany",
year = "2011",
bibdate = "Fri Mar 22 08:44:32 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
language = "German",
}
@Article{Campanario:2011:BLC,
author = "Juan Campanario and Mar{\'\i}a Coslado",
title = "{Benford}'s law and citations, articles and impact
factors of scientific journals",
journal = j-SCIENTOMETRICS,
volume = "88",
number = "2",
pages = "421--432",
month = aug,
year = "2011",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-011-0387-9",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Fri Nov 25 10:43:36 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11192-011-0387-9",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Cantu:2011:FDA,
author = "F. Cantu and S. M. Saiegh",
title = "Fraudulent Democracy? {An} Analysis of {Argentina}'s
Infamous Decade Using Supervised Machine Learning",
journal = j-POLIT-ANAL,
volume = "19",
number = "4",
pages = "409--433",
month = "Autumn",
year = "2011",
DOI = "https://doi.org/10.1093/pan/mpr033",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Mon Feb 18 18:24:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pan.oxfordjournals.org/content/19/4/409.abstract",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
keywords = "Benford's Law",
}
@Article{Chang:2011:CGR,
author = "Harry M. Chang",
title = "Constructing $n$-gram rules for natural language
models through exploring the limitation of the
{Zipf--Mandelbrot} law",
journal = j-COMPUTING,
volume = "91",
number = "3",
pages = "241--264",
month = mar,
year = "2011",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-010-0116-x",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68T50",
MRnumber = "2776088",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
acknowledgement = ack-nhfb,
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Chida:2011:LSI,
author = "Satoshi Chida and Naoto Miyoshi",
title = "Limiting size index distributions for ball-bin models
with {Zipf}-type frequencies",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "63",
number = "4",
pages = "745--768",
year = "2011",
CODEN = "AISXAD",
DOI = "https://doi.org/10.1007/s10463-010-0276-7",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
MRclass = "60C05 (60F15 60J27)",
MRnumber = "2805906 (2012f:60035)",
MRreviewer = "Elvira Di Nardo",
bibdate = "Mon Feb 18 16:48:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of the Institute of Statistical Mathematics
(Tokyo)",
journal-URL = "http://link.springer.com/journal/10463",
}
@Article{Corominas-Murtra:2011:EZL,
author = "Bernat Corominas-Murtra and Jordi Fortuny and Ricard
V. Sol{\'e}",
title = "Emergence of {Zipf}'s law in the evolution of
communication",
journal = j-PHYS-REV-E,
volume = "83",
number = "1",
pages = "036115",
day = "28",
month = mar,
year = "2011",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.83.036115",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036115",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "9",
}
@Article{Deckert:2011:BLD,
author = "Joseph Deckert and Mikhail Myagkov and Peter C.
Ordeshook",
title = "{Benford's Law} and the Detection of Election Fraud",
journal = j-POLIT-ANAL,
volume = "19",
number = "3",
pages = "245--268",
month = "Summer",
year = "2011",
DOI = "https://doi.org/10.1093/pan/mpr014",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Mon Feb 18 18:26:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mebane:2011:CBL} for a rebuttal.",
URL = "http://pan.oxfordjournals.org/content/19/3/245.abstract",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
remark = "The authors argue that application of Benford's Law
tests to election results to detect fraud is
inconclusive and ``essentially equivalent to a toss of
a coin''.",
}
@Article{Dixit:2011:EEP,
author = "U. J. Dixit and M. Jabbari Nooghabi",
title = "Efficient estimation in the {Pareto} distribution with
the presence of outliers",
journal = j-STAT-METHODOL,
volume = "8",
number = "4",
pages = "340--355",
month = jul,
year = "2011",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:47 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312711000141",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Article{Doyle:2011:ITA,
author = "Laurance R. Doyle and Brenda McCowan and Simon
Johnston and Sean F. Hanser",
title = "Information theory, animal communication, and the
search for extraterrestrial intelligence",
journal = j-ACTA-ASTRONAUT,
volume = "68",
number = "3--4",
pages = "406--417",
month = feb # "\slash " # mar,
year = "2011",
CODEN = "AASTCF",
DOI = "https://doi.org/10.1016/j.actaastro.2009.11.018",
ISSN = "0094-5765 (print), 1879-2030 (electronic)",
ISSN-L = "0094-5765",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "{SETI} Special Edition",
URL = "http://www.sciencedirect.com/science/article/pii/S0094576509005682",
abstract = "We present ongoing research in the application of
information theory to animal communication systems with
the goal of developing additional detectors and
estimators for possible extraterrestrial intelligent
signals. Regardless of the species, for intelligence
(i.e., complex knowledge) to be transmitted certain
rules of information theory must still be obeyed. We
demonstrate some preliminary results of applying
information theory to socially complex marine mammal
species (bottlenose dolphins and humpback whales) as
well as arboreal squirrel monkeys, because they almost
exclusively rely on vocal signals for their
communications, producing signals which can be readily
characterized by signal analysis. Metrics such as
Zipf's Law and higher-order information-entropic
structure are emerging as indicators of the
communicative complexity characteristic of an
intelligent message content within these animals
signals, perhaps not surprising given these species
social complexity. In addition to human languages, for
comparison we also apply these metrics to pulsar
signals perhaps (arguably) the most organized of
stellar systems as an example of astrophysical systems
that would have to be distinguished from an
extraterrestrial intelligence message by such
information theoretic filters. We also look at a
message transmitted from Earth (Arecibo Observatory)
that contains a lot of meaning but little information
in the mathematical sense we define it here. We
conclude that the study of non-human communication
systems on our own planet can make a valuable
contribution to the detection of extraterrestrial
intelligence by providing quantitative general measures
of communicative complexity. Studying the complex
communication systems of other intelligent species on
our own planet may also be one of the best ways to
deprovincialize our thinking about extraterrestrial
communication systems in general.",
acknowledgement = ack-nhfb,
fjournal = "Acta Astronautica",
keywords = "Animal communication; Benford's Law; Information
theory; Zipf's Law; {SETI}",
}
@Article{Edwards:2011:LFP,
author = "Roderick Edwards and Laura Collins",
title = "Lexical Frequency Profiles and {Zipf's Law}",
journal = "Language Learning",
volume = "61",
number = "1",
pages = "1--30",
year = "2011",
DOI = "https://doi.org/10.1111/j.1467-9922.2010.00616.x",
ISSN = "0023-8333 (print), 1467-9922 (electronic)",
ISSN-L = "0023-8333",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "L2 vocabulary learning; L2 vocabulary size; modeling
vocabulary learning; Zipf's law",
}
@Article{Egghe:2011:BLS,
author = "Leo Egghe",
title = "{Benford}'s law is a simple consequence of {Zipf}'s
law",
journal = "ISSI Newsletter",
volume = "7",
number = "3",
pages = "55--56",
month = sep,
year = "2011",
DOI = "????",
bibdate = "Mon Feb 18 18:27:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.issi-society.info/archives/newsletter27.pdf",
abstract = "We show that benford's law (describing the logarithmic
distribution of the numbers 1, 2, \ldots{}, 9 as first
digits of data in decimal form) can be deduced from the
classical law of zipf. this explains Bensford's law as
a scientometric or informetric law.",
acknowledgement = ack-nhfb,
}
@TechReport{Eliahou:2011:MDP,
author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique
Schneider",
title = "On the mantissa distribution of powers of natural and
prime numbers",
type = "Preprint",
institution = "Universit{\'e} du Littoral C{\^o}te d'Opale",
address = "Nord-Pas-de-Calais, France",
pages = "14",
day = "15",
month = nov,
year = "2011",
bibdate = "Mon Feb 18 18:27:51 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale;
http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf",
acknowledgement = ack-nhfb,
}
@Article{Eliazar:2011:LLZ,
author = "Iddo Eliazar",
title = "Limit laws for {Zipf}'s law",
journal = j-J-PHYS-A,
volume = "44",
number = "2",
pages = "022001",
year = "2011",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/1751-8113/44/2/022001",
ISSN = "1751-8113 (print), 1751-8121 (electronic)",
ISSN-L = "0305-4470",
MRclass = "62G30 (91D20)",
MRnumber = "2749082 (2011i:62083)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
ZMnumber = "Zbl 1204.62196",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics. A. Mathematical and Theoretical",
journal-URL = "http://iopscience.iop.org/0305-4470",
pagecount = "6",
}
@Misc{Farbaniec:2011:AFD,
author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
title = "Application of the first digit law in credibility
evaluation of the financial accounting data based on
particular cases",
howpublished = "Lecture slides for 10th International Congress on
Internal Control, Internal Audit, Fraud and
Anti-Corruption Issues, Krak{\'o}w, September 14--16,
2011.",
pages = "27",
year = "2011",
bibdate = "Thu Dec 01 21:27:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://benford.pl/documents/benford_pikw.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Farbaniec:2011:UBL,
author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
editor = "????",
booktitle = "10th International Congress on Internal Control,
Internal Audit, Fraud and Anti-Corruption Issues,
Krak{\'o}w, September 14--16, 2011",
title = "Using {Benford}'s law to detect irregularities in the
collection of data",
publisher = "????",
address = "????",
pages = "??--??",
year = "2011",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Dec 01 21:32:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Garcia:2011:FPA,
author = "Juan Manuel Garcia Garcia",
title = "A fixed-point algorithm to estimate the {Yule-Simon}
distribution parameter",
journal = j-APPL-MATH-COMP,
volume = "217",
number = "21",
pages = "8560--8566",
day = "1",
month = jul,
year = "2011",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2011.03.092",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 25 12:05:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300311004607",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@InCollection{Gauvrit:2011:SRI,
author = "N. Gauvrit and J-P. Delahaye",
title = "Scatter and Regularity Implies {Benford's Law}\ldots{}
and More",
crossref = "Zenil:2011:RTC",
pages = "53--69",
year = "2011",
bibdate = "Mon Feb 18 18:29:00 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Giuliano:2011:WCS,
author = "Rita Giuliano",
title = "Weak convergence of sequences from fractional parts of
random variables and applications",
journal = j-THEORY-PROBAB-MATH-STAT,
volume = "83",
number = "??",
pages = "49--58",
month = "????",
year = "2011",
CODEN = "TPMSCO",
DOI = "????",
ISSN = "0094-9000 (print), 1547-7363 (electronic)",
ISSN-L = "0094-9000",
MRclass = "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)",
MRnumber = "http://www.ams.org/mathscinet-getitem?mr=2768848",
bibdate = "Mon Feb 18 17:47:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and Mathematical Statistics",
journal-URL = "http://www.ams.org/publications/journals/journalsframework/tpms",
keywords = "Benford's Law",
}
@Book{Henriques:2011:WLB,
author = "Diana B. Henriques",
title = "The wizard of lies: {Bernie Madoff} and the death of
trust",
publisher = "Times Books/Henry Holt",
address = "New York, NY, USA",
pages = "xxiv + 419",
year = "2011",
ISBN = "0-8050-9134-3",
ISBN-13 = "978-0-8050-9134-2",
LCCN = "HV6692.M33 H46 2011",
bibdate = "Fri Mar 22 08:51:50 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Madoff, Bernard L; Swindlers and swindling; United
States; Biography; Ponzi schemes; Commercial crimes",
tableofcontents = "An earthquake on Wall Street \\
Becoming bernie \\
The hunger for yield \\
The big four \\
The cash spigot \\
What they wanted to believe \\
Warning signs \\
A near-death experience \\
Madoff's world \\
The year of living dangerously \\
Waking up in the rubble \\
Reckoning the damage \\
Net winners and net losers \\
The sins of the father \\
The wheels of justice \\
Hope, lost and found",
}
@Article{Hill:2011:LEB,
author = "Theodore P. Hill",
title = "Letter to the Editor: {Benford's Law} Blunders",
journal = j-AMER-STAT,
volume = "65",
number = "2",
pages = "141--141",
month = may,
year = "2011",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2011.10179",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Feb 18 18:34:43 2013",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
remark = "Brief comment on a error in Feller's derivation of
Benford's Law, with pointer to a corrected proof in
\cite{Berger:2011:BLS}.",
}
@Article{Hisano:2011:PVD,
author = "Ryohei Hisano and Didier Sornette and Takayuki
Mizuno",
title = "Predicted and verified deviations from {Zipf}'s law in
ecology of competing products",
journal = j-PHYS-REV-E,
volume = "84",
number = "2",
pages = "026117",
day = "24",
month = aug,
year = "2011",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.84.026117",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.84.026117",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Zipf's Law",
pagecount = "8",
}
@Article{Hui:2011:BLN,
author = "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min",
title = "{Benford's Law} in Nuclear Structure Physics",
journal = j-CHIN-PHYS-LETT,
volume = "28",
number = "3",
pages = "32101--32104",
month = mar,
year = "2011",
CODEN = "CPLEEU",
DOI = "https://doi.org/10.1088/0256-307X/28/3/032101",
ISSN = "0256-307X (print), 1741-3540 (electronic)",
ISSN-L = "0256-307X",
bibdate = "Fri Nov 25 10:37:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Chinese Physics Letters",
}
@Article{Janvresse:2011:AAU,
author = "{\'E}lise Janvresse and Thierry {De La Rue}",
title = "Averaging along Uniform Random Integers",
journal = "ArXiv e-prints",
year = "2011",
bibdate = "Mon Nov 21 07:06:41 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1103.1719",
abstract = "Motivated by giving a meaning to ``The probability
that a random integer has initial digit $d$'', we
define a URI-set as a random set $E$ of natural
integers such that each $ n > 0$ belongs to $E$ with
probability $ 1 / n$, independently of other integers.
This enables us to introduce two notions of densities
on natural numbers: The URI-density, obtained by
averaging along the elements of $E$, and the local
URI-density, which we get by considering the $k$-th
element of $E$ and letting $k$ go to infinity. We prove
that the elements of $E$ satisfy Benford's law, both in
the sense of URI-density and in the sense of local
URI-density. Moreover, if $ b_1 $ and $ b_2 $ are two
multiplicatively independent integers, then the
mantissae of a natural number in base $ b_1 $ and in
base $ b_2 $ are independent. Connections of
URI-density and local URI-density with other well-known
notions of densities are established: Both are stronger
than the natural density, and URI-density is equivalent
to log-density. We also give a stochastic
interpretation, in terms of URI-set, of the $ H_\infty
$-density.",
acknowledgement = ack-nhfb,
}
@Article{Jiang:2011:BLN,
author = "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao",
title = "{Benford}'s law in nuclear structure physics",
journal = j-CHIN-PHYS-LETT,
volume = "28",
number = "3",
pages = "032101",
month = "????",
year = "2011",
CODEN = "CPLEEU",
DOI = "https://doi.org/10.1088/0256-307X/28/3/032101",
ISSN = "0256-307X (print), 1741-3540 (electronic)",
ISSN-L = "0256-307X",
bibdate = "Mon Nov 14 16:16:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See also \cite{Ferreira:2015:LPA}.",
acknowledgement = ack-nhfb,
ajournal = "Chin. Phys. Lett.",
fjournal = "Chinese Physics Letters",
pagecount = "4",
}
@InProceedings{Kalinin:2011:UEF,
author = "K. Kalinin and Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{Proceedings of the 2011 Annual Meeting of the Midwest
Political Science Association, Chicago, IL, March
31--April 2, 2011}",
title = "Understanding Electoral Frauds through Evolution of
{Russian} Federalism: From ``Bargaining Loyalty'' to
``Signaling Loyalty''",
publisher = "????",
address = "????",
pages = "??--??",
year = "2011",
bibdate = "Sat Sep 10 12:37:47 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kim:2011:ZAS,
author = "SeongKi Kim and HaYoon Song and SangYong Han",
title = "{ZipfAllocation}: an algorithm for static allocation
of movies in a cluster of video servers",
journal = j-SPE,
volume = "41",
number = "6",
pages = "695--716",
month = may,
year = "2011",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.1027",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Tue Jun 21 17:09:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soft{\-}ware\emdash Prac{\-}tice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "25 Nov 2010",
}
@Misc{Li:2011:ZLB,
author = "Wentian Li",
title = "{Zipf's Law} bibliography",
howpublished = "Web site.",
month = aug,
year = "2011",
bibdate = "Fri Nov 25 08:58:21 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The site holds 870 references (in untagged
reference-list form) up to 11 August 2011.",
URL = "http://www.nslij-genetics.org/wli/zipf/",
acknowledgement = ack-nhfb,
lastaccess = "25 November 2011",
}
@Article{Liu:2011:BLC,
author = "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren",
title = "{Benford}'s law and cross-sections of {$ A(n, \alpha)
B $} reactions",
journal = j-EUR-PHYS-J-A,
volume = "47",
pages = "78",
month = jun,
year = "2011",
CODEN = "EPJAFV",
DOI = "https://doi.org/10.1140/epja/i2011-11078-3",
ISSN = "1434-6001 (print), 1434-601X (electronic)",
ISSN-L = "1434-6001",
bibdate = "Mon Nov 14 18:00:32 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011EPJA...47...78L",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal A: Hadrons and Nuclei",
journal-URL = "http://www.springerlink.com/content/1434-6001",
}
@InProceedings{Lyons:2011:NSF,
author = "M. Lyons and E. Carl-Ludwig Siegel",
booktitle = "APS March Meeting Abstracts",
title = "{NON-Shor} Factorization via {BEQS BEC}: {Watkins}
Number-Theory ``Pure''-Mathematics $ \cup $ with
Statistical-Physics: {Benford} Log-Law Inversion to
{ONLY} {BEQS} digit $ d = 0 $ {BEC}!!!",
publisher = "American Physical Society",
address = "????",
pages = "K1142",
month = mar,
year = "2011",
bibdate = "Mon Nov 14 18:08:39 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L",
acknowledgement = ack-nhfb,
}
@Article{Malevergne:2011:TPA,
author = "Yannick Malevergne and Vladilen Pisarenko and Didier
Sornette",
title = "Testing the {Pareto} against the lognormal
distributions with the uniformly most powerful unbiased
test applied to the distribution of cities",
journal = j-PHYS-REV-E,
volume = "83",
number = "3",
pages = "036111",
day = "22",
month = mar,
year = "2011",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.83.036111",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Feb 26 06:40:57 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036111",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
keywords = "Pareto distribution; Zipf's Law",
pagecount = "11",
}
@Article{Martinez-Rodriguez:2011:MUE,
author = "A. M. Mart{\'\i}nez-Rodr{\'\i}guez and A. J.
S{\'a}ez-Castillo and A. Conde-S{\'a}nchez",
title = "Modelling using an extended {Yule} distribution",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "55",
number = "1",
pages = "863--873",
day = "1",
month = jan,
year = "2011",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:03 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947310002872",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Masse:2011:SWD,
author = "Bruno Mass{\'e} and Dominique Schneider",
title = "A survey on weighted densities and their connection
with the first digit phenomenon",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "41",
number = "5",
pages = "1395--1415",
month = "????",
year = "2011",
CODEN = "RMJMAE",
DOI = "https://doi.org/10.1216/RMJ-2011-41-5-1395",
ISSN = "0035-7596 (print), 1945-3795 (electronic)",
ISSN-L = "0035-7596",
MRclass = "60B10 (11B05 11K99)",
MRnumber = "2838069 (2012k:60009)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Mon Feb 18 18:47:30 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf",
acknowledgement = ack-nhfb,
fjournal = "Rocky Mountain Journal of Mathematics",
journal-URL = "http://projecteuclid.org/euclid.rmjm",
keywords = "Benford's law; first digit phenomenon; hierarchy;
mantissa; weighted density",
}
@Book{McGrayne:2011:TWH,
author = "Sharon Bertsch McGrayne",
title = "The theory that would not die: how {Bayes}' rule
cracked the {Enigma} code, hunted down {Russian}
submarines, and emerged triumphant from two centuries
of controversy",
publisher = pub-YALE,
address = pub-YALE:adr,
pages = "xiii + 320",
year = "2011",
ISBN = "0-300-16969-8",
ISBN-13 = "978-0-300-16969-0",
LCCN = "QA279.5 .M415 2011",
bibdate = "Wed May 11 14:42:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Bayes' rule appears to be a straightforward, one-line
theorem: by updating our initial beliefs with objective
new information, we get a new and improved belief. To
its adherents, it is an elegant statement about
learning from experience. To its opponents, it is
subjectivity run amok. In the first-ever account of
Bayes' rule for general readers, Sharon Bertsch
McGrayne explores this controversial theorem and the
human obsessions surrounding it. She traces its
discovery by an amateur mathematician in the 1740s
through its development into roughly its modern form by
French scientist Pierre Simon Laplace. She reveals why
respected statisticians rendered it professionally
taboo for 150 years --- at the same time that
practitioners relied on it to solve crises involving
great uncertainty and scanty information, even breaking
Germany's Enigma code during World War II, and explains
how the advent of off-the-shelf computer technology in
the 1980s proved to be a game-changer. Today, Bayes'
rule is used everywhere from DNA de-coding to Homeland
Security. Drawing on primary source material and
interviews with statisticians and other scientists, The
Theory That Would Not Die is the riveting account of
how a seemingly simple theorem ignited one of the
greatest controversies of all time.",
acknowledgement = ack-nhfb,
remark = "This book has important comments on the battles among
Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
Pearson, supplementing the extensive discussion of
those conflicts in \cite{Ziliak:2008:CSS}.",
subject = "Bayesian statistical decision theory; history; science
/ history; mathematics / history and philosophy",
}
@Article{Mebane:2011:CBL,
author = "Walter R. {Mebane, Jr.}",
title = "Comment on {Benford's Law} and the Detection of
Election Fraud",
journal = j-POLIT-ANAL,
volume = "19",
number = "3",
pages = "269--272",
day = "18",
month = "Summer",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1093/pan/mpr024",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Fri Nov 25 11:00:46 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Deckert:2011:BLD}.",
URL = "http://pan.oxfordjournals.org/content/19/3/269.abstract",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
}
@Article{Michel:2011:QAC,
author = "Jean-Baptiste Michel and Yuan Kui Shen and Aviva
Presser Aiden and Adrian Veres and Matthew K. Gray and
{The Google Books Team} and Joseph P. Pickett and Dale
Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant
and Steven Pinker and Martin A. Nowak and Erez
Lieberman Aiden",
title = "Quantitative Analysis of Culture Using Millions of
Digitized Books",
journal = j-SCIENCE,
volume = "331",
number = "6014",
pages = "176--182",
day = "14",
month = jan,
year = "2011",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.1199644",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Fri Dec 09 11:06:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/331/6014/176.abstract",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "Zipf's law",
remark = "This papers reports results from a large study of
cultural phenomena, fame, and word usage from 4\% of
all books ever printed. Among the findings is this
quote from the first page: ``we estimated the number of
words in the English lexicon as 544,000 in 1900,
597,000 in 1950, and 1,022,000 in 2000. The lexicon is
enjoying a period of enormous growth: The addition of $
\approx 8500 $ words/year has increased the size of the
language by over 70\% during the past 50 years.'' From
page 177: ``Consistent with Zipf's famous law, a large
fraction of the words in our lexicon (63\%) were in
this lowest-frequency bin. As a result, we estimated
that 52\% of the English lexicon --- the majority of
the words used in English books --- consists of lexical
`dark matter' undocumented in standard references
(12).''",
}
@Article{Mir:2011:LLD,
author = "Tariq Ahmad Mir",
title = "Law of the leading digits and the ideological struggle
for numbers",
journal = "ArXiv e-prints",
pages = "11",
year = "2011",
bibdate = "Mon Nov 21 07:02:48 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1104.3948",
abstract = "Benford's law states that the occurrence of
significant digits in many data sets is not uniform but
tends to follow a logarithmic distribution such that
the smaller digits appear as first significant digits
more frequently than the larger ones. We investigate
here numerical data on the country-wise adherent
distribution of seven major world religions i.e.,
Christianity, Islam, Buddhism, Hinduism, Sikhism,
Judaism and Baha'ism to see if the proportion of the
leading digits occurring in the distribution conforms
to Benford's law. We find that the adherent data of all
the religions, except Christianity, excellently does
conform to Benford's law. Furthermore, unlike the
adherent data on Christianity, the significant digit
distribution of the three major Christian denominations
i.e. Catholicism, Protestantism and Orthodoxy obeys the
law. Thus in spite of their complexity general laws can
be established for the evolution of the religious
groups.",
acknowledgement = ack-nhfb,
}
@Article{Muller:2011:HAS,
author = "Hans Christian M{\"u}ller",
title = "How an arcane statistical law could have prevented the
{Greek} disaster",
journal = "Economics Intelligence",
volume = "??",
number = "??",
pages = "??",
day = "28",
month = jul,
year = "2011",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Nov 20 10:04:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/",
abstract = "If we had known what we know today, Greece would not
have been able to enter the Euro area. The
macroeconomic data the country reported to Eurostat in
Luxembourg were heavily tweaked. Unfortunately,
however, this only became clear years after it was too
late.",
acknowledgement = ack-nhfb,
}
@InCollection{Nigrini:2011:BLA,
author = "Mark J. Nigrini",
title = "{Benford's Law}: Assessing Conformity",
crossref = "Nigrini:2011:FAM",
pages = "109--129",
year = "2011",
DOI = "https://doi.org/10.1002/9781118386798.ch6",
bibdate = "Sat Feb 23 17:26:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Kolmogorov-Smirnoff tests; mantissa arc
test; mean absolute deviation; Z-statistic",
tableofcontents = "One Digit at a Time: The Z-statistic \\
The Chi-square and Kolmogorov--Smirnoff Tests \\
The Mean Absolute Deviation (MAD) Test \\
Tests Based on the Logarithmic Basis of Benford's Law
\\
Creating a Perfect Synthetic Benford Set \\
The Mantissa Arc Test \\
Summary",
}
@InCollection{Nigrini:2011:BLB,
author = "Mark J. Nigrini",
title = "{Benford's Law}: The Basics",
crossref = "Nigrini:2011:FAM",
pages = "85--108",
year = "2011",
DOI = "https://doi.org/10.1002/9781118386798.ch5",
bibdate = "Sat Feb 23 17:26:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
tableofcontents = "An Overview of Benford's Law \\
From Theory to Application in 60 Years \\
Which Data Sets should Conform to Benford's Law? \\
The Effect of Data Set Size \\
The Basic Digit Tests \\
Running the First-Two Digits Test in Access \\
Summary",
}
@InCollection{Nigrini:2011:BLN,
author = "Mark J. Nigrini",
title = "{Benford's Law}: The Number Duplication and Last-Two
Digits Tests",
crossref = "Nigrini:2011:FAM",
pages = "153--172",
year = "2011",
DOI = "https://doi.org/10.1002/9781118386798.ch8",
bibdate = "Sat Feb 23 17:26:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; COUNTIF formula; digits tests; last-two
digits tests; number duplication",
tableofcontents = "The Number Duplication Test \\
Running the Number Duplication Test in Access \\
Running the Number Duplication Test in Excel \\
The Last-Two Digits Test \\
Summary",
}
@InCollection{Nigrini:2011:BLS,
author = "Mark J. Nigrini",
title = "{Benford's Law}: The Second-Order and Summation
Tests",
crossref = "Nigrini:2011:FAM",
pages = "130--152",
year = "2011",
DOI = "https://doi.org/10.1002/9781118386798.ch7",
bibdate = "Sat Feb 23 17:26:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; digits tests; second-order;
second-order test; summation test",
tableofcontents = "A Description of the Second-Order Test \\
The Summation Test \\
Summary",
}
@Article{Osareh:2011:LLA,
author = "Farideh Osareh and Esmaeel Mostafavi",
title = "{Lotka's Law} and authorship distribution in Computer
Science using {Web of Science (WoS)} during
1986--2009",
journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
volume = "5",
number = "2",
pages = "171--183",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1080/09737766.2011.10700911",
ISSN = "0973-7766 (print), 2168-930X (electronic)",
ISSN-L = "0973-7766",
bibdate = "Thu Sep 10 17:47:07 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
acknowledgement = ack-nhfb,
fjournal = "Collnet Journal of Scientometrics and Information
Management",
journal-URL = "http://www.tandfonline.com/loi/tsim20",
}
@Article{Pericchi:2011:QAD,
author = "Luis Pericchi and David Torres",
title = "Quick anomaly detection by the {Newcomb--Benford} law,
with applications to electoral processes data from the
{USA}, {Puerto} {Rico} and {Venezuela}",
journal = j-STAT-SCI,
volume = "26",
number = "4",
pages = "502--516",
year = "2011",
CODEN = "STSCEP",
DOI = "https://doi.org/10.1214/09-STS296",
ISSN = "0883-4237 (print), 2168-8745 (electronic)",
ISSN-L = "0883-4237",
MRnumber = "2951385",
bibdate = "Thu Feb 14 07:02:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.ss/1330437932",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science. A Review Journal of the Institute
of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.ss",
}
@InProceedings{Qadir:2011:IFG,
author = "G. Qadir and X. Zhao and A. T. Ho and M. Casey",
booktitle = "2011 IEEE International Symposium of Circuits and
Systems (ISCAS)",
title = "Image forensic of glare feature for improving image
retrieval using {Benford's Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2661--2664",
month = may,
year = "2011",
DOI = "https://doi.org/10.1109/ISCAS.2011.5938152",
ISSN = "0271-4302",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benfords law; Brightness; computer forensics; discrete
wavelet high high sub bands; Discrete wavelet
transforms; Equations; Forensics; glare feature;
glare-based problems; Histograms; image analysis; image
forensic tool; image retrieval; light intensity
measurement; Mathematical model; probability;
Probability; probability intensity histogram; salient
features identification; visual examination",
}
@Article{Rauch:2011:FFE,
author = "Bernhard Rauch and Max G{\"o}ttsche and Gernot
Br{\"a}hler and Stefan Engel",
title = "Fact and Fiction in {EU}-Governmental Economic Data",
journal = j-GER-ECON-REV,
volume = "12",
number = "3",
pages = "243--255",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1111/j.1468-0475.2011.00542.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Sun Nov 20 09:58:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract",
abstract = "To detect manipulations or fraud in accounting data,
auditors have successfully used Benford's law as part
of their fraud detection processes. Benford's law
proposes a distribution for first digits of numbers in
naturally occurring data. Government accounting and
statistics are similar in nature to financial
accounting. In the European Union (EU), there is
pressure to comply with the Stability and Growth Pact
criteria. Therefore, like firms, governments might try
to make their economic situation seem better. In this
paper, we use a Benford test to investigate the quality
of macroeconomic data relevant to the deficit criteria
reported to Eurostat by the EU member states. We find
that the data reported by Greece shows the greatest
deviation from Benford's law among all euro states.",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
keywords = "auditing; Benford's law; fraud detection; government
statistics",
onlinedate = "28 April 2011",
}
@Article{Ravisankar:2011:DFS,
author = "P. Ravisankar and V. Ravi and G. Raghava Rao and I.
Bose",
title = "Detection of financial statement fraud and feature
selection using data mining techniques",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "2",
pages = "491--500",
month = jan,
year = "2011",
CODEN = "DSSYDK",
DOI = "https://doi.org/10.1016/j.dss.2010.11.006",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001879",
abstract = "Recently, high profile cases of financial statement
fraud have been dominating the news. This paper uses
data mining techniques such as Multilayer Feed Forward
Neural Network (MLFF), Support Vector Machines (SVM),
Genetic Programming (GP), Group Method of Data Handling
(GMDH), Logistic Regression (LR), and Probabilistic
Neural Network (PNN) to identify companies that resort
to financial statement fraud. Each of these techniques
is tested on a dataset involving 202 Chinese companies
and compared with and without feature selection. {PNN}
outperformed all the techniques without feature
selection, and {GP} and {PNN} outperformed others with
feature selection and with marginally equal
accuracies.",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law; Data mining; Feature selection;
Financial fraud detection; Neural networks;
t-statistic; {GP}; {SVM}",
}
@Article{Robledo:2011:LZB,
author = "Alberto Robledo",
title = "Laws of {Zipf} and {Benford}, intermittency, and
critical fluctuations",
journal = "Chinese Science Bulletin",
volume = "56",
number = "34",
publisher = "SP Science China Press",
pages = "3643--3648",
year = "2011",
DOI = "https://doi.org/10.1007/s11434-011-4827-y",
ISSN = "1001-6538 (print), 1861-9541 (electronic)",
ISSN-L = "1001-6538",
bibdate = "Wed Aug 12 09:46:47 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11434-011-4827-y",
acknowledgement = ack-nhfb,
keywords = "Benford's law; critical clusters; generalized
statistical mechanics; tangent bifurcation; Zipf's
law",
}
@Article{Romano:2011:NLR,
author = "Paul K. Romano and Harry McLaughlin",
title = "On Non-Linear Recursive Sequences and {Benford's
Law}",
journal = j-FIB-QUART,
volume = "49",
number = "2",
pages = "134--138",
month = may,
year = "2011",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "11K31 (11B37)",
MRnumber = "2801800",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/49-2.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Ross:2011:BLG,
author = "Kenneth A. Ross",
title = "{Benford's Law}, a Growth Industry",
journal = j-AMER-MATH-MONTHLY,
volume = "118",
number = "7",
pages = "571--583",
month = aug # "\slash " # sep,
year = "2011",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.118.07.571",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "62A99 (60F99)",
MRnumber = "2826449 (2012g:62014)",
bibdate = "Mon Jan 30 08:58:20 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.118.issue-7;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/10.4169;
http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.07.571.pdf;
http://www.maa.org/history/presidents/ross.html",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
remark = "The author was President of the Mathematical
Association of America (1995--1996).",
}
@Article{Sambridge:2011:BLF,
author = "Malcolm Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and
Pierre Arroucau",
title = "{Benford}'s law of first digits: from mathematical
curiosity to change detector",
journal = j-ASIA-PAC-MATH-NEWSL,
volume = "1",
number = "4",
pages = "1--6",
month = oct,
year = "2011",
ISSN = "2010-3484",
MRclass = "62A99",
MRnumber = "2894867",
MRreviewer = "Vladimir S. Anashin",
bibdate = "Thu Feb 14 07:02:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Asia Pac. Math. Newsl.",
fjournal = "Asia Pacific Mathematics Newsletter",
}
@Article{SenDe:2011:BLD,
author = "Aditi {Sen De} and Ujjwal Sen",
title = "{Benford}'s law detects quantum phase transitions
similarly as earthquakes",
journal = j-EUROPHYS-LETT,
volume = "95",
number = "5",
pages = "50008",
month = sep,
year = "2011",
CODEN = "EULEEJ",
DOI = "https://doi.org/10.1209/0295-5075/95/50008",
ISSN = "0295-5075 (print), 1286-4854 (electronic)",
ISSN-L = "0295-5075",
bibdate = "Mon Nov 14 17:52:09 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1103.5398",
abstract = "A century ago, it was predicted that the first
significant digit appearing in a data would be
nonuniformly distributed, with the number one appearing
with the highest frequency. This law goes by the name
of Benford's law. It holds for data ranging from
infectious disease cases to national greenhouse gas
emissions. Quantum phase transitions are cooperative
phenomena where qualitative changes occur in many-body
systems at zero temperature. We show that the
century-old Benford's law can detect quantum phase
transitions, much like it detects earthquakes.
Therefore, being certainly of very different physical
origins, seismic activity and quantum cooperative
phenomena may be detected by similar methods. The
result has immediate implications in precise
measurements in experiments in general, and for
realizable quantum computers in particular. It shows
that estimation of the first significant digit of
measured physical observables is enough to detect the
presence of quantum phase transitions in macroscopic
systems.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1103.5398",
fjournal = "Europhysics Letters",
journal-URL = "http://iopscience.iop.org/0295-5075",
primaryclass = "quant-ph",
}
@Misc{Shi:2011:ESP,
author = "Yun-Quing Shi and DongDong Fu",
title = "Apparatus and method for a generalized {Benford's Law}
analysis of {DCT} and {JPEG} coefficients",
howpublished = "US Patent 7940989.",
day = "10",
month = may,
year = "2011",
bibdate = "Mon Feb 18 18:49:54 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "US Patent Application 11/772,636 filed 2 July 2007. US
Patent issued 10 May 2011.",
URL = "http://www.google.com/patents/US7940989",
acknowledgement = ack-nhfb,
}
@Article{Shikano:2011:WDD,
author = "S. Shikano and V. Mack",
title = "When does 2nd Digit {Benford's Law}-Test signal an
election fraud? {Facts} or misleading test results",
journal = "Jahrb{\"u}cher f{\"u}r National{\"o}konomie und
Statistik",
volume = "231",
number = "5--6",
pages = "719--732",
month = "????",
year = "2011",
DOI = "????",
bibdate = "Mon Feb 18 18:51:04 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://benfordonline.net/fullreference/1015",
acknowledgement = ack-nhfb,
}
@Article{Tang:2011:ESP,
author = "Lian Tang and Da Hui Wang",
title = "An explanation of the shift parameter {$ \rho $} in
the {Zipf--Mandelbrot} law",
journal = "Beijing Shifan Daxue Xuebao",
volume = "47",
number = "1",
pages = "97--100",
year = "2011",
CODEN = "BSDKDH",
ISSN = "0476-0301",
ISSN-L = "0476-0301",
MRclass = "94A17",
MRnumber = "2807603",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Beijing Shifan Daxue Xuebao. Ziran Kexue Ban. Journal
of Beijing Normal University (Natural Science)",
}
@Article{Urzua:2011:TZL,
author = "Carlos M. Urz{\'u}a",
title = "Testing for {Zipf}'s law: a common pitfall",
journal = j-ECONOM-LETT,
volume = "112",
number = "3",
pages = "254--255",
day = "1",
month = sep,
year = "2011",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/j.econlet.2011.05.049",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "62F03 (91B82)",
MRnumber = "2848721",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165176511002266",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
keywords = "Zipf's Law",
}
@Article{Vallee:2011:BMF,
author = "Robert Vall{\'e}e",
title = "{Beno{\^\i}t Mandelbrot} --- further notes",
journal = "Kybernetes",
volume = "40",
number = "9--10",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "KBNTA3",
ISSN = "0368-492X (print), 1758-7883 (electronic)",
ISSN-L = "0368-492X",
bibdate = "Fri Nov 25 07:38:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=9/10&articleid=17003220",
acknowledgement = ack-nhfb,
}
@Misc{Wang:2011:BLD,
author = "Jialan Wang",
title = "{Benford's Law} and the Decreasing Reliability of
Accounting Data for {US} Firms. {Studies} in Everyday
Life: Investigations and experiments on food, ethics,
economics, and the environment",
howpublished = "Blog posting",
day = "9",
month = oct,
year = "2011",
bibdate = "Mon Feb 18 18:54:40 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://econerdfood.blogspot.com/2011/10/benfords-law-and-decreasing-reliability.html",
acknowledgement = ack-nhfb,
}
@Misc{Wang:2011:BLR,
author = "Jialan Wang",
title = "{Benford}'s law: a revised analysis",
howpublished = "Blog posting",
day = "24",
month = oct,
year = "2011",
bibdate = "Tue Feb 19 10:33:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://econerdfood.blogspot.com/2011/10/benfords-law-revised-analysis.html",
acknowledgement = ack-nhfb,
}
@Misc{Weisstein:2011:BL,
author = "Eric W. Weisstein",
title = "{Benford's Law}",
howpublished = "MathWorld---A Wolfram Web Resource",
year = "2011",
bibdate = "Tue Nov 15 08:40:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://mathworld.wolfram.com/BenfordsLaw.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Winter:2011:DFU,
author = "Christian Winter and Markus Schneider and York
Yannikos",
editor = "Gilbert Peterson and Sujeet Shenoi",
booktitle = "{Advances in Digital Forensics VII: 7th IFIP WG 11.9
International Conference on Digital Forensics, Orlando,
FL, USA, January 31-- February 2, 2011, Revised
Selected Papers}",
title = "Detecting Fraud Using Modified {Benford} Analysis",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xviii + 285",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-642-24212-0_10",
ISBN = "3-642-24211-1 (paperback), 3-642-24212-X (e-book)",
ISBN-13 = "978-3-642-24211-3 (paperback), 978-3-642-24212-0
(e-book)",
LCCN = "HV8079.C65 I357 2011",
bibdate = "Wed Aug 12 09:41:22 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
price = "US\$",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-24212-0_10/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-24212-0",
}
@Article{Xu:2011:PCG,
author = "B. Xu and J. Wang and G. Liu and Y. Dai",
title = "Photorealistic computer graphics forensics based on
leading digit law",
journal = "Journal of Electronics (China)",
volume = "28",
number = "1",
pages = "95--100",
month = "????",
year = "2011",
DOI = "https://doi.org/10.1007/s11767-011-0474-3",
bibdate = "Mon Feb 18 18:55:38 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11767-011-0474-3",
acknowledgement = ack-nhfb,
}
@Article{Zgela:2011:ATC,
author = "Mario {\v{Z}}gela and Jasminka Dob{\v{s}}a",
title = "Analysis of Top 500 {Central and East European}
Companies Net Income Using {Benford's Law}",
journal = j-J-INFO-ORG-SCI,
volume = "35",
number = "2",
pages = "215--228",
month = dec,
year = "2011",
ISSN = "1846-3312 (print), 1846-9418 (electronic)",
ISSN-L = "1846-3312",
bibdate = "Mon Feb 18 18:57:10 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Prosinac 2011 conference.",
URL = "http://hrcak.srce.hr/file/111658;
http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=111658",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informational and Organizational Sciences",
journal-URL = "http://jios.foi.hr/index.php/jios/index",
}
@Article{Zhang:2011:ETO,
author = "Qunzhi Zhang and Didier Sornette",
title = "Empirical test of the origin of {Zipf}'s law in
growing social networks",
journal = j-PHYSICA-A,
volume = "390",
number = "23--24",
pages = "4124--4130",
day = "1",
month = nov,
year = "2011",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2011.06.063",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437111005103",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Zorzi:2011:BL,
author = "Alberto Zorzi",
title = "95.22 {Benford}'s law and $ \pi $",
journal = j-MATH-GAZ,
volume = "95",
number = "533",
pages = "264--266",
month = jul,
year = "2011",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.1017/S0025557200002990",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Tue May 5 12:04:16 MDT 2015",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=95&issueId=533;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Gaz.",
fjournal = "The Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
remark = "The journal Web site lacks a search feature, and the
archives only cover up to 2007. JSTOR has only issues
up to 2007.",
}
@Article{Abrantes-Metz:2012:LM,
author = "Rosa M. Abrantes-Metz and Michael Kraten and Albert D.
Metz and Gim S. Seow",
title = "Libor manipulation?",
journal = "Journal of Banking \& Finance",
volume = "36",
number = "1",
pages = "136--150",
year = "2012",
DOI = "https://doi.org/10.1016/j.jbankfin.2011.06.014",
ISSN = "0378-4266 (print), 1872-6372 (electronic)",
ISSN-L = "0378-4266",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378426611002032",
abstract = "On May 29, 2008 the Wall Street Journal published an
article alleging that several global banks were
reporting Libor quotes significantly lower than those
implied by prevailing credit default swap (CDS)
spreads. While acknowledging that the analysis doesn t
prove that banks are lying or manipulating Libor, it
nevertheless conjectures that these banks may have been
low-balling their borrowing rates to avoid looking
desperate for cash. In this paper we compare Libor with
other short-term borrowing rates, analyze individual
bank quotes, and compare these individual quotes to
{CDS} spreads and market capitalization data during
three periods: 1/1/07 8/8/07 (Period 1), 8/9/07 4/16/08
(Period 2), and 4/17/08 5/30/08 (Period 3). We find
some anomalous individual quotes, but the evidence is
inconsistent with a material manipulation of the {US}
dollar 1-month Libor rate.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Bid-rigging; Collusion; Conspiracies;
Credit default swap spreads; Libor; Manipulations;
Price-fixing",
}
@Article{Anonymous:2012:SB,
author = "Anonymous",
title = "The scam busters",
journal = j-ECONOMIST,
volume = "??",
number = "??",
pages = "??--??",
day = "15",
month = dec,
year = "2012",
CODEN = "EONOEH",
ISSN = "0013-0613 (print), 1476-8860 (electronic)",
ISSN-L = "0013-0613",
bibdate = "Mon Feb 18 19:01:02 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters",
acknowledgement = ack-nhfb,
fjournal = "The Economist",
keywords = "Benford's Law",
}
@TechReport{Balanzario:2012:BLM,
author = "E. P. Balanzario",
title = "{Benford}'s law for mixtures",
type = "Preprint",
institution = "????",
address = "????",
month = "????",
year = "2012",
bibdate = "Mon Feb 18 19:02:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Bharath:2012:BLT,
author = "H. M. Bharath",
title = "{Benford's Law}: A theoretical explanation for base
$2$",
journal = "arXiv.org",
day = "24",
month = nov,
year = "2012",
bibdate = "Tue Jan 26 09:55:55 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1211.7008B",
acknowledgement = ack-nhfb,
eprint = "1211.7008",
keywords = "Statistics - Other Statistics",
primaryclass = "stat.OT",
}
@Article{Bharati:2012:CCO,
author = "Rakesh Bharati and Susan J. Crain and Vincent
Kaminski",
title = "Clustering in crude oil prices and the target pricing
zone hypothesis",
journal = "Energy Economics",
volume = "34",
number = "4",
pages = "1115--1123",
year = "2012",
DOI = "https://doi.org/10.1016/j.eneco.2011.09.009",
ISSN = "0140-9883 (print), 1873-6181 (electronic)",
ISSN-L = "0140-9883",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0140988311002258",
abstract = "This paper studies the target pricing zone (TPZ)
hypothesis for crude oil by examining price clustering
in the dollar digit. It is hypothesized that price
clustering occurs within an established {TPZ} if {OPEC}
is able to defend the upper and lower bounds through
output changes. The results show that prices strongly
cluster around the dollar digit value of 9 within the
{TPZ} sub-periods, but not outside the sub-periods.
Furthermore, the degree of clustering declines when
production capacity utilization is high and when
production significantly exceeds quotas, consistent
with OPEC's inability to defend the zone. Nine-centered
clustering also results in lower contemporaneous and
next-day volatility. These results support the target
pricing zone hypothesis of crude oil.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Clustering; Crude oil; Target pricing
zone; {OPEC}",
}
@Article{Chen:2012:MRB,
author = "Yanguang Chen",
title = "The mathematical relationship between {Zipf}'s law and
the hierarchical scaling law",
journal = j-PHYSICA-A,
volume = "391",
number = "11",
pages = "3285--3299",
day = "1",
month = jun,
year = "2012",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2011.12.031",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437111009678",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Chen:2012:ZLF,
author = "Yanguang Chen",
title = "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "45",
number = "1",
pages = "63--73",
day = "15",
month = jan,
year = "2012",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2011.10.001",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0960077911001901",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
keywords = "Zipf's Law",
}
@Article{Chen:2012:ZLH,
author = "Yanguang Chen",
title = "{Zipf}'s law, hierarchical structure, and
cards-shuffling model for urban development",
journal = j-DISCRETE-DYN-NAT-SOC,
pages = "480196",
year = "2012",
CODEN = "DDNSFA",
DOI = "https://doi.org/10.1155/2012/480196",
ISSN = "1026-0226 (print), 1607-887X (electronic)",
ISSN-L = "1026-0226",
MRclass = "91D10",
MRnumber = "2914043",
MRreviewer = "Sandra L. Arlinghaus",
bibdate = "Mon Feb 18 16:48:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Discrete Dyn. Nat. Soc.",
fjournal = "Discrete Dynamics in Nature and Society. An
International Multidisciplinary Research and Review
Journal",
pagecount = "21",
}
@Article{Clippe:2012:BLT,
author = "Paulette Clippe and Marcel Ausloos",
title = "{Benford's Law} and {Theil} transform of financial
data",
journal = j-PHYSICA-A,
volume = "391",
number = "24",
pages = "6556--6567",
day = "15",
month = dec,
year = "2012",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2012.07.063",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437112007546",
abstract = "Among econophysics investigations, studies of
religious groups have been of interest. On the one
hand, the present paper concerns the Antoinist
community financial reports a community which appeared
at the end of the 19-th century in Belgium. Several
growth decay regimes have been previously found over
different time spans. However, there is common
suspicion about sect finances. In that spirit, the
Antoinist community yearly financial reports, income
and expenses, are hereby examined through the so-called
Benford's Law. The latter is often used as a test about
possible accounting wrongdoings. On the other hand,
Benford's Law is known to be invariant under scale and
base transformation. Therefore, as a further test, of
both such data and the use of Benford's Law, the yearly
financial reports are nonlinearly remapped through a
sort of Theil transformation, i.e. based on a
log-transformation. The resulting data is again
analyzed along the Benford's Law scheme. Bizarre,
puzzling, features are seen. However, it is emphasized
that such a non-linear transformation can shift the
argument toward a more objective conclusion. In an
appendix, some brief discussion is made on why the
original Theil mapping should not be used. In a second
appendix, an imperfect Benford's Law-like form better
suited for anomalous distributions is presented.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Benford's Laws; Expenses; Income;
Religious community; Theil map; Time series",
}
@Article{Cristelli:2012:TMT,
author = "Matthieu Cristelli and Michael Batty and Luciano
Pietronero",
title = "There is More than a Power Law in {Zipf}",
journal = j-SCI-REP,
volume = "2",
number = "??",
pages = "1--7",
month = nov,
year = "2012",
CODEN = "SRCEC3",
DOI = "https://doi.org/10.1038/srep00812",
ISSN = "2045-2322",
ISSN-L = "2045-2322",
bibdate = "Tue Feb 26 07:32:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html",
accepted = "28 August 2012",
acknowledgement = ack-nhfb,
articleno = "812",
fjournal = "Scientific Reports",
journal-URL = "http://www.nature.com/srep/",
onlinedate = "08 November 2012",
received = "15 August 2012",
}
@Article{Diekmann:2012:MUB,
author = "Andreas Diekmann",
title = "Making Use of ``{Benford's Law}'' for the Randomized
Response Technique",
journal = j-SOC-METH-RES,
volume = "41",
number = "2",
pages = "325--334",
month = may,
year = "2012",
DOI = "https://doi.org/10.1177/0049124112452525",
ISSN = "0049-1241 (print), 1552-8294 (electronic)",
ISSN-L = "0049-1241",
MRnumber = "3190709",
bibdate = "Mon Feb 18 19:03:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://smr.sagepub.com/content/41/2/325;
http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf",
acknowledgement = ack-nhfb,
fjournal = "Sociological Methods and Research",
}
@Book{Dorrell:2012:FFB,
author = "Darrell D. Dorrell and Gregory A. Gadawski",
title = "Financial forensics body of knowledge",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 541",
year = "2012",
DOI = "https://doi.org/10.1002/9781119200734",
ISBN = "0-470-88085-6 (hardcover), 1-118-21897-3 (e-book),
1-118-21896-5 (e-book), 1-118-21898-1 (e-book),
1-119-20073-3 (e-book)",
ISBN-13 = "978-0-470-88085-2 (hardcover), 978-1-118-21897-6
(e-book), 978-1-118-21896-9 (e-book), 978-1-118-21898-3
(e-book), 978-1-119-20073-4 (e-book)",
LCCN = "HV6769 .D675 2012",
bibdate = "Thu Oct 13 06:54:34 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley finance",
URL = "http://catalogimages.wiley.com/images/db/jimages/9780470880852.jpg;
http://site.ebrary.com/id/10534000",
abstract = "The definitive, must-have guide for the forensic
accounting professionalA comprehensive and practical
overview of civil and criminal forensic accounting
methodology, Forensic Accounting Body of Knowledge
defines the profession of forensic accounting,
capturing and codifying methods that define the body of
knowledge. Filled with practical forensic accounting
tips, tools and techniques, the book contains
contributions from US and global professionals spanning
all aspects of the financial community, including the
law enforcement, investment, investigative, and
regulatory arenas. Provides immediately useful tools
Includes more than 200 tips and techniques Globally
relevant content, with cutting-edge counterterrorism
forensic accounting methodology Supported by a
continually updated Internet-based software application
Offers contributions from twenty financial experts in
law enforcement, investigative, and regulatory fields
Accompanied by a frequently updated Internet-based
software application, Forensic Accounting Body of
Knowledge will refine financial information users'
approaches, techniques, and methods with useful tools
and tips that reflect the continually growing body of
forensic accounting knowledge.",
acknowledgement = ack-nhfb,
subject = "Commercial crimes; Forensic accounting; Fraud
investigation",
tableofcontents = "Foundational phase \\
Interpersonal phase \\
Data collection and analysis phase: part I \\
Data collection and analysis phase: part II \\
Data collection and analysis phase: part III \\
Trial and reports phase \\
Counterterrorism: conventional tools for unconventional
warfare \\
Civil versus criminal law comparison \\
Appendix. Forensic inventory: forensic tools,
techniques, methods, and methodologies",
}
@Article{Egghe:2012:AGL,
author = "Leo Egghe and Raf Guns",
title = "Applications of the generalized law of {Benford} to
informetric data",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "63",
number = "8",
pages = "1662--1665",
month = aug,
year = "2012",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.22690",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Mon Feb 18 19:05:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract",
abstract = "In a previous work (Egghe, 2011), the first author
showed that Benford's law (describing the logarithmic
distribution of the numbers 1, 2, \ldots{}, 9 as first
digits of data in decimal form) is related to the
classical law of Zipf with exponent 1. The work of
Campanario and Coslado (2011), however, shows that
Benford's law does not always fit practical data in a
statistical sense. In this article, we use a
generalization of Benford's law related to the general
law of Zipf with exponent $ \beta > 0 $. Using data
from Campanario and Coslado, we apply nonlinear least
squares to determine the optimal $ \beta $ and show
that this generalized law of Benford fits the data
better than the classical law of Benford.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}
@Article{Egghe:2012:BCA,
author = "Leo Egghe and Raf Guns",
title = "Brief Communication: Applications of the generalized
law of {Benford} to informetric data",
journal = j-J-AM-SOC-INF-SCI-TECHNOL,
volume = "63",
number = "8",
pages = "1662--1665",
month = aug,
year = "2012",
CODEN = "JASIEF",
DOI = "https://doi.org/10.1002/asi.22690",
ISSN = "1532-2882 (print), 1532-2890 (electronic)",
ISSN-L = "1532-2882",
bibdate = "Fri Sep 11 10:43:15 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jasist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science and Technology: JASIST",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
onlinedate = "26 Jun 2012",
}
@Article{Egghe:2012:TPS,
author = "Leo Egghe and Ronald Rousseau",
title = "Theory and practice of the shifted {Lotka} function",
journal = j-SCIENTOMETRICS,
volume = "91",
number = "1",
pages = "295--301",
month = apr,
year = "2012",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-011-0539-y",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Thu Sep 3 07:35:27 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-011-0539-y",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Eliahou:2012:MDP,
author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique
Schneider",
title = "On the mantissa distribution of powers of natural and
prime numbers",
journal = "Acta Mathematica Hungarica",
volume = "139",
number = "1--2",
pages = "1--5",
month = apr,
year = "2013",
DOI = "https://doi.org/10.1007/s10474-012-0244-1",
ISSN = "0001-5954, 0236-5294, 1588-2632",
ISSN-L = "0001-5954",
bibdate = "Mon Feb 18 19:06:54 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s10474-012-0244-1",
acknowledgement = ack-nhfb,
}
@Article{Eliazar:2012:PLC,
author = "Iddo I. Eliazar and Morrel H. Cohen",
title = "Power-law connections: From {Zipf} to {Heaps} and
beyond",
journal = j-INFO-PROC-MAN,
volume = "23",
number = "3",
pages = "56--74",
day = "1",
month = may,
year = "2012",
CODEN = "IPMADK",
DOI = "https://doi.org/10.1016/j.aop.2013.01.013",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0003491613000171",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
journal-URL = "http://www.sciencedirect.com/science/journal/03064573",
keywords = "Zipf's Law",
}
@Article{Friar:2012:GSB,
author = "James L. Friar and Terrance Goldman and Juan
P{\'e}rez-Mercader",
title = "Genome Sizes and the {Benford} Distribution",
journal = j-PLOS-ONE,
volume = "7",
number = "5",
pages = "e36624:1--e36624:9",
month = may,
year = "2012",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0036624",
ISSN = "1932-6203",
ISSN-L = "1932-6203",
bibdate = "Mon Feb 18 19:08:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0036624",
abstract = "Data on the number of Open Reading Frames (ORFs) coded
by genomes from the 3 domains of Life show the presence
of some notable general features. These include
essential differences between the Prokaryotes and
Eukaryotes, with the number of ORFs growing linearly
with total genome size for the former, but only
logarithmically for the latter.",
accepted = "11 April 2012",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
onlinedate = "18 May 2012",
received = "7 April 2011",
}
@Article{Gambini:2012:PDD,
author = "Alessandro Gambini and Giovanni Mingari Scarpello and
Daniele Ritelli",
title = "Probability of digits by dividing random numbers: A $
\psi $ and $ \zeta $ functions approach",
journal = j-EXPO-MATH,
volume = "30",
number = "3",
pages = "223--238",
month = "????",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.exmath.2012.03.001",
ISSN = "0723-0869 (print), 1878-0792 (electronic)",
ISSN-L = "0723-0869",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0723086912000230",
abstract = "This paper begins with the statistics of the decimal
digits of $ n / d $ with $ (n, d) \in N^2 $ randomly
chosen. Starting with a statement by Ces{\`a}ro on
probabilistic number theory, see Ces{\`a}ro (1885)
[3,4], we evaluate, through the Euler function, an
integral appearing there. Furthermore the probabilistic
statement itself is proved, using a different approach:
in any case the probability of a given digit $r$ to be
the first decimal digit after dividing a couple of
random integers is $ p_r = 1 / 20 + 1 / 2 \{ \psi (r /
10 + 11 / 10) - \psi (r / 10 10 + 1) \} $. The theorem
is then generalized to real numbers (Theorem 1, holding
a proof of both $ n / d$ results) and to the $ \alpha $
th power of the ratio of integers (Theorem 2), via an
elementary approach involving the function and the
Hurwitz function. The article provides historic
remarks, numerical examples, and original theoretical
contributions: also it complements the recent renewed
interest in {Benford's Law} among number theorists.",
acknowledgement = ack-nhfb,
ajournal = "Expo. Math.",
fjournal = "Expositiones Mathematicae",
hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) -
psi(r/10 + 1)))",
hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r,
p(r)); println {""}",
journal-URL = "http://www.sciencedirect.com/science/journal/07230869",
keywords = "Benford's Law; Elementary probability; Euler $\psi$
function; Euler function; Hurwitz $\zeta$ function;
Hurwitz function",
remark = "This paper proves formulas for the probability of
first-digit occurrences in the ratios of random
integers, and compares the predictions with the
somewhat different ones from Benford's Law. Their work
simplifies a result of Ces{\`a}ro (1885), and predicts
that the probability of the first quotient digit being
$r$ is given by $ p(r) = 1 / 20 + (1 / 2)*(\psi ((r +
11) / 10) - \psi (r / 10 + 1)) $. That predicts these
pairs of $ (r, p(r)) $: $ (0, 0.12673) $, $ (1,
0.11736) $, $ (2, 0.10992) $, $ (3, 0.10390) $, $ (4,
0.09894) $, $ (5, 0.09478) $, $ (6, 0.09125) $, $ (7,
0.08822) $, $ (8, 0.08560) $, $ (9, 0.08330) $. Those
values may be compared with the Benford's Law
prediction for the second digit (possibly zero) of $
(0, 0.120) $, $ (1, 0.114) $, $ (2, 0.109) $, $ (3,
0.104) $, $ (4, 0.100) $, $ (5, 0.097) $, $ (6, 0.093)
$, $ (7, 0.090) $, $ (8, 0.088) $, and $ (9, 0.085)
$.",
}
@Article{Geyer:2012:ABL,
author = "A. Geyer and J. Mart{\'\i}",
title = "Applying {Benford}'s law to volcanology",
journal = "Geology",
volume = "40",
number = "4",
pages = "327--330",
month = apr,
year = "2012",
DOI = "https://doi.org/10.1130/G32787.1",
bibdate = "Mon Feb 18 19:11:36 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://geology.gsapubs.org/content/40/4/327",
acknowledgement = ack-nhfb,
}
@InCollection{Gorroochurn:2012:BPB,
author = "Prakash Gorroochurn",
title = "{Benford} and the Peculiar Behavior of the First
Significant Digit (1938)",
crossref = "Gorroochurn:2012:CPP",
chapter = "27",
pages = "233--239",
year = "2012",
DOI = "https://doi.org/10.1002/9781118314340.ch27",
bibdate = "Sat Feb 23 17:26:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "(Benford) distribution; a distribution of
distributions; and Benford's law; Benford and the
peculiar behavior of the first significant digit
(1938); First 100 Fibonacci Numbers; first-digit law or
Benford's law; scale invariance; the leading digit and
its behavior",
}
@InProceedings{Guettler:2012:BGQ,
author = "S. Guettler and F. Thiemann and R. A. E. Mueller",
editor = "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K.
Hildebrand and B. Theuvsen",
booktitle = "{Informationstechnologie f{\"u}r eine nachhaltige
Landbewirtschaftung. Fokus Forstwirtschaft. Referate
der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz
2012, Freising}. ({German}) [Information technology for
sustainable land management. Focus on forestry. Papers
of the 32nd GIL Annual Conference 29, February--1 March
2012, Freising]",
title = "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r
statistische Reihen angewendet auf Handelsdaten f{\"u}r
Agrarprodukte}. ({German}) [{Benford's Law}: a quality
test applied for statistical series on trade data for
agricultural products]",
volume = "194",
publisher = "Gesellschaft f{\"u}r Informatik.",
address = "Bonn, Germany",
bookpages = "334 (est.)",
pages = "111--114",
year = "2012",
ISBN = "3-88579-288-5",
ISBN-13 = "978-3-88579-288-8",
ISSN = "1617-5468",
LCCN = "????",
bibdate = "Tue Feb 19 05:44:08 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Informatics",
URL = "http://www.gil-net.de/Publikationen/24_111.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Hein:2012:SFF,
author = "J. Hein and R. Zobrist and C. Konrad and G.
Schuepfer",
title = "Scientific fraud in 20 falsified anesthesia papers",
journal = "{Der Anaesthesist}",
volume = "61",
number = "6",
pages = "543--549",
month = jun,
year = "2012",
CODEN = "ANATAE",
DOI = "https://doi.org/10.1007/s00101-012-2029-x",
ISSN = "0003-2417 (print), 1432-055X (electronic)",
ISSN-L = "0003-2417",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s00101-012-2029-x",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/101",
keywords = "Benford's Law",
}
@Article{Henselmann:2012:ABL,
author = "Klaus Henselmann and Elisabeth Scherr and Dominik
Ditter",
title = "Applying {Benford's Law} to individual financial
reports: An empirical investigation on the basis of
{SEC XBRL} filings",
journal = "Working Papers in Accounting Valuation Auditing",
volume = "2012-1",
pages = "1--23",
year = "2012",
bibdate = "Thu Oct 13 07:14:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://hdl.handle.net/10419/88418;
http://www.econstor.eu/bitstream/10419/88418/1/773918388.pdf",
acknowledgement = ack-nhfb,
}
@MastersThesis{Iudica:2012:BLM,
author = "Federico Iudica",
title = "{Benford's Law}: Mathematical Properties and Forensic
Accounting Applications",
type = "{Master}'s Thesis",
school = "Facolt{\`a} di Impresa e Management, Cattedra di
Matematica, Luiss Guido Carli University",
address = "Rome, Italy",
pages = "iv + 56",
year = "2012",
bibdate = "Tue Feb 19 05:54:59 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf",
acknowledgement = ack-nhfb,
advisor = "Marco Dall'Aglio",
}
@Article{Janvresse:2012:AAU,
author = "{\'E}lise Janvresse and Thierry {De La Rue}",
title = "Averaging along Uniform Random Integers",
journal = "Uniform Distribution Theory",
volume = "7",
number = "2",
pages = "35--60",
month = "????",
year = "2012",
DOI = "????",
ISSN = "1336-913X",
ISSN-L = "1336-913X",
bibdate = "Tue Feb 19 05:56:13 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://www.boku.ac.at/MATH/udt/",
keywords = "Benford's Law",
}
@PhdThesis{Janvresse:2012:QCP,
author = "{\'E}lise Janvresse",
title = "Quelques contributions aux probabilit{\'e}s et {\`a}
la th{\'e}orie ergodique. ({French}) [Some
contributions to probability theory and ergodic
theory]",
type = "Document de synth{\`e}se pr{\'e}sent{\'e} pour
l'{Habilitation {\`a} Diriger des Recherches}",
school = "l'Universit{\'e} de Rouen",
address = "Rouen, France",
pages = "67",
day = "17",
month = feb,
year = "2012",
bibdate = "Tue Feb 19 05:57:33 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
language = "French",
}
@InProceedings{Khosravani:2012:TIB,
author = "A. Khosravani and C. Rasinariu",
title = "Transformation invariance of {Benford} variables and
their numerical modeling",
crossref = "Niola:2012:RRA",
pages = "57--61",
year = "2012",
bibdate = "Tue Feb 19 06:01:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kim:2012:BLN,
author = "Sangrak Kim",
title = "{Benford's Law} in non-equilibrium processes: Droplet
collisions case",
journal = j-PHYSICA-A,
volume = "391",
number = "20",
pages = "4970--4975",
day = "15",
month = oct,
year = "2012",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2012.05.043",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437112004141",
abstract = "Benford's Law is investigated for the simulation
results generated from non-equilibrium molecular
dynamics. A statistic to measure how closely a set of
the numbers follows Benford's Law is defined. The
simulation data are from the collisions of two nano
droplets with different impact velocities. When a
non-equilibrium system returns to its equilibrium
state, some physical quantities relevant to the
non-equilibrium settings follow Benford's Law more
closely. The initial settings for the non-equilibrium
state can be interpreted as a data fabrication of its
corresponding equilibrium state. A connection with the
Shannon entropy for the first digit distribution is
also discussed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Molecular dynamics; Non-equilibrium
process",
}
@Article{Kossovsky:2012:SNR,
author = "Alex Ely Kossovsky",
title = "Statistician's New Role as a Detective --- Testing
Data for Fraud",
journal = "Ciencias Econ{\'o}mica",
volume = "30",
number = "2",
pages = "179--200",
month = "????",
year = "2012",
ISSN = "0252-9521 (print), 2215-3489 (electronic)",
ISSN-L = "0252-9521",
bibdate = "Thu Oct 13 07:24:48 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://revistas.ucr.ac.cr/index.php/economicas/article/view/8015/7634",
acknowledgement = ack-nhfb,
journal-URL = "http://revistas.ucr.ac.cr/index.php/economicas/index",
keywords = "Benford's Law",
}
@Article{Li:2012:DTR,
author = "Xiang Hua Li and Yu Qian Zhao and Miao Liao and Frank
Y. Shih and Yun Q. Shi",
title = "Detection of tampered region for {JPEG} images by
using mode-based first digit features",
journal = j-EURASIP-J-ADV-SIGNAL-PROCESS,
volume = "2012",
number = "1",
pages = "190:1--190:??",
month = aug,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1186/1687-6180-2012-190",
ISSN = "1687-6172 (print), 1687-6180 (electronic)",
ISSN-L = "1687-6172",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1186/1687-6180-2012-190",
acknowledgement = ack-nhfb,
fjournal = "EURASIP Journal on Advances in Signal Processing",
journal-URL = "http://www.asp.eurasipjournals.com/;
http://asp.eurasipjournals.springeropen.com/",
keywords = "Benford's Law",
}
@Article{LimKaiJie:2012:CES,
author = "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan",
title = "A Critical Evaluation of the Significance of Round
Numbers in {European} Equity Markets in Light of the
Predictions from {Benford's Law}",
journal = "International Research Journal of Finance and
Economics",
volume = "95",
number = "??",
pages = "196--210",
day = "28",
month = aug,
year = "2012",
DOI = "????",
ISSN = "1450-2887",
bibdate = "Tue Feb 19 06:04:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://mpra.ub.uni-muenchen.de/40960/;
http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Marcus:2012:UFA,
author = "Adam Marcus",
title = "Update on {Fujii}: Anesthesia journal finds
overwhelming statistical evidence of data fabrication",
howpublished = "Web site article.",
day = "8",
month = mar,
year = "2012",
bibdate = "Wed Jun 20 14:33:00 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://retractionwatch.com/2012/03/08/update-on-fujii-anesthesia-journal-finds-overwhelming-statistical-evidence-of-data-fabrication/",
acknowledgement = ack-nhfb,
}
@Article{Masse:2012:RNS,
author = "Bruno Mass{\'e} and Dominique Schneider",
title = "Random number sequences and the first digit
phenomenon",
journal = j-ELECTRON-J-PROBAB,
volume = "17",
pages = "86:1--86:17",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v17-1900",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
MRclass = "60B10 (11A63 11B05)",
MRnumber = "2988401",
MRreviewer = "Rita Giuliano Antonini",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ejp.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ejp.ejpecp.org/article/view/1900",
abstract = "The sequences of mantissa of positive integers and of
prime numbers are known not to be distributed as
Benford's law in the sense of the natural density. We
show that we can correct this defect by selecting the
integers or the primes by means of an adequate random
process and we investigate the rate of convergence. Our
main tools are uniform bounds for deterministic and
random trigonometric polynomials. We then adapt the
random process to prove the same result for logarithms
and iterated logarithms of integers. Finally we show
that, in many cases, the mantissa law of the $n$ th
randomly selected term converges weakly to the
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Benford's law; density; mantissa; weak convergence",
}
@InProceedings{Mebane:2012:SDT,
author = "Walter R. {Mebane, Jr.}",
editor = "????",
booktitle = "{Proceedings of the 2012 Annual Meeting of the Midwest
Political Science Association, Chicago, IL, April
11--14, 2012}",
title = "Second-Digit Tests for Voters' Election Strategies and
Election Fraud",
publisher = "????",
address = "????",
pages = "??--??",
year = "2012",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Sat Sep 10 14:22:55 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Mir:2012:LDD,
author = "T. A. Mir",
title = "The leading digit distribution of the worldwide
illicit financial flows",
journal = "ArXiv e-prints",
year = "2012",
bibdate = "Tue Feb 19 06:07:33 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1201.3432",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Mir:2012:LLD,
author = "Tariq Ahmad Mir",
title = "The law of the leading digits and the world
religions",
journal = j-PHYSICA-A,
volume = "391",
number = "3",
pages = "792--798",
day = "1",
month = feb,
year = "2012",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2011.09.001",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437111007175",
abstract = "Benford's Law states that the occurrence of
significant digits in many data sets is not uniform but
tends to follow a logarithmic distribution such that
the smaller digits appear as first significant digits
more frequently than the larger ones. We investigate
here numerical data on the country-wise adherent
distribution of seven major world religions i.e.
Christianity, Islam, Buddhism, Hinduism, Sikhism,
Judaism and Baha'ism to see if the proportion of the
leading digits occurring in the distribution conforms
to Benford's Law. We find that the adherent data of all
the religions, except Christianity, excellently does
conform to Benford's Law. Furthermore, unlike the
adherent data on Christianity, the significant digit
distribution of the three major Christian denominations
i.e., Catholicism, Protestantism and Orthodoxy obeys
the law. Thus in spite of their complexity, general
laws can be established for the evolution of religious
groups.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Adherents; Benford's Law; Religion",
}
@Article{Nebel:2012:DHG,
author = "J.-C. Nebel and S. Pezzulli",
title = "Distribution of Human Genes Observes {Zipf's Law}",
journal = "Kingston University Research \& Innovation Reports
(KURIR)",
volume = "8",
number = "??",
pages = "1--9",
month = "????",
year = "2012",
DOI = "????",
ISSN = "1749-5652",
ISSN-L = "1749-5652",
bibdate = "Tue Feb 19 06:09:05 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://kurir.kingston.ac.uk/",
remark = "Kingston University, London, UK. Year 2012 volume is
not yet online on 19 February 2013.",
}
@Book{Nigrini:2012:BLA,
author = "Mark J. (Mark John) Nigrini",
title = "{Benford's Law}: Applications for Forensic Accounting,
Auditing, and Fraud Detection",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xviii + 330",
year = "2012",
ISBN = "1-118-15285-9 (hardcover), 1-118-28226-4,
1-118-28284-1, 1-118-28686-3",
ISBN-13 = "978-1-118-15285-0 (hardcover), 978-1-118-28226-7,
978-1-118-28284-7, 978-1-118-28686-9",
LCCN = "HV6691 .N54 2012",
bibdate = "Sun Feb 17 10:03:10 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.scribd.com/doc/86733139/Benford-s-Law-Applications-for-Forensic-Accounting-Auditing-and-Fraud-Detection",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword / xi \\
Preface / xiii \\
About the Author / xix \\
Chapter 1: Introduction and Mathematical Foundations /
1 \\
Benford's Expected Digit Frequencies / 5 \\
Defining the First and First-Two Digits / 6 \\
Digit Patterns of U.S. Census Data / 8 \\
Logging on to Benford's Law / 10 \\
General Significant Digit Law / 13 \\
Log and Behold, the Census Data / 13 \\
Love at First Sight / 15 \\
Mantissa Test and Census Data / 19 \\
Number of Records and Benford's Law Tests / 20 \\
When Should Data Conform to Benford's Law? / 21 \\
Conclusions / 23 \\
Chapter 2: Theorems, Truisms, and a Little Trivia / 25
\\
Digits of Corporate Payments Data / 26 \\
Digits of Lake Data / 28 \\
Scale Invariance Theorem / 31 \\
Mean Absolute Deviation / 34 \\
Scale Invariance and Census Data / 34 \\
Scale Invariance and Corporate Payments / 35 \\
Scale Invariance and Lake Data / 36 \\
A Level Playing Field Becomes Benford / 38 \\
Multiplication by $1 / x$ / 42 \\
All Distributions Lead to Benford / 43 \\
Getting a Gripf on Benford and Zipf / 46 \\
Conclusions / 50 \\
Chapter 3: More Formulas and Facts, and a Little
Fibonacci / 51 \\
Fibonacci Numbers / 51 \\
Lucas Numbers / 53 \\
Back to Square One / 55 \\
$3 n + 1$ Problem / 58 \\
Ultimate Uniform Distribution / 60 \\
Benford Embraces Other Bases / 62 \\
Nigrini's Second Last Theorem / 65 \\
Conclusions / 69 \\
Chapter 4: Primary Benford's Law Tests / 71 \\
Corporate Payments Data / 72 \\
Data Profile / 72 \\
First Come, First Served / 74 \\
Playing Second Fiddle / 75 \\
First-Two Digits Test / 78 \\
Running the Digit Tests in Excel / 80 \\
Running the Digit Tests in Access / 83 \\
Conclusions / 87 \\
Chapter 5: Advanced Benford's Law Tests / 89 \\
Summation Test / 90 \\
Running the Summation Test in Excel / 94 \\
Running the Summation Test in Access / 95 \\
Second-Order Test / 97 \\
An Analysis of Payments Data / 102 \\
An Analysis of Journal Entry Data / 104 \\
An Analysis of Census Data / 107 \\
Running the Second-Order Test in Excel / 108 \\
Excel, Thanks a Million(s) / 110 \\
Scale Invariance and the Second-Order Test / 113 \\
Conclusions / 114 \\
Chapter 6: Associated Benford's Law Tests / 117 \\
Number Duplication Test / 117 \\
An Analysis of Payments Data / 119 \\
An Analysis of Census Data / 121 \\
Running the Number Duplication Test in Excel / 122 \\
Running the Number Duplication Test in Access / 126 \\
Last-Two Digits Test / 129 \\
An Analysis of Payments Data / 130 \\
An Analysis of Census Data / 131 \\
An Analysis of Election Results / 132 \\
Running the Last-Two Digits Test in Excel / 135 \\
Running the Last-Two Digits Test in Access / 136 \\
Distortion Factor Model / 138 \\
Distortion and the Census Data / 145 \\
Conclusions / 146 \\
Chapter 7: Assessing Conformity to Benford's Law / 149
\\
$Z$-Statistic / 150 \\
Chi-Square Test / 153 \\
Kolmogorov--Smirnoff Test / 157 \\
Mean Absolute Deviation Test / 158 \\
The Logarithmic Basis of Benford's Law / 160 \\
Creating a Perfect Synthetic Benford Set / 163 \\
Mantissa Arc Test / 165 \\
Conclusions / 169 \\
Chapter 8: Examples of Fraudulent Data / 171 \\
The Inside Story / 172 \\
The Vendor Who Never Was / 174 \\
Not Paying Attention / 175 \\
Funny Money / 177 \\
The Heart of the Matter / 181 \\
Going the Extra Mile / 182 \\
Laugh All the Way to the Bank / 184 \\
Culture Shock / 187 \\
Having a Bad Hair Day / 189 \\
An Unclean Bill of Health / 191 \\
Turning the Table on Tax Evasion / 193 \\
Conclusions / 196 \\
Chapter 9: Fraudulent Financial Statements, Part I /
199 \\
Number Crunching / 200 \\
Wrong Numbers / 205 \\
A Look at Enron's and AIG's Numbers / 207 \\
Figuring Out the Controllers / 210 \\
Conclusions / 213 \\
Chapter 10: Fraudulent Financial Statements, Part II /
215 \\
Digital Yoga by Absaroka / 216 \\
Can't See the Forest for the Trees / 218 \\
Digit a Little Deeper into Papua New Guinea / 221 \\
The Good, the Bad, and the Ugly / 227 \\
Dig a Little Deeper / 233 \\
There Are More Questions than Answers / 237 \\
Conclusions / 244 \\
Chapter 11: Madoff and Other Ponzi Schemes / 247 \\
The Madoff Claims / 248 \\
Don't Bank on Kaupthing / 249 \\
The Whole Ball of Waxenberg / 252 \\
General Motors Demoted to Private / 253 \\
Chrysler Unable to Dodge Bankruptcy / 255 \\
Discussion of the Claims Results / 258 \\
A Review of the Madoff Returns / 259 \\
Apple, Dell, Berkshire, and Benford / 262 \\
Discussion of the Returns Results / 265 \\
Chapter 12: Earth Science and Income Tax Applications /
267 \\
Still Waters Run Deep / 268 \\
The Lay of the Lake / 274 \\
For a Few Dollars Less / 281 \\
A Clean Bill of Clinton / 286 \\
Conclusions / 290 \\
Chapter 13: Future Directions and Conclusions / 293 \\
My Law / 295 \\
Insights into Number Invention / 300 \\
Lehman's Charitable Gifts / 306 \\
The Bottom Line / 310 \\
Glossary of Selected Terms / 315 \\
References / 323 \\
Index / 327",
}
@InCollection{Odueke:2012:TFA,
author = "Adeola Odueke and George R. S. Weir",
editor = "George R. S. Weir and A. Al-Nemrat",
booktitle = "Issues in Cybercrime, Security and Digtal Forensics",
title = "Triage in Forensic Accounting using {Zipf's Law}",
publisher = "University of Strathclyde Publishing",
address = "Glasgow, UK",
bookpages = "????",
pages = "33--43",
year = "2012",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Feb 19 06:11:19 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.cis.strath.ac.uk/cis/research/publications/papers/strath_cis_publication_2590.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Regan:2012:BLB,
author = "K. W. Regan",
title = "{Benford's Law} and Baseball",
howpublished = "Web document",
day = "29",
month = jul,
year = "2012",
bibdate = "Sat Feb 16 12:48:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rjlipton.wordpress.com/2012/07/29/benfords-law-and-baseball/",
acknowledgement = ack-nhfb,
}
@Article{Ross:2012:FDS,
author = "Kenneth A. Ross",
title = "First Digits of Squares and Cubes",
journal = j-MATH-MAG,
volume = "85",
number = "1",
pages = "37--43",
month = feb,
year = "2012",
CODEN = "MAMGA8",
ISSN = "0025-570X",
ISSN-L = "0025-570X",
bibdate = "Tue Feb 19 06:14:55 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.maa.org/history/presidents/ross.html",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
keywords = "Benford's Law",
remark = "The author was President of the Mathematical
Association of America (1995--1996).",
}
@Article{Schupfer:2012:FWG,
author = "G. Sch{\"u}pfer and J. Hein and M. Casutt and L.
Steiner and C. Konrad",
title = "{Vom Finanz- zum Wissenschaftsbetrug: Methode, den
Irrungen in der medizinischen Literatur beizukommen}.
({German}) [{From} financial to scientific fraud:
Method to overcome errors in the medical literature]",
journal = "Der Anaesthesist",
volume = "61",
number = "6",
pages = "537--542",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1007/s00101-012-2028-y",
ISSN = "0003-2417 (print), 1432-055X (electronic)",
ISSN-L = "0003-2417",
bibdate = "Wed Jun 20 14:26:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "https://link.springer.com/journal/101",
keywords = "Benford's law; distribution; Medicine; scientific
fraud; statistics",
language = "German",
}
@Article{Shelburne:2012:ED,
author = "Brian Shelburne",
title = "The {ENIAC}'s 1949 Determination of $ \pi $",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "99",
number = "PrePrints",
year = "2012",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/MAHC.2011.61",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Fri Feb 3 15:38:23 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
abstract = "In January 1950, George W. Reitwiesner published ``An
ENIAC Determination of $ \pi $ and $e$ to more than
2000 Decimal Places'' in Mathematical Tables and Other
Aides to Computation \cite{Reitwiesner:1950:EDM} which
described the first use of a computer, the ENIAC, to
calculate the decimal expansion of $ \pi $. Since the
history of $ \pi $ stretches back over thousands of
years, the use of the ENIAC to determine $ \pi $ is an
important historical and technological milestone. It is
especially interesting since the ENIAC was not designed
to perform this type of calculation as it could only
store 200 decimal digits while the determination of e
and $ \pi $ required manipulating numbers 2000+ digits
long. Starting with Reitwiesner's description of the
calculation, the known architecture of the ENIAC, how
it was programmed, and the mathematics used, we examine
why the calculation was undertaken, how the calculation
had to be done, and what was subsequently learned.",
acknowledgement = ack-nhfb,
fjournal = "IEEE annals of the history of computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
pdfdate = "8 August 2011",
remark = "This paper contains an interesting survey of work on
the calculation of $ \pi $ up to the early 1950s, with
a detailed reconstruction of its determination on the
ENIAC. From page 1 of the paper: ``Early in June, 1949,
Professor John von Neumann expressed an interest in the
possibility that the ENIAC might sometime be employed
to determine the value of $ \pi $ and $e$ to many
decimal places with a view toward obtaining a
statistical measure of the randomness of the
distribution of the digits.'' From page 2: ``\ldots{}
Augustus De Morgan (1806--1871) who noticed the smaller
number of appearances of the digit 7 in Shank's 607
digit determination of $ \pi $. It was later determined
that Shank's determination had an error beginning at
the 528th digit.'' From page 11: ``A preliminary
investigation has indicated that the digits of $e$
deviate significantly from randomness (in the sense of
staying closer to their expected values than a random
sequence of this length normally would) while for $ \pi
$ no significant deviations have so far been
detected.'' See \cite{Metropolis:1950:STV} for that
analysis.",
}
@Article{Song:2012:QEM,
author = "Jongwoo Song and Seongjoo Song",
title = "A quantile estimation for massive data with
generalized {Pareto} distribution",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "56",
number = "1",
pages = "143--150",
day = "1",
month = jan,
year = "2012",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:18 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947311002477",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@InCollection{Sorell:2012:ZLV,
author = "C. Joseph Sorell",
editor = "Carol A. Chapelle",
booktitle = "The Encyclopedia of Applied Linguistics",
title = "{Zipf's Law} and Vocabulary",
publisher = pub-WILEY,
address = pub-WILEY:adr,
year = "2012",
DOI = "https://doi.org/10.1002/9781405198431.wbeal1302",
ISBN = "1-4051-9843-5",
ISBN-13 = "978-1-4051-9843-1",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1002/9781405198431",
keywords = "child language; computational linguistics; corpus;
pragmatics; second language acquisition; vocabulary",
}
@Article{Sottili:2012:BLT,
author = "Gianluca Sottili and Danilo M. Palladino and Biagio
Giaccio and Paolo Messina",
title = "{Benford's Law} in Time Series Analysis of Seismic
Clusters",
journal = j-MATH-GEOSCI,
volume = "44",
number = "5",
pages = "619--634",
month = jul,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11004-012-9398-1",
ISSN = "1874-8953 (print), 1874-8961 (electronic)",
ISSN-L = "1874-8953",
bibdate = "Tue Feb 19 06:15:52 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11004-012-9398-1",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Geosciences",
journal-URL = "http://link.springer.com/journal/11004",
}
@MastersThesis{Stanton:2012:DFU,
author = "Gabriella Stanton",
title = "Detecting Fraud: Utilizing New Technology to Advance
the Audit Profession",
type = "Honors thesis",
school = "University of New Hampshire",
address = "Durham, NH 03824, USA",
pages = "26",
month = "Spring",
year = "2012",
bibdate = "Thu Oct 13 09:10:26 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://scholars.unh.edu/cgi/viewcontent.cgi?article=1017&context=honors",
acknowledgement = ack-nhfb,
advisor = "Jake Rose",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Strauch:2012:UP,
author = "O. Strauch",
title = "Unsolved Problems",
journal = "Uniform Distribution Theory",
volume = "??",
number = "??",
publisher = "Mathematical Institute of the Slovak Academy of
Sciences and BOKU --- University of Natural Resources
and Life Sciences",
address = "Bratislava, Slovakia and Vienna, Austria",
pages = "1--98",
month = "????",
year = "2012",
DOI = "????",
ISSN = "1336-913X",
ISSN-L = "1336-913X",
bibdate = "Tue Feb 19 06:17:17 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unsolved Problems Section on the home page of
\booktitle{Uniform Distribution Theory}.",
URL = "http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://www.boku.ac.at/MATH/udt/",
}
@InProceedings{Taimori:2012:PTS,
author = "A. Taimori and F. Razzazi and A. Behrad and A. Ahmadi
and M. Babaie-Zadeh",
booktitle = "2012 IEEE International Symposium on Signal Processing
and Information Technology (ISSPIT)",
title = "A proper transform for satisfying {Benford's Law} and
its application to double {JPEG} image forensics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "000240--000244",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1109/ISSPIT.2012.6621294",
ISSN = "2162-7843",
ISSN-L = "2162-7843",
bibdate = "Sat Sep 10 11:40:17 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ieeexplore.ieee.org/document/6621294/",
acknowledgement = ack-nhfb,
keywords = "2D discrete cosine transform; Benford law; Benford's
Law; data compression; discrete cosine transform;
discrete cosine transforms; Discrete wavelet
transforms; double JPEG; double JPEG image forensics;
filtering theory; image coding; image forensics; image
manipulation; Kullback-Leibler divergence; Lighting;
Matched filters; natural image data; normalized cross
correlation; Pearson chi-square test statistic;
significant digits statistics; single compressed
images; statistical analysis; statistical fitness
criteria; transform domain; variance filter; variance
filtering",
}
@Article{Tavangar:2012:SUC,
author = "Mahdi Tavangar and Majid Asadi",
title = "Some unified characterization results on the
generalized {Pareto} distributions based on generalized
order statistics",
journal = j-METRIKA,
volume = "75",
number = "7",
pages = "997--1007",
month = oct,
year = "2012",
CODEN = "MTRKA8",
DOI = "https://doi.org/10.1007/s00184-011-0364-6",
ISSN = "0026-1335 (print), 1435-926X (electronic)",
ISSN-L = "0026-1335",
bibdate = "Mon Feb 2 16:28:42 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/metrika.bib",
URL = "http://link.springer.com/article/10.1007/s00184-011-0364-6",
acknowledgement = ack-nhfb,
fjournal = "Metrika",
journal-URL = "http://link.springer.com/journal/184",
}
@Article{Valadier:2012:BPR,
author = "Michel Valadier",
title = "The {Benford} phenomenon for random variables.
{Discussion} of {Feller}'s way",
journal = "ArXiv e-prints",
pages = "23",
day = "9",
month = mar,
year = "2012",
bibdate = "Tue Feb 19 06:20:32 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1203.2518",
acknowledgement = ack-nhfb,
}
@Article{Wang:2012:LPW,
author = "Dongbo Wang and Danhao Zhu and Xinning Su",
title = "{Lotka} phenomenon in the words' syntactic
distribution complexity",
journal = j-SCIENTOMETRICS,
volume = "90",
number = "2",
pages = "483--498",
month = feb,
year = "2012",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-011-0546-z",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:38 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-011-0546-z",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Book{Wapner:2012:UEC,
author = "Leonard M. Wapner",
title = "Unexpected expectations: the curiosities of a
mathematical crystal ball",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xvi + 204",
year = "2012",
ISBN = "1-56881-721-5 (hardback)",
ISBN-13 = "978-1-56881-721-7 (hardback)",
LCCN = "QA95 .W34 2012",
bibdate = "Tue May 5 16:15:08 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Mathematical expectation or expected value represents
the long-term average numerical outcome to an
experiment performed a large number of times. Routinely
used in the physical sciences, business, and economics,
mathematical expectation has also been used to
calculate strategies in games of chance and even to
justify the belief in God. How can this expression,
which is trivial to calculate, have such broad
applications and at the same time yield unexpected
irresolvable paradoxes? In an easily accessible
presentation, this book explores these puzzling and
entertaining mysteries.",
acknowledgement = ack-nhfb,
author-dates = "1948--",
subject = "Mathematical recreations",
tableofcontents = "Dedication \\
Table of Contents \\
Acknowledgments \\
The Crystal Ball \\
1. Looking Back \\
2. The ABCs of E \\
3. Doing the Right Thing \\
4. Aversion Perversion \\
5. And the Envelope Please! \\
6. Parrondo's Paradox: You Can Win for Losing \\
7. Imperfect Recall \\
8. Non-zero-sum Games: The Inadequacy of Individual
Rationality \\
9. Newcomb's Paradox \\
10. Benford's Law \\
Let the Mystery Be! \\
Bibliography",
}
@Article{Zea:2012:BEP,
author = "Luz Milena Zea and Rodrigo B. Silva and Marcelo
Bourguignon and Andrea M. Santos and Gauss M.
Cordeiro",
title = "The Beta Exponentiated {Pareto} Distribution with
Application to Bladder Cancer Susceptibility",
journal = j-INT-J-STAT-PROBAB,
volume = "1",
number = "2",
pages = "8--??",
month = "????",
year = "2012",
CODEN = "????",
ISSN = "1927-7032 (print), 1927-7040 (electronic)",
ISSN-L = "1927-7032",
bibdate = "Tue Jun 9 14:40:16 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/intjstatprobab.bib",
URL = "http://www.ccsenet.org/journal/index.php/ijsp/article/view/16301",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Statistics and Probability",
journal-URL = "http://www.ccsenet.org/journal/index.php/ijsp/issue/archive",
}
@Article{Zeng:2012:TMB,
author = "Jianping Zeng and Jiangjiao Duan and Wenjun Cao and
Chengrong Wu",
title = "Topics modeling based on selective {Zipf}
distribution",
journal = j-EXPERT-SYST-APPL,
volume = "39",
number = "7",
pages = "6541--6546",
day = "1",
month = jun,
year = "2012",
CODEN = "ESAPEH",
DOI = "https://doi.org/10.1016/j.eswa.2011.12.051",
ISSN = "0957-4174 (print), 1873-6793 (electronic)",
ISSN-L = "0957-4174",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0957417411017222",
acknowledgement = ack-nhfb,
fjournal = "Expert Systems with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/09574174",
keywords = "Zipf's Law",
}
@Article{Abu-Dayyeh:2013:ESS,
author = "Walid Abu-Dayyeh and Aissa Assrhani and Kamarulzaman
Ibrahim",
title = "Estimation of the shape and scale parameters of
{Pareto} distribution using ranked set sampling",
journal = j-STAT-PAPERS,
volume = "54",
number = "1",
pages = "207--225",
month = feb,
year = "2013",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-011-0420-3",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:38 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-011-0420-3",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{Alali:2013:BLA,
author = "Fatima A. Alali and Silvia Romero",
title = "{Benford's Law}: Analyzing a Decade of Financial
Data",
journal = "Journal of Emerging Technologies in Accounting",
volume = "10",
number = "1",
pages = "1--39",
month = dec,
year = "2013",
DOI = "https://doi.org/10.2308/jeta-50749",
ISSN = "1554-1908 (print), 1558-7940 (electronic)",
ISSN-L = "1554-1908",
bibdate = "Thu Oct 13 08:07:00 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaajournals.org/doi/pdf/10.2308/jeta-50749",
acknowledgement = ack-nhfb,
}
@Article{Andriotis:2013:JSD,
author = "Panagiotis Andriotis and George Oikonomou and Theo
Tryfonas",
title = "{JPEG} steganography detection with {Benford's Law}",
journal = "Digital Investigation",
volume = "9",
number = "3--4",
pages = "246--257",
year = "2013",
DOI = "https://doi.org/10.1016/j.diin.2013.01.005",
ISSN = "1742-2876 (print), 1873-202X (electronic)",
ISSN-L = "1742-2876",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1742287613000066",
abstract = "In this paper we present a novel approach to the
problem of steganography detection in {JPEG} images by
applying a statistical attack. The method is based on
the empirical Benford's Law and, more specifically, on
its generalized form. We prove and extend the validity
of the logarithmic rule in colour images and introduce
a blind steganographic method which can flag a file as
a suspicious stego-carrier. The proposed method
achieves very high accuracy and speed and is based on
the distributions of the first digits of the quantized
Discrete Cosine Transform coefficients present in
JPEGs. In order to validate and evaluate our algorithm,
we developed steganographic tools which are able to
analyse image files and we subsequently applied them on
the popular Uncompressed Colour Image Database.
Furthermore, we demonstrate that not only can our
method detect steganography but, if certain criteria
are met, it can also reveal which steganographic
algorithm was used to embed data in a {JPEG} file.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Data hiding; Generalized Benford's Law;
Quantized DCT coefficients; Quantized {DCT}
coefficients; Steganalysis; Steganography detection",
}
@Misc{Anonymous:2013:NBL,
author = "Anonymous",
title = "Number 1 and {Benford's Law} --- Numberphile",
howpublished = "Web video lecture.",
day = "20",
month = jan,
year = "2013",
bibdate = "Fri Oct 09 06:28:24 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.youtube.com/watch?v=XXjlR2OK1kM",
acknowledgement = ack-nhfb,
}
@Article{Aron:2013:CFM,
author = "Jacob Aron",
title = "Crime-fighting maths law confirms planetary riches",
journal = j-NEW-SCIENTIST,
volume = "220",
number = "2945",
pages = "12-",
year = "2013",
CODEN = "NWSCAL",
DOI = "https://doi.org/10.1016/S0262-4079(13)62775-X",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S026240791362775X",
abstract = "The statistical tool called Benford's law has been
shown to work for our catalogue of exoplanets, backing
up predictions that the galaxy is brimming with alien
worlds.",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
}
@Article{Banks:2013:BLM,
author = "David G. Banks",
title = "{Benford's Law} Made Easy: Common Software Eases use
of Fraud Search Theorem",
journal = "Fraud Magazine",
volume = "??",
number = "??",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2013",
ISSN = "1553-6645",
ISSN-L = "1553-6645",
bibdate = "Sun Feb 17 08:11:01 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fraud-magazine.com/article.aspx?id=4294968485",
acknowledgement = ack-nhfb,
fjournal = "Fraud Magazine. {A} Publication of the Association of
Certified Fraud Examiners",
}
@Article{Birajdar:2013:DIF,
author = "Gajanan K. Birajdar and Vijay H. Mankar",
title = "Digital image forgery detection using passive
techniques: A survey",
journal = "Digital Investigation",
volume = "10",
number = "3",
pages = "226--245",
year = "2013",
DOI = "https://doi.org/10.1016/j.diin.2013.04.007",
ISSN = "1742-2876 (print), 1873-202X (electronic)",
ISSN-L = "1742-2876",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1742287613000364",
abstract = "Today manipulation of digital images has become easy
due to powerful computers, advanced photo-editing
software packages and high resolution capturing
devices. Verifying the integrity of images and
detecting traces of tampering without requiring extra
prior knowledge of the image content or any embedded
watermarks is an important research field. An attempt
is made to survey the recent developments in the field
of digital image forgery detection and complete
bibliography is presented on blind methods for forgery
detection. Blind or passive methods do not need any
explicit priori information about the image. First,
various image forgery detection techniques are
classified and then its generalized structure is
developed. An overview of passive image authentication
is presented and the existing blind forgery detection
techniques are reviewed. The present status of image
forgery detection technique is discussed along with a
recommendation for future research.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Image authentication; Image forensic;
Image manipulation detection; Image tampering
detection; Passive/blind image forgery detection",
}
@InCollection{Cali:2013:FA,
author = "J. Cali",
editor = "Jay A. Siegel and Pekka J. Saukko and Max M. Houck",
booktitle = "Encyclopedia of Forensic Sciences",
title = "Forensic Accounting",
publisher = "Academic Press",
address = "Waltham",
pages = "423--431",
year = "2013",
DOI = "https://doi.org/10.1016/B978-0-12-382165-2.00218-X",
ISBN = "0-12-382166-5",
ISBN-13 = "978-0-12-382166-9",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B978012382165200218X",
abstract = "Forensic accounting is defined as the action of
identifying, recording, settling, extracting, sorting,
reporting, and verifying past financial data or other
accounting activities for settling current or
prospective legal disputes or using such past financial
data for projecting future financial data to settle
legal disputes. Forensic accountants practice a special
area of accountancy that requires them to have
knowledge of the courtroom, rules of evidence, and
investigative techniques in addition to generally
accepted accounting principles and generally accepted
auditing standards. The practice of forensic accounting
is used in criminal investigations to prosecute fraud,
embezzlement, ponzi, and terrorist-financing schemes.
While in civil litigation disputes, forensic accounting
methods are employed to determine the value of economic
damages related to insurance claims, lost profits,
bankruptcy, qui-tam actions, and divorce. The ultimate
role of the forensic accountant is to use their
forensic accounting skills to prepare a written report
and to provide expert testimony based on the findings
in the written report that will help the judge and the
members of the jury to better understand complex
financial transactions.",
acknowledgement = ack-nhfb,
keywords = "Arson for profit; Bank Secrecy Act; Benford's Law;
Business interruption claims; Civil litigation
disputes; Currency transaction reports; Divorce;
Economic damages; Financial motive; FinCEN; Forensic
accounting; Forensic auditing; Fraud; Fraud
examination; Fraud investigation; Fraud schemes; Hidden
assets; Income from unknown sources; Income
reconstruction; Insurance fraud; Life care plans; Lost
profit computations; Money laundering; Mortgage fraud;
Offshore accounts; Patriot Act; Ponzi scheme; Qui-tam
actions; Securities fraud; Specified unlawful acts;
Suspicious activity reports",
}
@Article{Deligny:2013:RRL,
author = "Hugues Deligny and Paul Jolissaint",
title = "Relations de r{\'e}currence lin{\'e}aires,
primitivit{\'e} et loi de {Benford}. ({French})
[{Linear} recurrence relations, primitivity, and
{Benford}'s law]",
journal = j-ELEM-MATH,
volume = "68",
number = "1",
pages = "9--21",
year = "2013",
DOI = "https://doi.org/10.4171/EM/213",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "11K36",
MRnumber = "3016461",
MRreviewer = "Simon Kristensen",
bibdate = "Thu Feb 14 07:02:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{deVries:2013:CLN,
author = "Pepijn de Vries and Albertinka J. Murk",
title = "Compliance of {LC50} and {NOEC} data with {Benford's
Law}: An indication of reliability?",
journal = "Ecotoxicology and Environmental Safety",
volume = "98",
number = "0",
pages = "171--178",
year = "2013",
DOI = "https://doi.org/10.1016/j.ecoenv.2013.09.002",
ISSN = "0147-6513 (print), 1090-2414 (electronic)",
ISSN-L = "0147-6513",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0147651313003692",
abstract = "Reliability of research data is essential, especially
when potentially far-reaching conclusions will be based
on them. This is also, amongst others, the case for
ecotoxicological data used in risk assessment.
Currently, several approaches are available to classify
the reliability of ecotoxicological data. The process
of classification, such as using the Klimisch score, is
time-consuming and focuses on the application of
standardised protocols and the documentation of the
study. The presence of irregularities and the integrity
of the performed work, however, are not addressed. The
present study shows that Benford's Law, based on the
occurrence of first digits following a logarithmic
scale, can be applied to ecotoxicity test data for
identifying irregularities. This approach is already
successfully applied in accounting. Benford's Law can
be used as reliability indicator, in addition to
existing reliability classifications. The law can be
used to efficiently trace irregularities in large data
sets of interpolated (no) effect concentrations such as
LC50s (possibly the result of data manipulation),
without having to evaluate the source of each
individual record. Application of the law to systems in
which large amounts of toxicity data are registered
(e.g., European Commission Regulation concerning the
Registration, Evaluation, Authorisation and Restriction
of Chemicals) can therefore be valuable.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Data evaluation; LC50; NOEC; Quality
assessment; Reliability; {LC50}; {NOEC}",
}
@Article{diGiovanni:2013:FET,
author = "Julian di Giovanni and Andrei A. Levchenko",
title = "Firm entry, trade, and welfare in {Zipf}'s world",
journal = j-J-INT-ECON,
volume = "89",
number = "2",
pages = "283--296",
day = "15",
month = mar,
year = "2013",
CODEN = "JIECBE",
DOI = "https://doi.org/10.1016/j.jinteco.2012.08.002",
ISSN = "0022-1996 (print), 1873-0353 (electronic)",
ISSN-L = "0022-1996",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022199612001365",
acknowledgement = ack-nhfb,
fjournal = "Journal of International Economics",
journal-URL = "http://www.sciencedirect.com/science/journal/09247963",
keywords = "Zipf's Law",
}
@Article{Egghe:2013:FRB,
author = "L. Egghe",
title = "The functional relation between the impact factor and
the uncitedness factor revisited",
journal = j-J-INFORMETRICS,
volume = "7",
number = "1",
pages = "183--189",
year = "2013",
DOI = "https://doi.org/10.1016/j.joi.2012.10.007",
ISSN = "1751-1577 (print), 1875-5879 (electronic)",
ISSN-L = "1751-1577",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1751157712000909",
abstract = "We give a heuristic proof of the relation between the
impact factor (IF) and the uncitedness factor (U), the
fraction of the papers that are uncited: $ U = 1 / (1 +
I F) $. This generalizes the proof of Hsu and Huang
[Physica A 391, 2129 2134, 2012] who obtain the same
result but based on the assumption of the validity of
the Matthew-effect. This new informetric function opens
the discussion on universal informetric laws,
distribution dependent laws and parameter dependent
laws of which examples from the informetrics literature
are given.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informetrics",
journal-URL = "http://www.sciencedirect.com/science/journal/17511577",
keywords = "Benford's Law; Distribution dependent law; Impact
factor; Parameter dependent law; Uncitedness factor;
Universal informetric law",
}
@Article{Eliazar:2013:BLP,
author = "Iddo I. Eliazar",
title = "{Benford's Law}: A {Poisson} perspective",
journal = j-PHYSICA-A,
volume = "392",
number = "16",
pages = "3360--3373",
year = "2013",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2013.03.057",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "62E10 (60G55 82C05)",
MRnumber = "3069159",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437113002902",
abstract = "Benford's Law is a counterintuitive statistical law
asserting that the distribution of leading digits,
taken from a large ensemble of positive numerical
values that range over many orders of scale, is
logarithmic rather than uniform (as intuition
suggests). In this paper we explore Benford's Law from
a Poisson perspective, considering ensembles of
positive numerical values governed by Poisson-process
statistics. We show that this Poisson setting naturally
accommodates Benford's Law and: (i) establish a Poisson
characterization and a Poisson multidigit-extension of
Benford's Law; (ii) study a system-invariant
leading-digit distribution which generalizes Benford's
Law, and establish a Poisson characterization and a
Poisson multidigit-extension of this distribution;
(iii) explore the universal emergence of the
system-invariant leading-digit distribution, couple
this universal emergence to the universal emergence of
the Weibull and Fr{\'e}chet extreme-value
distributions, and distinguish the special role of
Benford's Law in this universal emergence; (iv) study
the continued-fractions counterpart of the
system-invariant leading-digit distribution, and
establish a Poisson characterization of this
distribution; and (v) unveil the elemental connection
between the system-invariant leading-digit distribution
and its continued-fractions counterpart. This paper
presents a panoramic Poisson approach to Benford's Law,
to its system-invariant generalization, and to its
continued-fractions counterpart.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Continued fractions; Extreme-value
statistics; Invariance; Poisson limit theorems;
Power-laws; Universality",
}
@Article{Fernandez:2013:SPC,
author = "Arturo J. Fern{\'a}ndez",
title = "Smallest {Pareto} confidence regions and
applications",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "62",
number = "??",
pages = "11--25",
month = jun,
year = "2013",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:41 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947312004501",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@InCollection{Gangopadhyay:2013:EZL,
author = "Kausik Gangopadhyay and Banasri Basu",
title = "Evolution of {Zipf}'s law for {Indian} urban
agglomerations via-{\`a}-vis {Chinese} urban
agglomerations",
crossref = "Abergel:2013:ESR",
pages = "119--129",
year = "2013",
DOI = "https://doi.org/10.1007/978-88-470-2553-0_8",
MRclass = "91B80",
MRnumber = "2963609",
bibdate = "Mon Feb 18 16:48:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "New Econ. Windows",
acknowledgement = ack-nhfb,
}
@Article{GomesdaSilva:2013:SAS,
author = "Carlos {Gomes da Silva} and Pedro M. R. Carreira",
title = "Selecting Audit Samples Using {Benford's Law}",
journal = j-AUDITING,
volume = "32",
number = "2",
pages = "53--65",
month = may,
year = "2013",
DOI = "https://doi.org/10.2308/ajpt-50340",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Thu Oct 13 08:05:18 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaajournals.org/doi/pdf/10.2308/ajpt-50340",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@TechReport{Grammatikos:2013:UBL,
author = "T. Grammatikos and N. I. Papanikolaou",
title = "Using {Benford's Law} to Detect Fraudulent Practices
in Banking",
type = "SSRN Scholarly Paper",
number = "2352775",
institution = "Social Science Research Network",
address = "Rochester, NY, USA",
year = "2013",
bibdate = "Sat Sep 10 11:54:44 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InProceedings{Haferkorn:2013:HVA,
author = "Martin Haferkorn",
editor = "Fethi Rabhi and Peter Gomber",
booktitle = "{Enterprise applications and services in the finance
industry: 6th International Workshop, FinanceCom 2012,
Barcelona, Spain, June 10, 2012. Revised papers}",
title = "Humans vs. Algorithms --- Who Follows
{Newcomb--Benford's Law} Better with Their Order
Volume?",
chapter = "4",
publisher = pub-SV,
address = pub-SV:adr,
pages = "61--70",
year = "2013",
DOI = "https://doi.org/10.1007/978-3-642-36219-4_4",
ISBN = "3-642-36219-2",
ISBN-13 = "978-3-642-36219-4",
LCCN = "HG173 .I58 2012",
bibdate = "Wed Feb 13 19:15:28 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4",
acknowledgement = ack-nhfb,
book-URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4",
remark = "This may be the first publication to reference this
bibliography. It examines trading patterns of several
days on the German Stock Exchange (Deutsche B{\"o}rse),
with a total volume of almost 10 million trades, split
almost equally between human and algorithmic traders.
It finds that the algorithmic trades follow Benford's
Law closely, but the human trades do not. It points out
that algorithmic trading could be manipulated to make
it look more like human trades, so as not to alert
competitors to its actions.",
subject = "Financial services industry; Information technology;
Congresses; Data processing",
}
@Article{Hofmarcher:2013:FSD,
author = "P. Hofmarcher and K. Hornik",
title = "First Significant Digits and the Credit Derivative
Market During the Financial Crisis",
journal = "Contemporary Economics",
volume = "7",
number = "2",
pages = "21--29",
month = "????",
year = "2013",
DOI = "https://doi.org/10.5709/ce.1897-9254.80",
bibdate = "Sat Sep 10 12:11:42 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286063",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Hubert:2013:DID,
author = "Mia Hubert and Goedele Dierckx and Dina Vanpaemel",
title = "Detecting influential data points for the {Hill}
estimator in {Pareto}-type distributions",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "65",
number = "??",
pages = "13--28",
month = sep,
year = "2013",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:43 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016794731200285X",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Khosravani:2013:DBD,
author = "Azar Khosravani and Constantin Rasinariu",
title = "$n$-digit {Benford} distributed random variables",
journal = j-ADV-APPL-STAT,
volume = "36",
number = "2",
pages = "119--130",
month = oct,
year = "2013",
CODEN = "????",
ISSN = "0972-3617",
ISSN-L = "0972-3617",
MRclass = "60E05 (11K45)",
MRnumber = "3134635",
bibdate = "Wed Aug 16 09:06:43 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.pphmj.com/abstract/7887.htm",
acknowledgement = ack-nhfb,
fjournal = "Advances and Applications in Statistics",
journal-URL = "http://www.pphmj.com/journals/contents/adas.htm",
}
@Article{Kossovsky:2013:RQO,
author = "A. Ely Kossovsky",
title = "On the Relative Quantities Occurring within Physical
Data Sets",
journal = "arxiv.org",
month = may,
year = "2013",
bibdate = "Thu Oct 13 07:31:45 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1305.1893E",
acknowledgement = ack-nhfb,
keywords = "Mathematics - Statistics Theory",
primaryclass = "math.ST",
}
@Article{Lu:2013:DZH,
author = "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou",
title = "Deviation of {Zipf}'s and {Heaps' Laws} in Human
Languages with Limited Dictionary Sizes",
journal = j-SCI-REP,
volume = "3",
number = "??",
pages = "1--7",
month = "????",
year = "2013",
CODEN = "SRCEC3",
DOI = "https://doi.org/10.1038/srep01082",
ISSN = "2045-2322",
bibdate = "Tue Feb 26 07:39:15 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html",
accepted = "21 December 2012",
acknowledgement = ack-nhfb,
articleno = "1082",
fjournal = "Scientific Reports",
journal-URL = "http://www.nature.com/srep/",
onlinedate = "30 January 2013",
received = "11 June 2012",
}
@InProceedings{Mebane:2013:SDI,
author = "Walter R. {Mebane, Jr.} and T. Kent",
editor = "????",
booktitle = "{Proceedings of the 2013 Annual Meeting of the Midwest
Political Science Association, Chicago, IL, April
11--14, 2013}",
title = "Second Digit Implications of Voters' Strategies and
Mobilizations in the {United States} during the 2000s",
publisher = "????",
address = "????",
pages = "??--??",
year = "2013",
bibdate = "Sat Sep 10 14:33:23 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Michalski:2013:DCF,
author = "T. Michalski and G. Stoltz",
title = "Do Countries Falsify Economic Data Strategically?
{Some} Evidence That They Might",
journal = j-REV-ECON-STAT,
volume = "95",
number = "2",
pages = "591--616",
month = may,
year = "2013",
CODEN = "RECSA9",
DOI = "https://doi.org/10.1162/REST_a_00274",
ISSN = "0034-6535 (print), 1530-9142 (electronic)",
ISSN-L = "0034-6535",
bibdate = "Sat Sep 10 14:35:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.mitpressjournals.org/doi/abs/10.1162/REST_a_00274",
acknowledgement = ack-nhfb,
fjournal = "Review of Economics and Statistics",
journal-URL = "http://www.jstor.org/journal/revieconstat;
http://www.mitpressjournals.org/loi/rest",
keywords = "Benford's Law",
}
@InProceedings{Milani:2013:AAB,
author = "S. Milani and M. Tagliasacchi and S. Tubaro",
booktitle = "2013 IEEE International Conference on Acoustics,
Speech and Signal Processing",
title = "Antiforensics attacks to {Benford's Law} for the
detection of double compressed images",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3053--3057",
month = may,
year = "2013",
DOI = "https://doi.org/10.1109/ICASSP.2013.6638219",
ISSN = "1520-6149",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "antiforensics attack strategy; Benford's law; data
compression; Detectors; digit statistics; digital
forensics; double image compression detectors; first
digit law; Forensics; fraud detection methods; image
coding; Image coding; Image reconstruction; object
detection; PSNR; Quantization (signal); statistical
analysis; Transform coding",
}
@Book{Newbold:2013:SBE,
author = "Paul Newbold and William L. (William Lee) Carlson and
Betty Thorne",
title = "Statistics for Business and Economics",
publisher = "Pearson Education",
address = "Harlow, Essex, UK",
edition = "Eighth",
pages = "792",
year = "2013",
ISBN = "0-273-76706-2",
ISBN-13 = "978-0-273-76706-0",
LCCN = "HF1017 .N48 2013",
bibdate = "Fri Mar 22 09:03:53 MDT 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-mjn # "\slash " # ack-nhfb,
keywords = "Benford's Law",
subject = "Commercial statistics; Economics; Statistical methods;
Statistics",
}
@Article{Norris:2013:NRA,
author = "Pippa Norris",
title = "The new research agenda studying electoral integrity",
journal = j-ELECT-STUDIES,
volume = "32",
number = "4",
pages = "563--575",
year = "2013",
DOI = "https://doi.org/10.1016/j.electstud.2013.07.015",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Special Symposium: The new research agenda on
electoral integrity",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379413001157",
abstract = "A rapidly-growing research agenda shared by scholars
and applied policy analysts is beginning to explore
three questions: when do elections meet standards of
electoral integrity? When do they fail to do so? And
what can be done to mitigate these problems? To address
these issues, Part 1 in this paper outlines the concept
of electoral integrity, proposing a comprehensive and
broad definition founded upon global norms and
international conventions. Part 2 argues that several
sub-fields contribute towards the study of electoral
integrity, although commonly fragmented at present,
including (i) public sector management; (ii) political
culture; (iii) comparative institutions; and (iv)
security studies. The emerging research agenda focused
on electoral integrity, cutting across these
conventional disciplinary boundaries, is characterized
by its problem-oriented focus and global comparative
framework, as well as by its use of pluralistic methods
and analytical techniques. Part 3 outlines the
contribution of papers in this symposium. The
conclusion summarizes the key features of this new
research agenda studying electoral integrity.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Benford's Law; Corruption; Democracy and
democratization; Elections; Electoral integrity; Fraud;
Voting",
}
@Article{Ozer:2013:BLD,
author = "G. Ozer and B. Babacan",
title = "{Benford's Law} and Digital Analysis: Application on
{Turkish} Banking Sector",
journal = "Business and Economics Research Journal",
volume = "4",
number = "1",
pages = "29--41",
month = "",
year = "2013",
DOI = "",
ISSN = "1309-2448",
bibdate = "Sat Sep 10 15:29:55 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "",
acknowledgement = ack-nhfb,
journal-URL = "http://www.berjournal.com/",
keywords = "Benford's Law",
}
@Article{Pain:2013:RSA,
author = "Jean-Christophe Pain",
title = "Regularities and symmetries in atomic structure and
spectra",
journal = "High Energy Density Physics",
volume = "9",
number = "3",
pages = "392--401",
month = sep,
year = "2013",
CODEN = "HEDPBW",
DOI = "https://doi.org/10.1016/j.hedp.2013.04.007",
ISSN = "1574-1818 (print), 1878-0563 (electronic)",
ISSN-L = "1574-1818",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1574181813000475",
abstract = "The use of statistical methods for the description of
complex quantum systems was primarily motivated by the
failure of a line-by-line interpretation of atomic
spectra. Such methods reveal regularities and trends in
the distributions of levels and lines. In the past,
much attention was paid to the distribution of energy
levels (Wigner surmise, random-matrix model). However,
information about the distribution of the lines (energy
and strength) is lacking. Thirty years ago, Learner
found empirically an unexpected law: the logarithm of
the number of lines whose intensities lie between
$^{2k}I_0$ and $^{2k + 1}I_0$, $ I_0$ being a reference
intensity and $k$ an integer, is a decreasing linear
function of $k$. In the present work, the fractal
nature of such an intriguing regularity is outlined and
a calculation of its fractal dimension is proposed.
Other peculiarities are also presented, such as the
fact that the distribution of line strengths follows
Benford's law of anomalous numbers, the existence of
additional selection rules (PH coupling), the symmetry
with respect to a quarter of the subshell in the
spin-adapted space (LL coupling) and the odd even
staggering in the distribution of quantum numbers,
pointed out by Bauche and Coss{\'e}.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.sciencedirect.com/science/journal/15741818",
keywords = "Atomic physics; Benford's Law; Fractals; Group theory;
High-energy-density matter; Hot plasmas; Symmetries",
}
@Article{Phatarfod:2013:SAB,
author = "Ravi Phatarfod",
title = "Some aspects of the {Benford} law of leading
significant digits",
journal = "The Mathematical Scientist",
volume = "38",
number = "2",
pages = "73--85",
year = "2013",
ISSN = "0312-3685 (print), 1475-6080 (electronic)",
ISSN-L = "0312-3685",
MRclass = "62P99 (11A63)",
MRnumber = "3184679",
bibdate = "Tue Jan 26 11:01:15 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://appliedprobability.org/content.aspx?Group=tms&Page=tmsabstracts38_2#one",
acknowledgement = ack-nhfb,
ajournal = "Math. Sci.",
fjournal = "The Mathematical Scientist",
journal-URL = "http://www.appliedprobability.org/content.aspx?Group=tms&Page=tms",
}
@Article{Piva:2013:OIF,
author = "Alessandro Piva",
title = "An Overview on Image Forensics",
journal = "ISRN Signal Processing",
volume = "2013",
number = "??",
pages = "496701",
month = "????",
year = "2013",
DOI = "https://doi.org/10.1155/2013/496701",
ISSN = "2090-5041 (print), 2090-505X (electronic)",
ISSN-L = "2090-5041",
bibdate = "Tue Feb 19 06:21:47 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.isrn.com/journals/sp/2013/496701/",
accepted = "26 November 2012",
acknowledgement = ack-nhfb,
fjournal = "International Scholarly Research Network Signal
Processing",
journal-URL = "http://www.isrn.com/journals/sp/",
keywords = "Benford's Law",
pagecount = "22",
received = "6 November 2012",
}
@Article{Rauch:2013:LME,
author = "Bernhard Rauch and M. G{\"o}ttsche and Florian {El
Mouaaouy}",
title = "{LIBOR} Manipulation --- Empirical Analysis of
Financial Market Benchmarks Using {Benford's Law}",
journal = "Social Sciences Research Network",
volume = "??",
number = "??",
pages = "26",
day = "5",
month = dec,
year = "2013",
DOI = "https://doi.org/10.2139/ssrn.2363895",
bibdate = "Sat Sep 10 15:58:05 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2363895",
acknowledgement = ack-nhfb,
keywords = "Benford's law; collusion; financial institutions;
inter-bank offered rates; manipulation; price-fixing",
}
@Article{Scollnik:2013:CTP,
author = "David P. M. Scollnik",
title = "Comments on two papers concerning estimation of the
parameters of the {Pareto} distribution in the presence
of outliers",
journal = j-STAT-METHODOL,
volume = "13",
number = "??",
pages = "1--11",
month = jul,
year = "2013",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:55 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312712000822",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Article{Slepkov:2013:BLT,
author = "Aaron D. Slepkov and Kevin B. Ironside and David
DiBattista",
title = "{Benford's Law}: Textbook Exercises and
Multiple-Choice Testbanks",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??",
day = "19",
month = nov,
year = "2013",
bibdate = "Tue Jan 26 09:56:51 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1311.4787v1",
abstract = "Benford's Law describes the finding that the
distribution of leading (or leftmost) digits of
innumerable datasets follows a well-defined logarithmic
trend, rather than an intuitive uniformity. In practice
this means that the most common leading digit is 1,
with an expected frequency of 30.1\%, and the least
common is 9, with an expected frequency of 4.6\%. The
history and development of Benford's Law is inexorably
linked to physics, yet there has been a dearth of
physics-related Benford datasets reported in the
literature. Currently, the most common application of
Benford's Law is in detecting number invention and
tampering such as found in accounting-, tax-, and
voter-fraud. We demonstrate that answers to
end-of-chapter exercises in physics and chemistry
textbooks conform to Benford's Law. Subsequently, we
investigate whether this fact can be used to gain
advantage over random guessing in multiple-choice
tests, and find that while testbank answers in
introductory physics closely conform to Benford's Law,
the testbank is nonetheless secure against such a
Benford's attack for banal reasons.",
acknowledgement = ack-nhfb,
}
@Article{Smith:2013:BNS,
author = "Aaron Carl Smith",
title = "{Benford--Newcomb} Subsequences for Fraud Detection",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??",
day = "22",
month = jan,
year = "2013",
bibdate = "Tue Jan 26 10:01:46 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1301.6086v1",
abstract = "Benford's law is frequently used to evaluate the
likihood that data is misrepresentative. Typically
statistical tests measure the likihood. Another method
of employing Benford's law is to compare the frequency
of leading digits to the probabilities of leading
digits over a subset of the natural numbers. This paper
proposes using the probabilities of leading digits from
uniform, natural numbers to establish interval criteria
for when to look more closely into the possibility of
misrepresentative data.",
acknowledgement = ack-nhfb,
}
@Article{Soo:2013:ZGG,
author = "Kwok Tong Soo",
title = "{Zipf}, {Gibrat} and geography: Evidence from {China},
{India} and {Brazil}",
journal = j-PAP-REG-SCI,
pages = "??--??",
year = "2013",
DOI = "https://doi.org/10.1111/j.1435-5957.2012.00477.x",
ISSN = "1056-8190 (print), 1435-5957 (electronic)",
ISSN-L = "1056-8190",
bibdate = "Mon Feb 25 06:13:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Papers in Regional Science",
keywords = "dynamic panel data models; Gibrat's Law; state
populations; Zipf's Law",
xxnote = "Online, but not yet in print with assigned page
numbers, on 25 February 2013.",
}
@Article{Srivastava:2013:FD,
author = "Tanya Kaushal Srivastava",
title = "The First Digit $1$",
journal = j-RESONANCE,
volume = "18",
number = "12",
pages = "1073--1085",
month = dec,
year = "2013",
CODEN = "RESOFE",
DOI = "https://doi.org/10.1007/s12045-013-0135-y",
ISSN = "0971-8044 (print), 0973-712X (electronic)",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s12045-013-0135-y",
acknowledgement = ack-nhfb,
fjournal = "Resonance",
journal-URL = "http://link.springer.com/journal/12045",
keywords = "Benford's Law",
}
@Article{Tavangar:2013:CGP,
author = "Mahdi Tavangar and Marzieh Hashemi",
title = "On characterizations of the generalized {Pareto}
distributions based on progressively censored order
statistics",
journal = j-STAT-PAPERS,
volume = "54",
number = "2",
pages = "381--390",
month = may,
year = "2013",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-012-0434-5",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Sun Feb 1 10:12:38 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-012-0434-5",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{vanZyl:2013:GPD,
author = "J. Martin van Zyl",
title = "The generalized {Pareto} distribution fitted to
research outputs of countries",
journal = j-SCIENTOMETRICS,
volume = "94",
number = "3",
pages = "1099--1109",
month = mar,
year = "2013",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-012-0798-2",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-012-0798-2",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Wainer:2013:VRS,
author = "Howard Wainer and Polina Harik and John Neter",
title = "Visual Revelations: {Stigler}'s {Law of Eponymy} and
{Marey}'s Train Schedule: Did {Serjev} Do It Before
{Ibry}, and What About {Jules Petiet}?",
journal = j-CHANCE,
volume = "26",
number = "1",
pages = "53--56",
year = "2013",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.2013.772394",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Tue Feb 3 09:42:07 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/chance.bib",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
}
@Article{Wjcik:2013:HFI,
author = "Micha{\l} Ryszard W{\'o}jcik",
title = "How fast increasing powers of a continuous random
variable converge to {Benford's Law}",
journal = j-STAT-PROB-LETT,
volume = "83",
number = "12",
pages = "2688--2692",
year = "2013",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2013.09.003",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715213002927",
abstract = "It is known that increasing powers of a continuous
random variable converge in distribution to Benford's
Law as the exponent approaches infinity. The rate of
convergence has been estimated using Fourier analysis,
but we present an elementary method, which is easier to
apply and provides a better estimation in the widely
studied case of a uniformly distributed random
variable.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Fourier coefficients; Mantissa
distribution; Significand distribution; Uniform
distribution modulo 1",
}
@Article{Wojcik:2013:HFI,
author = "Michal Ryszard W{\'o}jcik",
title = "How fast increasing powers of a continuous random
variable converge to {Benford's Law}",
journal = j-STAT-PROB-LETT,
volume = "83",
number = "12",
pages = "2688--2692",
month = dec,
year = "2013",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2013.09.003",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60F15 (60E05)",
MRnumber = "3118213",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715213002927",
abstract = "It is known that increasing powers of a continuous
random variable converge in distribution to {Benford's
Law} as the exponent approaches infinity. The rate of
convergence has been estimated using Fourier analysis,
but we present an elementary method, which is easier to
apply and provides a better estimation in the widely
studied case of a uniformly distributed random
variable.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law; Fourier coefficients; Mantissa
distribution; Significand distribution; Uniform
distribution modulo 1",
}
@Article{Yan:2013:CNE,
author = "Su Yan and W. Scott Spangler and Ying Chen",
title = "Chemical Name Extraction Based on Automatic Training
Data Generation and Rich Feature Set",
journal = j-TCBB,
volume = "10",
number = "5",
pages = "1218--1233",
month = sep,
year = "2013",
CODEN = "ITCBCY",
DOI = "https://doi.org/10.1109/TCBB.2013.101",
ISSN = "1545-5963 (print), 1557-9964 (electronic)",
ISSN-L = "1545-5963",
bibdate = "Thu Jan 9 15:34:03 MST 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tcbb.bib",
abstract = "The automation of extracting chemical names from text
has significant value to biomedical and life science
research. A major barrier in this task is the
difficulty of getting a sizable and good quality data
to train a reliable entity extraction model. Another
difficulty is the selection of informative features of
chemical names, since comprehensive domain knowledge on
chemistry nomenclature is required. Leveraging random
text generation techniques, we explore the idea of
automatically creating training sets for the task of
chemical name extraction. Assuming the availability of
an incomplete list of chemical names, called a
dictionary, we are able to generate well-controlled,
random, yet realistic chemical-like training documents.
We statistically analyze the construction of chemical
names based on the incomplete dictionary, and propose a
series of new features, without relying on any domain
knowledge. Compared to state-of-the-art models learned
from manually labeled data and domain knowledge, our
solution shows better or comparable results in
annotating real-world data with less human effort.
Moreover, we report an interesting observation about
the language for chemical names. That is, both the
structural and semantic components of chemical names
follow a Zipfian distribution, which resembles many
natural languages.",
acknowledgement = ack-nhfb,
fjournal = "IEEE/ACM Transactions on Computational Biology and
Bioinformatics",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J954",
}
@Article{Young:2013:ATL,
author = "D. S. Young",
title = "Approximate tolerance limits for {Zipf--Mandelbrot}
distributions",
journal = j-PHYSICA-A,
volume = "392",
number = "7",
pages = "1702--1711",
day = "1",
month = apr,
year = "2013",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2012.11.056",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Feb 27 07:32:55 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437112010497",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Zipf's Law",
}
@Article{Alexopoulos:2014:BLA,
author = "Theodoros Alexopoulos and Stefanos Leontsinis",
title = "{Benford}'s Law in Astronomy",
journal = j-J-ASTROPHYS-ASTRON,
volume = "35",
number = "4",
pages = "639--648",
year = "2014",
CODEN = "JASRD7",
DOI = "https://doi.org/10.1007/s12036-014-9303-z",
ISSN = "0250-6335 (print), 0973-7758 (electronic)",
ISSN-L = "0250-6335",
bibdate = "Wed Aug 12 10:02:04 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See follow-up \cite{Hill:2016:HLI}.",
URL = "http://link.springer.com/article/10.1007/s12036-014-9303-z",
acknowledgement = ack-nhfb,
fjournal = "Journal of Astrophysics and Astronomy",
journal-URL = "http://www.springerlink.com/content/0250-6335",
keywords = "Benford's law; galaxies; significant digit.; stars;
Universe",
}
@Article{Alexopoulos:2014:BLU,
author = "Theodoros Alexopoulos and Stefanos Leontsinis",
title = "{Benford's Law} and the {Universe}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "6",
day = "23",
month = jan,
year = "2014",
bibdate = "Tue Jan 26 10:06:48 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1401.5794v2",
abstract = "Benford's law predicts the occurrence of the nth digit
of numbers in datasets originating from various sources
of the world, ranging from financial data to atomic
spectra. It is intriguing that although many features
of Benford's law have been proven and analysed, it is
still not fully mathematically understood. In this
paper we investigate the distances of galaxies and
stars by comparing the first, second and third
significant digit probabilities with Benford's
predictions. It is found that the distances of galaxies
follow reasonably well the first digit law and the star
distances agree very well with the first, second and
third significant digit.",
acknowledgement = ack-nhfb,
}
@Article{Alves:2014:BLA,
author = "Alexandre Donizeti Alves and Horacio Hideki Yanasse
and Nei Yoshihiro Soma",
title = "{Benford's Law} and articles of scientific journals:
comparison of {JCR\reg} and {Scopus} data",
journal = j-SCIENTOMETRICS,
volume = "98",
number = "1",
pages = "173--184",
month = jan,
year = "2014",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-013-1030-8",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:05:57 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/content/pdf/10.1007/s11192-013-1030-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
keywords = "Articles; Benford's Law; JCR; Scopus",
}
@Article{Aron:2014:LLN,
author = "Jacob Aron",
title = "Looking for life in numbers",
journal = j-NEW-SCIENTIST,
volume = "222",
number = "2968",
pages = "46--47",
year = "2014",
CODEN = "NWSCAL",
DOI = "https://doi.org/10.1016/S0262-4079(14)60925-8",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407914609258",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
keywords = "Benford's Law",
}
@Article{Arshadi:2014:BLB,
author = "Laleh Arshadi and Amir Hossein Jahangir",
title = "{Benford's Law} behavior of {Internet} traffic",
journal = j-J-NETW-COMPUT-APPL,
volume = "40",
number = "0",
pages = "194--205",
year = "2014",
CODEN = "JNCAF3",
DOI = "https://doi.org/10.1016/j.jnca.2013.09.007",
ISSN = "1084-8045 (print), 1095-8592 (electronic)",
ISSN-L = "1084-8045",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1084804513001951",
abstract = "In this paper, we analyze the Internet traffic from a
different point of view based on Benford's law, an
empirical law that describes the distribution of
leading digits in a collection of numbers met in
naturally occurring phenomena. We claim that Benford's
law holds for the inter-arrival times of TCP flows in
case of normal traffic. Consequently, any type of
anomalies affecting TCP flows, including intentional
intrusions or unintended faults and network failures in
general, can be detected by investigating the
first-digit distributions of the inter-arrival times of
TCP SYN packets. In this paper we apply our findings to
the detection of intentional attacks, and leave other
types of anomalies for future works. We support our
claim with related researches that indicate the TCP
flow inter-arrival times can be modeled by Weibull
distribution with shape parameter less than 1, and show
the relation between Weibull distributed data and
Benford's law. Finally, we validate our findings on
real traffic and achieve encouraging results.",
acknowledgement = ack-nhfb,
ajournal = "J. netw. comput. appl.",
fjournal = "Journal of Network and Computer Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/10848045",
keywords = "Anomaly detection; Benford's law; Benford's Law;
Benford's law; Benford's Law; Computer network traffic
analysis; Weibull distribution",
}
@Article{Ausloos:2014:BBL,
author = "M. Ausloos and C. Herteliu and B. Ileanu",
title = "Breakdown of {Benford's Law} for birth data",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "17",
day = "6",
month = oct,
year = "2014",
bibdate = "Tue Jan 26 09:59:08 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1410.1755v1",
abstract = "Long birth time series for Romania are investigated
from Benford's law point of view, distinguishing
between families with a religious (Orthodox and
Non-Orthodox) affiliation. The data extend from Jan.
01, 1905 till Dec. 31, 2001, i.e. over 97 years or
35\,429 days. The results point to a drastic breakdown
of Benford's law. Some interpretation is proposed,
based on the statistical aspects due to population
sizes, rather than on human thought constraints when
the law breakdown is usually expected. Benford's law
breakdown clearly points to natural causes.",
acknowledgement = ack-nhfb,
}
@Article{Ausloos:2014:ZMP,
author = "Marcel Ausloos",
title = "{Zipf--Mandelbrot--Pareto} model for co-authorship
popularity",
journal = j-SCIENTOMETRICS,
volume = "101",
number = "3",
pages = "1565--1586",
month = dec,
year = "2014",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-014-1302-y",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:06:06 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-014-1302-y",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Beckett:2014:TPA,
author = "Phil Beckett",
title = "Taking a preventative approach towards the {Bribery
Act}",
journal = "Computer Fraud \& Security",
volume = "2014",
number = "6",
pages = "16--18",
year = "2014",
DOI = "https://doi.org/10.1016/S1361-3723(14)70502-0",
ISSN = "1361-3723 (print), 1873-7056 (electronic)",
ISSN-L = "1361-3723",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1361372314705020",
abstract = "The UK's Serious Fraud Office (SFO) recently tried to
reinvigorate activity around the Bribery Act.1 It
warned companies and banks that if they fail to prevent
financial crime by their staff, they could face great
fines and official blacklisting from European
contracts. This proposed amendment put forward by the
{SFO} would give the {UK} powers to take direct action
against corporates, enabling it to levy US-style fines
and brand them with assisted bribery. And so
organisations need to ensure that awareness of and
compliance with the Bribery Act is part of their risk
analysis and mitigation activities and they should
start by looking at their data.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@InCollection{Berger:2014:BSL,
author = "Arno Berger and Gideon Eshun",
editor = "Ziyad AlSharawi and Jim M. Cushing and Saber Elaydi",
booktitle = "{Theory and Applications of Difference Equations and
Discrete Dynamical Systems: ICDEA, Muscat, Oman, May
26--30, 2013}",
title = "{Benford} Solutions of Linear Difference Equations",
volume = "102",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xvi + 222",
pages = "23--60",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44140-4_2",
ISBN = "3-662-44139-X, 3-662-44140-3 (e-book)",
ISBN-13 = "978-3-662-44139-8, 978-3-662-44140-4 (e-book)",
LCCN = "QA218 .T446 2014",
MRclass = "60-02 (11A63 11K06 60C05 60F05)",
MRnumber = "3280199",
bibdate = "Wed Aug 12 09:51:04 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Springer Proceedings in Mathematics \& Statistics",
acknowledgement = ack-nhfb,
}
@Article{Berger:2014:CBL,
author = "Arno Berger and Gideon Eshun",
title = "A Characterization of {Benford's Law} in Discrete-Time
Linear Systems",
journal = j-J-DYN-DIFFER-EQU,
volume = "??",
number = "??",
pages = "1--39",
month = "????",
year = "2014",
CODEN = "JDDEEH",
DOI = "https://doi.org/10.1007/s10884-014-9393-y",
ISSN = "1040-7294 (print), 1572-9222 (electronic)",
ISSN-L = "1040-7294",
MRclass = "37A05, 37A45, 11J71, 62E20",
bibdate = "Wed Aug 12 10:09:25 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of dynamics and differential equations",
keywords = "$$\mathbb {Q}$$ Q -independence; 11J71; 37A05; 37A45;
62E20; Benford's sequence; Nonresonant set; Uniform
distribution mod 1",
}
@Article{Best:2014:BBZ,
author = "Andrew Best and Patrick Dynes and Xixi Edelsbrunner
and Brian McDonald and Steven J. Miller and Kimsy Tor
and Caroline Turnage-Butterbaugh and Madeleine
Weinstein",
title = "{Benford} Behavior of {Zeckendorf} Decompositions",
journal = j-FIB-QUART,
volume = "52",
number = "5",
pages = "35--??",
month = dec,
year = "2014",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "11B39 (11B05)",
MRnumber = "3479486",
MRreviewer = "Martin Johann Stein",
bibdate = "Mon Nov 25 10:05:44 MST 2019",
bibsource = "http://www.fq.math.ca/52-5.html;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Papers1/52-5/Best-Benford.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Bhole:2014:BDN,
author = "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh",
title = "{Benford} distributions in {NMR}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "6",
day = "27",
month = jun,
year = "2014",
bibdate = "Tue Jan 26 10:03:00 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1406.7077v1",
abstract = "Benford's Law is an empirical law which predicts the
frequency of significant digits in databases
corresponding to various phenomena, natural or
artificial. Although counter intuitive at the first
sight, it predicts a higher occurrence of digit $1$,
and decreasing occurrences to other larger digits. Here
we report the Benford analysis of various NMR databases
and draw several interesting inferences. We observe
that, in general, NMR signals follow Benford
distribution in time-domain as well as in frequency
domain. Our survey included NMR signals of various
nuclear species in a wide variety of molecules in
different phases, namely liquid, liquid-crystalline,
and solid. We also studied the dependence of Benford
distribution on NMR parameters such as signal to noise
ratio, number of scans, pulse angles, and apodization.
In this process we also find that, under certain
circumstances, the Benford analysis can distinguish a
genuine spectrum from a visually identical simulated
spectrum. Further we find that chemical-shift databases
and amplitudes of certain radio frequency pulses
generated using optimal control techniques also satisfy
Benford's law to a good extent.",
acknowledgement = ack-nhfb,
}
@Article{Cournane:2014:NAB,
author = "S. Cournane and N. Sheehy and J. Cooke",
title = "The novel application of {Benford}'s second order
analysis for monitoring radiation output in
interventional radiology",
journal = "Physica Medica",
volume = "30",
number = "4",
pages = "413--418",
year = "2014",
DOI = "https://doi.org/10.1016/j.ejmp.2013.11.004",
ISSN = "1120-1797 (print), 1724-191X (electronic)",
ISSN-L = "1120-1797",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1120179713004328",
abstract = "Benford's law is an empirical observation which
predicts the expected frequency of digits in naturally
occurring datasets spanning multiple orders of
magnitude, with the law having been most successfully
applied as an audit tool in accountancy. This study
investigated the sensitivity of the technique in
identifying system output changes using simulated
changes in interventional radiology Dose-Area-Product
(DAP) data, with any deviations from Benford's
distribution identified using z-statistics. The
radiation output for interventional radiology X-ray
equipment is monitored annually during quality control
testing; however, for a considerable portion of the
year an increased output of the system, potentially
caused by engineering adjustments or spontaneous system
faults may go unnoticed, leading to a potential
increase in the radiation dose to patients. In normal
operation recorded examination radiation outputs vary
over multiple orders of magnitude rendering the
application of normal statistics ineffective for
detecting systematic changes in the output. In this
work, the annual DAP datasets complied with Benford's
first order law for first, second and combinations of
the first and second digits. Further, a continuous
rolling second order technique was devised for trending
simulated changes over shorter timescales. This
distribution analysis, the first employment of the
method for radiation output trending, detected
significant changes simulated on the original data,
proving the technique useful in this case. The
potential is demonstrated for implementation of this
novel analysis for monitoring and identifying change in
suitable datasets for the purpose of system process
control.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Interventional radiology; Radiation
dose",
}
@Article{Dunstan:2014:GSD,
author = "D. J. Dunstan and A. J. Bushby",
title = "Grain size dependence of the strength of metals: The
{Hall--Petch} effect does not scale as the inverse
square root of grain size",
journal = j-INT-J-PLAST,
volume = "53",
number = "0",
pages = "56--65",
year = "2014",
CODEN = "IJPLER",
DOI = "https://doi.org/10.1016/j.ijplas.2013.07.004",
ISSN = "0749-6419 (print), 1879-2154 (electronic)",
ISSN-L = "0749-6419",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S074964191300140X",
abstract = "The classic data in the literature for the grain size
dependence of the strength in many metals are reviewed.
The exponent $x$ relating strength to grain size $
d^{-x}$ is not often the eponymous inverse square-root
relationship (known as the Hall--Petch effect), but is
widely scattered from values as low as $ x = 0.2$ to
values as high as $ x = 1$. These exponents for
individual datasets are shown to be largely
meaningless. For an ensemble of n selected datasets,
the fit to the functional form $ \ln [d] / d + {\rm
const}$ with $ n + 1$ free fitting parameters is found
to be almost as good as the fit to $ 1 / \sqrt [d] +
{\rm const}$ with $ 2 n$ fitting parameters (the
Hall--Petch fit). The probability that the former is
the preferable fit is high. Some data sets do not agree
with the $ \ln [d] / d$ fit, but their deviation is
readily explained on simple physical grounds. Moreover,
even when they are included in the fit, statistical
tests still show that the $ \ln [d] / d$ form is
preferable by a wide margin. The conclusion is that the
Hall--Petch effect is not another size effect sui
generis but is the same size effect as that observed in
epitaxial thin film growth and in micromechanical
testing of small specimens. Consequently we propose
that grain size strengthening of metals is driven by
constraints on stress and dislocation curvature
according to the space available.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Plasticity",
journal-URL = "http://www.sciencedirect.com/science/journal/07496419",
keywords = "Benford's Law; Dislocations; Grain boundaries;
Metallic material; Polycrystalline material; Yield
condition",
}
@TechReport{Edelsbrunner:2014:BLC,
author = "X. Edelsbrunner and K. Huan and B. Mackall and S. J.
Miller and J. Powell and C. Turnage-Butterbaugh and M.
Weinstein",
title = "{Benford's Law}, the {Cauchy} Distribution and
Financial Data",
type = "Report",
institution = "????",
address = "????",
year = "2014",
bibdate = "Sat Sep 10 11:09:53 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ferariu:2014:PGP,
author = "L. Ferariu and C. Cimpanu",
booktitle = "{2014 18th International Conference System Theory,
Control and Computing (ICSTCC)}",
title = "{Pareto} genetic path planning hybridized with
multi-objective {Dijkstra}'s algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "341--346",
year = "2014",
DOI = "https://doi.org/10.1109/ICSTCC.2014.6982439",
bibdate = "Wed Mar 18 11:11:53 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6982439",
acknowledgement = ack-nhfb,
}
@Article{Gonzalez-Alvarez:2014:POH,
author = "David L. Gonz{\'a}lez-{\'A}lvarez and Miguel A.
Vega-Rodr{\'\i}guez and {\'A}lvaro Rubio-Largo",
title = "Parallelizing and optimizing a hybrid differential
evolution with {Pareto} tournaments for discovering
motifs in {DNA} sequences",
journal = j-J-SUPERCOMPUTING,
volume = "70",
number = "2",
pages = "880--905",
month = nov,
year = "2014",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-014-1266-y",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Fri Feb 13 12:13:17 MST 2015",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=70&issue=2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
URL = "http://link.springer.com/article/10.1007/s11227-014-1266-y",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Gray:2014:TGR,
author = "Glen L. Gray and Roger S. Debreceny",
title = "A taxonomy to guide research on the application of
data mining to fraud detection in financial statement
audits",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "15",
number = "4",
pages = "357--380",
year = "2014",
CODEN = "IJAIA7",
DOI = "https://doi.org/10.1016/j.accinf.2014.05.006",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "2013 Research Symposium on Information Integrity \&
Information Systems Assurance",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089514000323",
abstract = "This paper explores the application of data mining
techniques to fraud detection in the audit of financial
statements and proposes a taxonomy to support and guide
future research. Currently, the application of data
mining to auditing is at an early stage of development
and researchers take a scatter-shot approach,
investigating patterns in financial statement
disclosures, text in annual reports and MD\&As, and the
nature of journal entries without appropriate guidance
being drawn from lessons in known fraud patterns. To
develop structure to research in data mining, we create
a taxonomy that combines research on patterns of
observed fraud schemes with an appreciation of areas
that benefit from productive application of data
mining. We encapsulate traditional views of data mining
that operates primarily on quantitative data, such as
financial statement and journal entry data. In
addition, we draw on other forms of data mining,
notably text and email mining.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Auditing; Benford's Law; Data mining; Fraud",
}
@Article{Hackl:2014:CPP,
author = "Franz Hackl and Michael E. Kummer and Rudolf
Winter-Ebmer",
title = "99 Cent: Price points in e-commerce",
journal = "Information Economics and Policy",
volume = "26",
number = "0",
pages = "12--27",
year = "2014",
DOI = "https://doi.org/10.1016/j.infoecopol.2013.10.001",
ISSN = "0167-6245 (print), 1873-5975 (electronic)",
ISSN-L = "0167-6245",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167624513000450",
abstract = "Setting prices ending in nines is a common feature of
many markets for consumer products. This prevalence has
been explained either by a specific image of such price
points or by the exploitation of rational inattention
on the part of the consumers who want to economize on
the cost of information processing. We use data from an
Austrian price comparison site and find a remarkable
prevalence of such price setting. Prices ending with
nine are also sticky: price-setters change them with a
significantly lower probability; rivals underbid these
prices more seldom if they represent the cheapest price
on the market, and we observe higher price jumps by
price leaders for these price points. Finally, we
explore the impact of these price points on the
consumers demand.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; E-commerce; Focal prices; Price
stability; Pricing behavior",
}
@Article{He:2014:EPD,
author = "Hui He and Na Zhou and Ruiming Zhang",
title = "On estimation for the {Pareto} distribution",
journal = j-STAT-METHODOL,
volume = "21",
number = "??",
pages = "49--58",
month = nov,
year = "2014",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:46:01 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312714000288",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Article{Holz:2014:QCG,
author = "Carsten A. Holz",
title = "The quality of {China}'s {GDP} statistics",
journal = "China Economic Review",
volume = "30",
number = "0",
pages = "309--338",
year = "2014",
DOI = "https://doi.org/10.1016/j.chieco.2014.06.009",
ISSN = "1043-951X (print), 1873-7781 (electronic)",
ISSN-L = "1043-951X",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1043951X14000753",
abstract = "Since the 1998 wind of falsification and
embellishment, Chinese official statistics on gross
domestic product (GDP) have repeatedly come under
scrutiny. This paper evaluates the quality of China's
GDP statistics in four stages. First, it reviews past
and ongoing suspicions of the quality of GDP data and
examines the evidence. Second, it documents the
institutional framework for data compilation and
concludes on the implications for data quality. Third,
it asks how the Chinese National Bureau of Statistics
could possibly go about credibly falsifying GDP data
without being found out. Fourth, it examines if the
first- and second-digit distributions of official GDP
data conform to established data regularities
(Benford's Law). The findings are that the supposed
evidence for GDP data falsification is not compelling,
that the National Bureau of Statistics has much
institutional scope for falsifying GDP data, and that
certain manipulations of nominal and real data would be
virtually undetectable. Official GDP data, however,
exhibit few statistical anomalies (conform to Benford's
Law) and the National Bureau of Statistics thus either
makes no significant use of its scope to falsify data,
or is aware of statistical data regularities when it
falsifies data.",
acknowledgement = ack-nhfb,
keywords = "Accuracy of national statistics; Benford's Law;
Compilation of {GDP} and sectoral value-added; National
income accounting; National statistical system",
}
@Article{Hou:2014:PFD,
author = "I-Hong Hou and Piyush Gupta",
title = "Proportionally fair distributed resource allocation in
multiband wireless systems",
journal = j-IEEE-TRANS-NETWORKING,
volume = "22",
number = "6",
pages = "1819--1830",
month = dec,
year = "2014",
CODEN = "IEANEP",
DOI = "https://doi.org/10.1109/TNET.2013.2284494",
ISSN = "1063-6692 (print), 1558-2566 (electronic)",
ISSN-L = "1063-6692",
bibdate = "Thu Feb 12 18:29:37 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
abstract = "A challenging problem in multiband multicell
self-organized wireless systems, such as
femtocells/picocells in cellular networks, multichannel
Wi-Fi networks, and more recent wireless networks over
TV white spaces, is of distributed resource allocation.
This in general involves four components: channel
selection, client association, channel access, and
client scheduling. In this paper, we present a unified
framework for jointly addressing the four components
with the global system objective of maximizing the
clients throughput in a proportionally fair manner. Our
formulation allows a natural dissociation of the
problem into two subparts. We show that the first part,
involving channel access and client scheduling, is
convex and derive a distributed adaptation procedure
for achieving a Pareto-optimal solution. For the second
part, involving channel selection and client
association, we develop a Gibbs-sampler-based approach
for local adaptation to achieve the global objective,
as well as derive fast greedy algorithms from it that
achieve good solutions often.",
acknowledgement = ack-nhfb,
fjournal = "IEEE\slash ACM Transactions on Networking",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771",
}
@Article{Huang:2014:GSP,
author = "Mu-Hsuan Huang and Wei-Tzu Huang and Cheng-Ching Chang
and Dar-Zen Chen and Chang-Pin Lin",
title = "The greater scattering phenomenon beyond {Bradford}'s
law in patent citation",
journal = j-J-ASSOC-INF-SCI-TECHNOL,
volume = "65",
number = "9",
pages = "1917--1928",
month = sep,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1002/asi.23092",
ISSN = "2330-1643 (print), 2330-1643 (electronic)",
ISSN-L = "2330-1643",
bibdate = "Fri Sep 11 12:15:14 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jaist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Information Science and
Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "8 Apr 2014",
}
@Article{Huettenberger:2014:DSM,
author = "Lars Huettenberger and Christian Heine and Christoph
Garth",
title = "Decomposition and Simplification of Multivariate Data
using {Pareto} Sets",
journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH,
volume = "20",
number = "12",
pages = "2684--2693",
month = dec,
year = "2014",
CODEN = "ITVGEA",
DOI = "https://doi.org/10.1109/TVCG.2014.2346447",
ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
ISSN-L = "1077-2626",
bibdate = "Thu Feb 12 16:40:54 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html",
abstract-URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journal-URL = "http://www.computer.org/csdl/trans/tg/index.html",
}
@InProceedings{Iorliam:2014:DBI,
author = "A. Iorliam and A. T. S. Ho and N. Poh and Y. Q. Shi",
booktitle = "2014 International Workshop on Biometrics and
Forensics (IWBF)",
title = "Do biometric images follow {Benford's Law}?",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
month = mar,
year = "2014",
DOI = "https://doi.org/10.1109/IWBF.2014.6914261",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "backend attack; Benford law; Benford's law; Biomedical
imaging; biometric image manipulation; biometric
images; biometric sample tampering; biometrics (access
control); data compression; digital forensics; Discrete
cosine transforms; double compressed face image; double
compressed fingerprint image; EER; equal error rate;
Face; Fingerprint recognition; forensic biometrics;
forensics; image coding; Image coding; Image matching;
malicious tampering detection; natural image tampering
detection; security concern; sensor level tampering;
single compressed face image; single compressed
fingerprint image; spoofing; template contamination;
Transform coding",
}
@Article{Jameson:2014:BLC,
author = "Marie Jameson and Jesse Thomer and Lynelle Ye",
title = "{Benford's Law} for Coefficients of Newforms",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "7",
month = jul,
year = "2014",
bibdate = "Sat Sep 10 12:26:03 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1407.1577",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Article{Kraus:2014:DWD,
author = "Cornelia Kraus and Raul Valverde",
title = "A Data Warehouse Design for the Detection of Fraud in
the Supply Chain by Using the {Benford's Law}",
journal = j-AM-J-APPL-SCI,
volume = "11",
number = "9",
pages = "1507--1518",
month = sep,
year = "2014",
CODEN = "AJASCJ",
DOI = "https://doi.org/10.3844/ajassp.2014.1507.1518",
ISSN = "1546-9239 (print), 1554-3641 (electronic)",
ISSN-L = "1546-9239",
bibdate = "Mon Jun 1 13:40:15 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Am. J. Appl. Sci.",
fjournal = "American Journal of Applied Sciences",
journal-URL = "https://thescipub.com/journals/ajas/archive",
}
@Article{Leemann:2014:SAS,
author = "Lucas Leemann and Daniel Bochsler",
title = "A systematic approach to study electoral fraud",
journal = j-ELECT-STUDIES,
volume = "35",
number = "0",
pages = "33--47",
year = "2014",
DOI = "https://doi.org/10.1016/j.electstud.2014.03.005",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379414000390",
abstract = "Integrity of elections relies on fair procedures at
different stages of the election process, and fraud can
occur in many instances and different forms. This paper
provides a general approach for the detection of fraud.
While most existing contributions focus on a single
instance and form of fraud, we propose a more
encompassing approach, testing for several empirical
implications of different possible forms of fraud. To
illustrate this approach we rely on a case of electoral
irregularities in one of the oldest democracies: In a
Swiss referendum in 2011, one in twelve municipalities
irregularly destroyed the ballots, rendering a recount
impossible. We do not know whether this happened due to
sloppiness, or to cover possible fraudulent actions.
However, one of our statistical tests leads to results,
which point to irregularities in some of the
municipalities, which lost their ballots: they reported
significantly fewer empty ballots than the other
municipalities. Relying on several tests leads to the
well known multiple comparisons problem. We show two
strategies and illustrate strengths and weaknesses of
each potential way to deal with multiple tests.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Benford's Law; Electoral forensics; Electoral fraud;
Referendums; Switzerland",
}
@Article{Lin:2014:CCE,
author = "Fengyi Lin and Sheng-Fu Wu",
title = "Comparison of cosmetic earnings management for the
developed markets and emerging markets: Some empirical
evidence from the {United States} and {Taiwan}",
journal = "Economic Modelling",
volume = "36",
number = "0",
pages = "466--473",
year = "2014",
DOI = "https://doi.org/10.1016/j.econmod.2013.10.002",
ISSN = "0264-9993 (print), 1873-6122 (electronic)",
ISSN-L = "0264-9993",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0264999313004288",
abstract = "This study examines the effect of the implementation
of corporate governance regulations on cosmetic
earnings management in developed and emerging markets
respectively. Using Benford's Law, the analysis employs
84,870 positive earnings observations for all publicly
listed US and Taiwan companies from 1990 to 2011. The
empirical results show that, regardless of developed
markets and emerging markets, the phenomenon of
cosmetic earnings management exists. In contrast to
developed markets, corporate managers of emerging
markets have stronger incentives to manipulate
earnings. More importantly, it was found that the
degree of earnings management is significantly less
after implementing corporate governance regulations
both in developed and emerging markets. This result
suggests that the implementation of corporate
governance regulations plays an important role in
reducing the earnings manipulative behavior. The
findings of the study add more evidence to the ongoing
debate about the effectiveness of corporate governance
regulations in preventing earnings management.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Corporate governance; Cosmetic earnings
management",
}
@Article{Lin:2014:RAA,
author = "Fengyi Lin and Chung-Min Wu and Tzu-Yi Fang and
Jheng-Ci Wun",
title = "The relations among accounting conservatism,
institutional investors and earnings manipulation",
journal = "Economic Modelling",
volume = "37",
number = "0",
pages = "164--174",
year = "2014",
DOI = "https://doi.org/10.1016/j.econmod.2013.10.020",
ISSN = "0264-9993 (print), 1873-6122 (electronic)",
ISSN-L = "0264-9993",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0264999313004471",
abstract = "Most scholars have indicated corporations using
accounting conservatism to reduce earnings
manipulation, although certain scholars believe that
firms have more incentive to increase earnings
manipulation. Institutional investors play an important
external monitoring role, and affect firm's earnings
manipulation. Previous studies adopted accruals as an
earnings manipulation proxy to detect the relationship
among accounting conservatism, institutional investor
shareholdings, and earnings manipulation. We further
investigate the relationship among accounting
conservatism, institutional investor shareholdings, and
earnings manipulation by using Benford's law. Our
results indicate that firms with more conservative
financial reporting have less probability of engaging
in earnings-manipulative activities. We also find the
negative association between earnings management and
institutional investor shareholdings. However, if
corporate financial statements tend toward
conservatism, institutional investor shareholdings
could increase managers' incentive to manage earnings.
Our findings have important implications for investors
to make investment decisions.",
acknowledgement = ack-nhfb,
keywords = "Accounting conservatism; Benford's law; Benford's Law;
Benford's law; Benford's Law; Earnings management;
Institutional investor shareholdings",
}
@Article{Lu:2014:ODE,
author = "Lu Lu and Christine M. Anderson-Cook and Dennis K. J.
Lin",
title = "Optimal designed experiments using a {Pareto} front
search for focused preference of multiple objectives",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "71",
number = "??",
pages = "1178--1192",
month = mar,
year = "2014",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:43:50 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947313001382",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Luca:2014:FDF,
author = "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
title = "On the first digits of the {Fibonacci} numbers and
their {Euler} function",
journal = "Uniform Distribution Theory",
volume = "9",
number = "1",
pages = "21--25",
year = "2014",
ISSN = "1336-913X (print), 2309-5377 (electronic)",
ISSN-L = "1336-913X",
MRclass = "11B39 (11K36)",
MRnumber = "3237073",
MRreviewer = "Huaning Liu",
bibdate = "Tue Jan 26 11:12:44 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "https://math.boku.ac.at/udt/vol09/no1/03LucaStanica.pdf",
acknowledgement = ack-nhfb,
ajournal = "Unif. Distrib. Theory",
fjournal = "Uniform Distribution Theory",
journal-URL = "https://doaj.org/toc/1336-913X",
}
@Article{MacDougall:2014:AIC,
author = "Margaret MacDougall",
title = "Assessing the Integrity of Clinical Data: When is
Statistical Evidence Too Good to be True?",
journal = "Topoi: An International Review of Philosophy",
volume = "33",
number = "2",
pages = "323--337",
month = oct,
year = "2014",
DOI = "https://doi.org/10.1007/s11245-013-9216-5",
ISSN = "0167-7411 (print), 1572-8749 (electronic)",
ISSN-L = "0167-7411",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11245-013-9216-5",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/11245",
keywords = "Benford's Law",
}
@Article{Marden:2014:APO,
author = "Jason R. Marden and H. Peyton Young and Lucy Y. Pao",
title = "Achieving {Pareto} Optimality Through Distributed
Learning",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "52",
number = "5",
pages = "2753--2770",
month = "????",
year = "2014",
CODEN = "SJCODC",
DOI = "https://doi.org/10.1137/110850694",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
bibdate = "Thu Feb 12 07:28:17 MST 2015",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/52/5;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
onlinedate = "January 2014",
}
@Book{Miller:2014:JFM,
author = "Irwin Miller and Marylees Miller",
title = "{John E. Freund}'s mathematical statistics with
applications",
publisher = "Pearson",
address = "Boston, MA, USA",
edition = "Eighth",
pages = "xi + 529",
year = "2014",
ISBN = "0-321-80709-X (hardcover)",
ISBN-13 = "978-0-321-80709-0 (hardcover)",
LCCN = "QA276 .M4726 2014",
bibdate = "Thu Oct 13 07:03:41 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1928--",
remark = "Revised edition of \cite{Miller:2004:JFM}.",
subject = "Mathematical statistics",
}
@Article{Mir:2014:BLB,
author = "T. A. Mir",
title = "The {Benford Law} behavior of the religious activity
data",
journal = j-PHYSICA-A,
volume = "408",
number = "0",
pages = "1--9",
year = "2014",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2014.03.074",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437114002854",
abstract = "An important aspect of religious association is that
adherents, as part of their religious duty, carry out
various activities. One religious group known for
keeping the elaborate records of day-to-day activities
of its members is the Jehovah's Witnesses (JWs) a
worldwide Christian religious group. We analyse the
historical records of the country-wide data associated
with twelve different religious activities of {JWs} to
see if there are any patterns in the distribution of
the first digits as predicted by Benford's Law. This
law states that the first digits of numbers in data
sets are not uniformly distributed but often, not
always, follow a logarithmic distribution such that the
numbers beginning with smaller digits appear more
frequently than those with larger ones. We find that
the data on religious activities like peak publishers,
pioneer publishers, baptizations, public meetings,
congregations, bible studies, time spent in
door-to-door contacts, attendances at the memorial
services, total literature and individual magazines
distributed, new subscriptions and back-calls received
excellently conforms to Benford's Law.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Jehovah's Witnesses; Religious
activities",
}
@Article{Mir:2014:BLP,
author = "Tariq Ahmad Mir and Marcel Ausloos and Roy Cerqueti",
title = "{Benford}'s law predicted digit distribution of
aggregated income taxes: the surprising conformity of
{Italian} cities and regions",
journal = j-EUR-PHYS-J-B,
volume = "87",
number = "11",
year = "2014",
CODEN = "EPJBFY",
DOI = "https://doi.org/10.1140/epjb/e2014-50525-2",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Wed Aug 12 10:00:00 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
eid = "261",
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
journal-URL = "http://link.springer.com/journal/10051",
keywords = "Statistical and Nonlinear Physics",
}
@Article{Mitov:2014:EAP,
author = "Kosto V. Mitov and Saralees Nadarajah",
title = "Extremal and additive processes generated by {Pareto}
distributed random vectors",
journal = j-ESAIM-PROBAB-STATIST,
volume = "18",
number = "??",
pages = "667--??",
month = "????",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1051/ps/2014001",
ISSN = "1292-8100 (print), 1262-3318 (electronic)",
ISSN-L = "1262-3318",
bibdate = "Mon Feb 9 06:54:48 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/esaim-probab-stat.bib",
acknowledgement = ack-nhfb,
fjournal = "ESAIM: Probability and Statistics",
journal-URL = "http://www.edpsciences.org/ps/",
}
@Book{Oleksy:2014:DMB,
author = "Marius Oleksy",
title = "{Data Mining und Benford's Law als
Controllinginstrumente}. ({German}) [{Data} mining and
{Benford's Law} as controlling instruments]",
volume = "45",
publisher = "EHV Academicpress",
address = "Bremen, Germany",
pages = "220",
year = "2014",
ISBN = "3-86741-923-X (paperback), 3-86741-928-0",
ISBN-13 = "978-3-86741-923-9 (paperback), 978-3-86741-928-4",
LCCN = "????",
bibdate = "Sat Jan 23 08:09:16 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wismarer Schriften zu Management und Recht",
URL = "http://deposit.d-nb.de/cgi-bin/dokserv?id=4627278\%26prov=M\%26dok\_var=1\%26dok\_ext=htm",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "1 Ziel und Abgrenzung der Arbeit / 16 \\
1.1 Ziel / 18 \\
1.2 Abgrenzung und die Hypothese / 18 \\
2 Die Menge von Benford, die Benford Verteilung / 19
\\
2.1 Untersuchungen der Benford-Verteilung / 20 \\
2.2 Anwendungen des Benford-Gesetzes im Finanzbereich /
24 \\
3 Datenursprung und Datenschutz / 25 \\
3.1 Gesch{\"a}ftsmodell der DekaBank Luxembourg S.A. /
26 \\
3.2 Systemarchitektur und die Datenquelle / 27 \\
3.3 Datenschutz / 28 \\
4 Orthodoxe Beweise der Verteilungskonformit{\"a}t / 30
\\
4.1 Anpassungstests / 30 \\
4.1.1 Nullhypothese und Fehlentscheidungen in der
Statistik / 31 \\
4.1.2 Normalverteilung / 33 \\
4.1.3 Signifikanztests / 40 \\
4.2 Auswahl der Anpassungstest / 50 \\
5 Konzept des Frameworks f{\"u}r das Data Mining / 51
\\
5.1 Einf{\"u}hrung in Data Mining / 51 \\
5.2 Data Mining Phasen und Prozesse / 53 \\
5.3 Biologische Grundlagen eines k{\"u}nstlichen
Neurons / 61 \\
5.4 K{\"u}nstliches Neuron / 62 \\
5.5 Architektur des K{\"u}nstlichen Neuronalen Netzes /
84 \\
5.6 Auswahl der Musterregeln / 94 \\
5.7 Entwicklung eines Testszenarios / 102 \\
5.8 Kriterien f{\"u}r Wissensextraktion / 104 \\
5.9 Kriterien f{\"u}r den Testbetrieb / 107 \\
6 Auswahl der Finanztransaktionen / 109 \\
6.1 Finanztransaktionen / 109 \\
6.2 Auswahl der Daten f{\"u}r die Untersuchung / 111
\\
7 Modellentwurf der Datentransformation / 114 \\
7.1 Import Datenmodell / 120 \\
7.2 Target Datenmodell / 123 \\
8 Datenstrukturen, Datenselection und Unwandlung / 128
\\
8.1 Datenstrukturen des Initialen Datenmodells / 130
\\
8.2 Datenstrukturen des Import Datenmodells / 133 \\
8.3 Datenstrukturen des Target Datenmodells / 136 \\
9. Data Mining / 140 \\
9.1 Bewertung der Transaktionen / 141 \\
9.2 Die Tests / 152 \\
9.3 Interpretation der Ergebnisse / 155 \\
9.4 Anwendung in der Praxis / 158 \\
Glossar / 166 \\
Literaturverzeichnis / 179 \\
Anh{\"a}nge / 181",
}
@Article{Olver:2014:MIM,
author = "F. W. J. Olver",
title = "Mathematics that has intrigued me",
journal = "Analysis and Applications (Singapore)",
volume = "12",
number = "4",
pages = "341--354",
year = "2014",
DOI = "https://doi.org/10.1142/S0219530514500262",
ISSN = "0219-5305 (print), 1793-6861 (electronic)",
ISSN-L = "0219-5305",
MRclass = "33-03 (01A70 39A06 65-03)",
MRnumber = "3218916",
bibdate = "Sun Nov 5 09:03:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Lecture delivered at Asymptotics and Applied Analysis,
Conference in Honor of Frank W. J. Olver's 75th
Birthday, January 10--14, 2000, San Diego State
University, San Diego, California.",
acknowledgement = ack-nhfb,
ajournal = "Anal. Appl. (Singap.)",
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
fjournal = "Analysis and Applications",
journal-URL = "https://www.worldscientific.com/worldscinet/aa",
remark = "This paper was completed after Frank Olver's death by
his son, Peter J. Olver, from handwritten notes. It
also contains a summary of Frank Olver's education and
career. In the paper, Frank Olver discusses the
application of Benford's Law to test data selection.",
}
@Article{Rane:2014:BLG,
author = "Ameya Deepak Rane and Utkarsh Mishra and Anindya
Biswas and Aditi Sen(De) and Ujjwal Sen",
title = "{Benford's Law} gives better scaling exponents in
phase transitions of quantum {$ X Y $} models",
journal = j-PHYS-REV-E,
volume = "90",
number = "2",
pages = "022144:1--022144:8",
day = "29",
month = aug,
year = "2014",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.90.022144",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Jan 26 10:14:12 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.90.022144",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
numpages = "8",
}
@Article{Rauch:2014:DPM,
author = "Bernhard Rauch and Max G{\"o}ttsche and Stephan
Langenegger",
title = "Detecting Problems in Military Expenditure Data Using
Digital Analysis",
journal = "Defence and Peace Economics",
volume = "25",
number = "2",
pages = "97--111",
month = "????",
year = "2014",
DOI = "https://doi.org/10.1080/10242694.2013.763438",
bibdate = "Sat Sep 10 15:55:05 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/10242694.2013.763438",
accepted = "07 Dec 2012",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/toc/gdpe20",
keywords = "Benford's Law; digital analysis; forensic accounting,;
military expenditure data",
received = "24 May 2012",
}
@Article{Rauch:2014:DVS,
author = "Bernhard Rauch and Max G{\"o}ttsche and Gernot
Br{\"a}hler and Thomas Kronfeld",
title = "Deficit versus Social Statistics: Empirical Evidence
for the Effectiveness of {Benford's Law}",
journal = j-APPL-ECON-LETT,
volume = "21",
number = "3",
pages = "147--151",
month = "????",
year = "2014",
DOI = "https://doi.org/10.1080/13504851.2013.844319",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Sep 10 15:51:42 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/13504851.2013.844319",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
journal-URL = "http://www.tandfonline.com/toc/RAEL20",
keywords = "Benford's Law",
}
@Article{Roukema:2014:FDA,
author = "Boudewijn F. Roukema",
title = "A first-digit anomaly in the {2009 Iranian
Presidential} election",
journal = j-J-APPL-STAT,
volume = "41",
number = "1",
pages = "164--199",
year = "2014",
DOI = "https://doi.org/10.1080/02664763.2013.838664",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRclass = "Database Expansion Item",
MRnumber = "3291207",
bibdate = "Wed Mar 5 08:09:17 MST 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/japplstat.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Savanur:2014:LLA,
author = "Kiran Savanur and S. Gayathri Devi and P. V. Konnur",
title = "{Lotka's Law} and Authorship Distribution in the
Journal of `{{\booktitle{Columbia Law Review}}}'",
journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
volume = "8",
number = "1",
pages = "193--208",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1080/09737766.2014.947840",
ISSN = "0973-7766 (print), 2168-930X (electronic)",
ISSN-L = "0973-7766",
bibdate = "Thu Sep 10 17:47:12 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
acknowledgement = ack-nhfb,
fjournal = "Collnet Journal of Scientometrics and Information
Management",
journal-URL = "http://www.tandfonline.com/loi/tsim20",
}
@Article{Sjoberg:2014:AAS,
author = "Fredrik M. Sjoberg",
title = "Autocratic adaptation: The strategic use of
transparency and the persistence of election fraud",
journal = j-ELECT-STUDIES,
volume = "33",
number = "0",
pages = "233--245",
year = "2014",
DOI = "https://doi.org/10.1016/j.electstud.2013.08.004",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379413001273",
abstract = "Why would an autocrat want, or at least make it appear
to want, to reduce election fraud? In recent years,
non-democratic rulers have surprisingly begun to
embrace fraud-reducing technologies, like web cameras
or transparent ballot boxes. The reason for this is
found in the relative ease by which one type of fraud
can be replaced with another. With the help of new
fraud identification techniques, I argue that the
installation of web cameras in polling stations changes
how fraud is conducted. Web cameras do not reduce
fraud, but rather make certain blatant forms of fraud,
like ballot box stuffing, more costly. Autocrats then
substitute for other types of fraud, such as
fabricating the vote count out of view of the
cameras.",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Autocracy; Benford's Law; Election fraud; Election
monitoring; Fraud forensics; Web cameras; {ICT}",
}
@Article{Tripathi:2014:IEP,
author = "Yogesh Mani Tripathi and Somesh Kumar and C.
Petropoulos",
title = "Improved estimators for parameters of a {Pareto}
distribution with a restricted scale",
journal = j-STAT-METHODOL,
volume = "18",
number = "??",
pages = "1--13",
month = may,
year = "2014",
CODEN = "????",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Fri Feb 6 07:45:59 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312713000749",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
}
@Article{Wojcik:2014:CBL,
author = "Micha{\l} Ryszard W{\'o}jcik",
title = "A characterization of {Benford's Law} through
generalized scale-invariance",
journal = j-MATH-SOC-SCI,
volume = "71",
number = "??",
pages = "1--5",
month = sep,
year = "2014",
DOI = "https://doi.org/10.1016/j.mathsocsci.2014.03.006",
ISSN = "0165-4896 (print), 1879-3118 (electronic)",
ISSN-L = "0165-4896",
MRclass = "60E05 (62E10)",
MRnumber = "3249768",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165489614000262",
abstract = "If $X$ is uniformly distributed modulo $1$ and $Y$ is
independent of $X$ then $ Y + X$ is also uniformly
distributed modulo $1$. We prove a converse for any
continuous random variable $Y$ (or a reasonable
approximation to a continuous random variable) so that
if $X$ and $ Y + X$ are equally distributed modulo $1$
and $Y$ is independent of $X$ then $X$ is uniformly
distributed modulo $1$ (or approximates the uniform
distribution equally reasonably). This translates into
a characterization of Benford's Law through a
generalization of scale-invariance: from multiplication
by a constant to multiplication by an independent
random variable.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Social Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/01654896",
keywords = "Benford's Law",
}
@Article{Xie:2014:GTK,
author = "Min Xie and Laks V. S. Lakshmanan and Peter T. Wood",
title = "Generating top-$k$ packages via preference
elicitation",
journal = j-PROC-VLDB-ENDOWMENT,
volume = "7",
number = "14",
pages = "1941--1952",
month = oct,
year = "2014",
CODEN = "????",
ISSN = "2150-8097",
ISSN-L = "2150-8097",
bibdate = "Wed Feb 4 17:20:43 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/vldbe.bib",
abstract = "There are several applications, such as play lists of
songs or movies, and shopping carts, where users are
interested in finding top-$k$ packages, consisting of
sets of items. In response to this need, there has been
a recent flurry of activity around extending classical
recommender systems (RS), which are effective at
recommending individual items, to recommend packages,
or sets of items. The few recent proposals for package
RS suffer from one of the following drawbacks: they
either rely on hard constraints which may be difficult
to be specified exactly by the user or on returning
Pareto-optimal packages which are too numerous for the
user to sift through. To overcome these limitations, we
propose an alternative approach for finding
personalized top-$k$ packages for users, by capturing
users' preferences over packages using a linear utility
function which the system learns. Instead of asking a
user to specify this function explicitly, which is
unrealistic, we explicitly model the uncertainty in the
utility function and propose a preference
elicitation-based framework for learning the utility
function through feedback provided by the user. We
propose several sampling-based methods which, given
user feedback, can capture the updated utility
function. We develop an efficient algorithm for
generating top-$k$ packages using the learned utility
function, where the rank ordering respects any of a
variety of ranking semantics proposed in the
literature. Through extensive experiments on both real
and synthetic datasets, we demonstrate the efficiency
and effectiveness of the proposed system for finding
top-$k$ packages.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the VLDB Endowment",
journal-URL = "http://portal.acm.org/citation.cfm?id=J1174",
}
@Article{Yang:2014:RAE,
author = "Z. K. Yang and D. M. Lin and M. Z. Xu",
title = "The Re-applicability Explore of {Lotka's Law} in
Patent Documents",
journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
volume = "8",
number = "1",
pages = "183--191",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1080/09737766.2014.916875",
ISSN = "0973-7766 (print), 2168-930X (electronic)",
ISSN-L = "0973-7766",
bibdate = "Thu Sep 10 17:47:12 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
acknowledgement = ack-nhfb,
fjournal = "Collnet Journal of Scientometrics and Information
Management",
journal-URL = "http://www.tandfonline.com/loi/tsim20",
}
@Article{Zahran:2014:EAS,
author = "Sammy Zahran and Terrence Iverson and Stephan Weiler
and Anthony Underwood",
title = "Evidence that the accuracy of self-reported lead
emissions data improved: A puzzle and discussion",
journal = j-J-RISK-UNCERT,
volume = "49",
number = "3",
pages = "235--257",
year = "2014",
CODEN = "JRUNEN",
DOI = "https://doi.org/10.1007/s11166-014-9204-1",
ISSN = "0895-5646 (print), 1573-0476 (electronic)",
ISSN-L = "0895-5646",
bibdate = "Sat Sep 10 14:35:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Risk and Uncertainty",
journal-URL = "http://link.springer.com/journal/11166",
keywords = "Benford's Law",
}
@Article{Zomaya:2014:POC,
author = "Albert Y. Zomaya",
title = "{Pareto}-Optimal Cloud Bursting",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "25",
number = "10",
pages = "2670--2682",
month = oct,
year = "2014",
CODEN = "ITDSEO",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Thu Feb 12 13:58:32 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
URL = "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html",
abstract-URL = "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
}
@Article{Abushal:2015:EPP,
author = "Tahani A. Abushal and Ahmed A. Soliman",
title = "Estimating the {Pareto} parameters under progressive
censoring data for constant-partially accelerated life
tests",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "85",
number = "5",
pages = "917--934",
year = "2015",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949655.2013.853768",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Wed Feb 11 16:24:25 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Ausloos:2015:BBL,
author = "M. Ausloos and C. Herteliu and B. Ileanu",
title = "Breakdown of {Benford's Law} for birth data",
journal = j-PHYSICA-A,
volume = "419",
number = "0",
pages = "736--745",
year = "2015",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2014.10.041",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437114008796",
abstract = "Long birth time series for Romania are investigated
from Benford's Law point of view, distinguishing
between families with a religious (Orthodox and
Non-Orthodox) affiliation. The data extend from Jan.
01, 1905 till Dec. 31, 2001, i.e. over 97 years or
35\,429 days. The results point to a drastic breakdown
of Benford's Law. Some interpretation is proposed,
based on the statistical aspects due to population
sizes, rather than on human thought constraints when
the law breakdown is usually expected. Benford's Law
breakdown clearly points to natural causes.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Benford's Laws; Births; Non-Orthodoxes;
Orthodoxes; Religious community; Time series",
}
@Book{Bahmann:2015:AMM,
author = "Paul Bahmann",
title = "{Eine Analyse von monet{\"a}ren, makro{\"o}konomischen
Daten der BRD und DDR: Ziffernanalyse auf Grundlage des
Benford's Law}. ({German}) [{An} analysis of monetary,
macroeconomic data of the {FRG} and the {GDR}: numeric
analysis on the basis of {Benford's Law}]",
publisher = "AV Akademikerverlag",
address = "Saarbr{\"u}cken, Germany",
pages = "76",
year = "2015",
ISBN = "3-639-80882-7",
ISBN-13 = "978-3-639-80882-7",
LCCN = "????",
bibdate = "Sat Jan 23 07:58:34 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Balanzario:2015:BLM,
author = "Eugenio P. Balanzario",
title = "{Benford's Law} for mixtures",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "44",
number = "4",
pages = "698--709",
year = "2015",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610926.2012.752849",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
MRclass = "60E05 (60G57)",
MRnumber = "3315782",
bibdate = "Tue Jan 26 11:02:38 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics. Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
}
@Article{Beck:2015:PPI,
author = "M{\'e}lanie Beck and Martin J. Gander",
title = "On the positivity of {Poisson} integrators for the
{Lotka--Volterra} equations",
journal = j-BIT-NUM-MATH,
volume = "55",
number = "2",
pages = "319--340",
month = jun,
year = "2015",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-014-0505-1",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Aug 8 13:47:11 MDT 2015",
bibsource = "http://link.springer.com/journal/10543/55/2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://link.springer.com/article/10.1007/s10543-014-0505-1",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Book{Berger:2015:IBL,
author = "Arno Berger and Theodore P. Hill",
title = "An introduction to {Benford's Law}",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 248",
year = "2015",
DOI = "https://doi.org/10.1515/9781400866588",
ISBN = "0-691-16306-5, 1-4008-6658-8 (e-book)",
ISBN-13 = "978-0-691-16306-2, 978-1-4008-6658-8 (e-book)",
LCCN = "QA273.6 .B474 2015",
bibdate = "Fri Jan 22 12:19:25 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "http://site.ebrary.com/id/11040167;
http://www.degruyter.com/viewbooktoc/product/465875",
acknowledgement = ack-nhfb,
subject = "Distribution; Probability measures",
tableofcontents = "Preface / vii 1 Introduction / 1 \\
1.1 History / 3 \\
1.2 Empirical evidence / 4 \\
1.3 Early explanations / 6 \\
1.4 Mathematical framework / 7 \\
2 Significant Digits and the Significand / 11 \\
2.1 Significant digits / 11 \\
2.2 The significand / 12 \\
2.3 The significand s-algebra / 14 \\
3 The Benford Property / 22 \\
3.1 Benford sequences / 23 \\
3.2 Benford functions / 28 \\
3.3 Benford distributions and random variables / 29 \\
4 The Uniform Distribution and Benford's Law / 43 \\
4.1 Uniform distribution characterization of Benford's
law / 43 \\
4.2 Uniform distribution of sequences and functions /
46 \\
4.3 Uniform distribution of random variables / 54 \\
5 Scale-, Base-, and Sum-Invariance / 63 \\
5.1 The scale-invariance property / 63 \\
5.2 The base-invariance property / 74 \\
5.3 The sum-invariance property / 80 \\
6 Real-valued Deterministic Processes / 90 \\
6.1 Iteration of functions / 90 \\
6.2 Sequences with polynomial growth / 93 \\
6.3 Sequences with exponential growth / 97 \\
6.4 Sequences with super-exponential growth / 101 \\
6.5 An application to Newton's method / 111 \\
6.6 Time-varying systems / 116 \\
6.7 Chaotic systems: Two examples / 124 \\
6.8 Differential equations / 127 \\
7 Multi-dimensional Linear Processes / 135 \\
7.1 Linear processes, observables, and difference
equations / 135 \\
7.2 Nonnegative matrices / 139 \\
7.3 General matrices / 145 \\
7.4 An application to Markov chains / 162 \\
7.5 Linear difference equations / 165 \\
7.6 Linear differential equations / 170 \\
8 Real-valued Random Processes / 180 \\
8.1 Convergence of random variables to Benford's law /
180 \\
8.2 Powers, products, and sums of random variables /
182 \\
8.3 Mixtures of distributions / 202 \\
8.4 Random maps / 213 \\
9 Finitely Additive Probability and Benford's Law / 216
\\
9.1 Finitely additive probabilities / 217 \\
9.2 Finitely additive Benford probabilities / 219 \\
10 Applications of Benford's Law / 223 \\
10.1 Fraud detection / 224 \\
10.2 Detection of natural phenomena / 225 \\
10.3 Diagnostics and design / 226 \\
10.4 Computations and Computer Science / 228 \\
10.5 Pedagogical tool / 230 \\
List of Symbols / 231 \\
Bibliography / 234 \\
Index / 245",
}
@Article{Berger:2015:MLF,
author = "Arno Berger",
title = "Most linear flows on {$ R^d $} are {Benford}",
journal = j-J-DIFFER-EQU,
volume = "259",
number = "5",
pages = "1933--1957",
year = "2015",
CODEN = "JDEQAK",
DOI = "https://doi.org/10.1016/j.jde.2015.03.016",
ISSN = "0022-0396 (print), 1090-2732 (electronic)",
ISSN-L = "0022-0396",
MRclass = "60F99 (11J71 11K41 37A05 37A45 62E20)",
MRnumber = "3349424",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022039615001527",
abstract = "A necessary and sufficient condition (exponential
nonresonance) is established for every signal obtained
from a linear flow on $ R^d $ by means of a linear
observable to either vanish identically or else exhibit
a strong form of Benford's Law (logarithmic
distribution of significant digits). The result extends
and unifies all previously known (sufficient)
conditions. Exponential nonresonance is shown to be
typical for linear flows, both from a topological and a
measure-theoretical point of view.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Differential Equations",
keywords = "(Continuous) uniform distribution mod 1;
(Exponentially) nonresonant set; Benford function;
Linear flow; Observable; Q -independence",
}
@InCollection{Berger:2015:SIM,
author = "Arno Berger and T. P. Hill",
title = "A short introduction to the mathematical theory of
{Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "23--67",
year = "2015",
DOI = "https://doi.org/10.1515/9781400866588",
MRclass = "37A45 (11K06 60-02 60F15 60G57 62E10)",
MRnumber = "3411057",
bibdate = "Sat Mar 25 08:23:36 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Bermano:2015:DST,
author = "Amit Bermano and Thabo Beeler and Yeara Kozlov and
Derek Bradley and Bernd Bickel and Markus Gross",
title = "Detailed spatio-temporal reconstruction of eyelids",
journal = j-TOG,
volume = "34",
number = "4",
pages = "44:1--44:??",
month = aug,
year = "2015",
CODEN = "ATGRDF",
DOI = "https://doi.org/10.1145/2766924",
ISSN = "0730-0301 (print), 1557-7368 (electronic)",
ISSN-L = "0730-0301",
bibdate = "Tue Jul 28 17:22:44 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/tog/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tog.bib",
abstract = "In recent years we have seen numerous improvements on
3D scanning and tracking of human faces, greatly
advancing the creation of digital doubles for film and
video games. However, despite the high-resolution
quality of the reconstruction approaches available,
current methods are unable to capture one of the most
important regions of the face --- the eye region. In
this work we present the first method for detailed
spatio-temporal reconstruction of eyelids. Tracking and
reconstructing eyelids is extremely challenging, as
this region exhibits very complex and unique skin
deformation where skin is folded under while opening
the eye. Furthermore, eyelids are often only partially
visible and obstructed due to self-occlusion and
eyelashes. Our approach is to combine a geometric
deformation model with image data, leveraging
multi-view stereo, optical flow, contour tracking and
wrinkle detection from local skin appearance. Our
deformation model serves as a prior that enables
reconstruction of eyelids even under strong
self-occlusions caused by rolling and folding skin as
the eye opens and closes. The output is a
person-specific, time-varying eyelid reconstruction
with anatomically plausible deformations. Our
high-resolution detailed eyelids couple naturally with
current facial performance capture approaches. As a
result, our method can largely increase the fidelity of
facial capture and the creation of digital doubles.",
acknowledgement = ack-nhfb,
articleno = "44",
fjournal = "ACM Transactions on Graphics",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J778",
}
@Article{Berzunza:2015:YPR,
author = "Gabriel Berzunza",
title = "{Yule} processes with rare mutation and their
applications to percolation on $b$-ary trees",
journal = j-ELECTRON-J-PROBAB,
volume = "20",
number = "??",
pages = "43:1--43:23",
month = "????",
year = "2015",
CODEN = "????",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Fri Aug 7 10:50:36 MDT 2015",
bibsource = "http://ejp.ejpecp.org/index.php/ejp/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/3789",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Bhole:2015:BAU,
author = "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh",
title = "{Benford} analysis: A useful paradigm for
spectroscopic analysis",
journal = j-CHEM-PHYS-LETT,
volume = "639",
number = "??",
pages = "36--40",
year = "2015",
CODEN = "CHPLBC",
DOI = "https://doi.org/10.1016/j.cplett.2015.08.061",
ISSN = "0009-2614 (print), 1873-4448 (electronic)",
ISSN-L = "0009-2614",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0009261415006582",
abstract = "Benford's law is a statistical inference to predict
the frequency of significant digits in naturally
occurring numerical databases. In such databases this
law predicts a higher occurrence of the digit $1$ in
the most significant place and decreasing occurrences
to other larger digits. Although counter-intuitive at
first sight, Benford's law has seen applications in a
wide variety of fields like physics, earth-science,
biology, finance, etc. In this work, we have explored
the use of Benford's law for various spectroscopic
applications. Although, we use NMR signals as our
databases, the methods described here may also be
extended to other spectroscopic techniques. In
particular, with the help of Benford analysis, we
demonstrate emphasizing weak NMR signals and spectral
corrections. We also explore a potential application of
Benford analysis in the image-processing of MRI data.",
acknowledgement = ack-nhfb,
fjournal = "Chemical Physics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00092614",
}
@Article{Biau:2015:FDF,
author = "Damien Biau",
title = "The first-digit frequencies in data of turbulent
flows",
journal = j-PHYSICA-A,
volume = "440",
number = "??",
pages = "147--154",
day = "15",
month = dec,
year = "2015",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2015.08.016",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "76F20 (82B05)",
MRnumber = "3398896",
bibdate = "Tue Jan 26 11:15:41 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Brunsch:2015:ISA,
author = "Tobias Brunsch and Heiko R{\"o}glin",
title = "Improved Smoothed Analysis of Multiobjective
Optimization",
journal = j-J-ACM,
volume = "62",
number = "1",
pages = "4:1--4:??",
month = feb,
year = "2015",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/2699445",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Mar 3 12:47:00 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "We present several new results about smoothed analysis
of multiobjective optimization problems. Motivated by
the discrepancy between worst-case analysis and
practical experience, this line of research has gained
a lot of attention in the last decade. We consider
problems in which d linear and one arbitrary objective
function are to be optimized over a set $ S \subseteq
\{ 0, 1 \}^n $ of feasible solutions. We improve the
previously best known bound for the smoothed number of
Pareto-optimal solutions to $ O(n^{2 d} \phi^d) $,
where $ \phi $ denotes the perturbation parameter.
Additionally, we show that for any constant $c$ the $c$
th moment of the smoothed number of Pareto-optimal
solutions is bounded by $ O((n^{2 d} \phi^d)^c)$. This
improves the previously best known bounds
significantly. Furthermore, we address the criticism
that the perturbations in smoothed analysis destroy the
zero-structure of problems by showing that the smoothed
number of Pareto-optimal solutions remains polynomially
bounded even for zero-preserving perturbations. This
broadens the class of problems captured by smoothed
analysis and it has consequences for nonlinear
objective functions. One corollary of our result is
that the smoothed number of Pareto-optimal solutions is
polynomially bounded for polynomial objective
functions. Our results also extend to integer
optimization problems.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Cacciari:2015:DMC,
author = "I. Cacciari and P. Nieri and S. Siano",
title = "{$3$D} Digital Microscopy for Characterizing
Punchworks on Medieval Panel Paintings",
journal = j-JOCCH,
volume = "7",
number = "4",
pages = "19:1--19:??",
month = feb,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2594443",
ISSN = "1556-4673 (print), 1556-4711 (electronic)",
ISSN-L = "1556-4673",
bibdate = "Wed Feb 11 13:42:37 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/jocch/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jocch.bib",
abstract = "This article is devoted to a novel application of the
micro-3D modeling based on shape from focus. A 3D
portable digital microscope prototype has been used for
the first time in order to analyze gold punchwork on
medieval panel paintings. In general, the 3D domain
provides a more flexible and complete characterization
of these decorative elements than traditional
photographic documentation. Low-magnification 3D
digital microscopy is well suited for analyzing
morphologies, depths, and profiles of different punch
marks. Here, we used these parameters for interpreting
the punching process and recognizing sliding and
bouncing effects. The 3D reconstruction of the surface
engraved also allowed identifying types of anomalies
that could be useful as possible authentication
markers. The advantages of the present approach with
respect to the photographic documentation are of
general valence and can be exploited in order to
document, parameterize, and interpret a variety of
engraving works on panel paintings and metal
artifacts.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "Journal on Computing and Cultural Heritage (JOCCH)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}
@Article{Carrera:2015:TER,
author = "C{\'e}sar Carrera",
title = "Tracking exchange rate management in {Latin America}",
journal = "Review of Financial Economics",
volume = "25",
number = "??",
pages = "35--41",
year = "2015",
DOI = "https://doi.org/10.1016/j.rfe.2015.02.004",
ISSN = "1058-3300 (print), 1873-5924 (electronic)",
ISSN-L = "1058-3300",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Special Issue on Changing Dynamics in Financial
Economics",
URL = "http://www.sciencedirect.com/science/article/pii/S105833001500018X",
abstract = "One way to track exchange-rate deviations from its
long-run value is to examine numerical patterns in
exchange rates to see if those patterns appear to have
been subjected to some degree of policy management. We
apply Benford's Law to exchange rates in Latin American
countries, computing and comparing the distribution of
exchange-rate observed values with those of Benford's
Law. For most cases we find that the exchange rate for
the US dollar does not satisfy Benford's Law, however
this law holds when the euro is considered. This result
may be explained by the fact that these countries are
characterized for having different degrees of
dollarization and intervention in the US dollar forex
market while there is almost no policy intervention in
the euro forex market. Our approach is an alternative
view of how these characteristics play a role inducing
deviations with respect to an implied equilibrium
exchange rate.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Exchange rate; Forex; FX intervention;
International reserves",
}
@Article{Chaves-Gonzalez:2015:DEP,
author = "Jos{\'e} M. Chaves-Gonz{\'a}lez and Miguel A.
P{\'e}rez-Toledano",
title = "Differential evolution with {Pareto} tournament for
the multi-objective next release problem",
journal = j-APPL-MATH-COMP,
volume = "252",
number = "??",
pages = "1--13",
day = "1",
month = feb,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Feb 18 09:36:18 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314016257",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Cuff:2015:WDB,
author = "Victoria Cuff and Allison Lewis and Steven J. Miller",
title = "The {Weibull} distribution and {Benford's Law}",
journal = "Involve",
volume = "8",
number = "5",
pages = "859--874",
year = "2015",
DOI = "https://doi.org/10.2140/involve.2015.8.859",
ISSN = "1944-4176 (print), 1944-4184 (electronic)",
ISSN-L = "1944-4176",
MRclass = "60F05 (11K06 42A16 60E10 62E15 62P99)",
MRnumber = "3404662",
MRreviewer = "Nikolai Volodin",
bibdate = "Tue Jan 26 11:03:29 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Involve. A Journal of Mathematics",
journal-URL = "http://msp.org/involve/",
}
@Article{Dandurand:2015:DCP,
author = "Brian Dandurand and Margaret M. Wiecek",
title = "Distributed Computation of {Pareto} Sets",
journal = j-SIAM-J-OPT,
volume = "25",
number = "2",
pages = "1083--1109",
month = "????",
year = "2015",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/130929564",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
bibdate = "Sat Aug 8 07:33:46 MDT 2015",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/25/2;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
onlinedate = "January 2015",
}
@Article{delCastillo:2015:LIG,
author = "Joan del Castillo and Isabel Serra",
title = "Likelihood inference for generalized {Pareto}
distribution",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "83",
number = "??",
pages = "116--128",
month = mar,
year = "2015",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:44:05 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167947314003065",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Ferreira:2015:LPA,
author = "Anselmo Ferreira and Luiz C. Navarro and Giuliano
Pinheiro and Jefersson A. dos Santos and Anderson
Rocha",
title = "Laser printer attribution: Exploring new features and
beyond",
journal = "Forensic Science International",
volume = "247",
number = "0",
pages = "105--125",
year = "2015",
DOI = "https://doi.org/10.1016/j.forsciint.2014.11.030",
ISSN = "0379-0738 (print), 1872-6283 (electronic)",
ISSN-L = "0379-0738",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
note = "See also \cite{Jiang:2010:NMS}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0379073814005064",
abstract = "With a huge amount of printed documents nowadays,
identifying their source is useful for criminal
investigations and also to authenticate digital copies
of a document. In this paper, we propose novel
techniques for laser printer attribution. Our solutions
do not need very high resolution scanning of the
investigated document and explore the multidirectional,
multiscale and low-level gradient texture patterns
yielded by printing devices. The main contributions of
this work are: (1) the description of printed areas
using multidirectional and multiscale co-occurring
texture patterns; (2) description of texture on
low-level gradient areas by a convolution texture
gradient filter that emphasizes textures in specific
transition areas and (3) the analysis of printer
patterns in segments of interest, which we call frames,
instead of whole documents or only printed letters. We
show by experiments in a well documented dataset that
the proposed methods outperform techniques described in
the literature and present near-perfect classification
accuracy being very promising for deployment in
real-world forensic investigations.",
acknowledgement = ack-nhfb,
keywords = "Banding; Benford's Law; Printer forensics; Texture
patterns",
}
@Article{Garrabrant:2015:ALU,
author = "Scott Garrabrant and Siddharth Bhaskar and Abram
Demski and Joanna Garrabrant and George Koleszarik and
Evan Lloyd",
title = "Asymptotic Logical Uncertainty and The {Benford}
Test",
journal = "CoRR",
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.48550/arXiv.1510.03370",
ISSN = "????",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1510.03370;
https://dblp.org/db/journals/corr/corr1510.html#GarrabrantBDGKL15",
abstract = "We give an algorithm A which assigns probabilities to
logical sentences. For any simple infinite sequence of
sentences whose truth-values appear indistinguishable
from a biased coin that outputs ``true'' with
probability $p$, we have that the sequence of
probabilities that A assigns to these sentences
converges to $p$.",
acknowledgement = ack-nhfb,
dblp-key = "journals/corr/GarrabrantBDGKL15",
dblp-mdate = "2018-08-13",
}
@Article{Goegebeur:2015:ETI,
author = "Yuri Goegebeur and Armelle Guillou and Michael
Osmann",
title = "An estimator for the tail index of an integrated
conditional {Pareto--Weibull}-type model",
journal = j-STAT-PROB-LETT,
volume = "103",
number = "??",
pages = "8--16",
month = aug,
year = "2015",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Mon Jun 8 18:57:37 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715215001182",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
}
@Article{Goel:2015:PCA,
author = "Gagan Goel and Vahab Mirrokni and Renato Paes Leme",
title = "Polyhedral Clinching Auctions and the {AdWords}
Polytope",
journal = j-J-ACM,
volume = "62",
number = "3",
pages = "18:1--18:??",
month = jun,
year = "2015",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/2757277",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Aug 7 10:12:49 MDT 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "A central issue in applying auction theory in practice
is the problem of dealing with budget-constrained
agents. A desirable goal in practice is to design
incentive compatible, individually rational, and Pareto
optimal auctions while respecting the budget
constraints. Achieving this goal is particularly
challenging in the presence of nontrivial combinatorial
constraints over the set of feasible allocations.
Toward this goal and motivated by AdWords auctions, we
present an auction for polymatroidal environments
satisfying these properties. Our auction employs a
novel clinching technique with a clean geometric
description and only needs an oracle access to the
submodular function defining the polymatroid. As a
result, this auction not only simplifies and
generalizes all previous results, it applies to several
new applications including AdWords Auctions, bandwidth
markets, and video on demand. In particular, our
characterization of the AdWords auction as
polymatroidal constraints might be of independent
interest. This allows us to design the first mechanism
for Ad Auctions taking into account simultaneously
budgets, multiple keywords and multiple slots. We show
that it is impossible to extend this result to generic
polyhedral constraints. This also implies an
impossibility result for multiunit auctions with
decreasing marginal utilities in the presence of budget
constraints.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Gunasekera:2015:GIR,
author = "Sumith Gunasekera",
title = "Generalized inferences of {$ R = \Pr (X > Y) $} for
{Pareto} distribution",
journal = j-STAT-PAPERS,
volume = "56",
number = "2",
pages = "333--351",
month = may,
year = "2015",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-014-0584-8",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Fri Apr 10 15:56:09 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/article/10.1007/s00362-014-0584-8",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{Han:2015:PSS,
author = "Qixing Han and Daqing Jiang",
title = "Periodic solution for stochastic non-autonomous
multispecies {Lotka--Volterra} mutualism type
ecosystem",
journal = j-APPL-MATH-COMP,
volume = "262",
number = "??",
pages = "204--217",
day = "1",
month = jul,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon May 18 12:21:15 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315005007",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Hu:2015:EES,
author = "Yangzi Hu and Fuke Wu",
title = "Exponential extinction of a stochastic
{Lotka--Volterra} model with expectations in
coefficients",
journal = j-IMA-J-APPL-MATH,
volume = "80",
number = "4",
pages = "1219--1234",
month = aug,
year = "2015",
CODEN = "IJAMDM",
DOI = "https://doi.org/10.1093/imamat/hxu050",
ISSN = "0272-4960 (print), 1464-3634 (electronic)",
ISSN-L = "0272-4960",
bibdate = "Sat Jul 25 19:12:11 MDT 2015",
bibsource = "http://imamat.oxfordjournals.org/contentcontent/80/4.toc;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/imajapplmath.bib",
URL = "http://imamat.oxfordjournals.org/content/80/4/1219",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Applied Mathematics",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
onlinedate = "October 23, 2014",
}
@Article{Hurlimann:2015:BLS,
author = "Werner H{\"u}rlimann",
title = "{Benford's Law} in Scientific Research",
journal = j-INT-J-SCI-ENG-RESEARCH,
volume = "6",
number = "7",
pages = "143--148",
month = jul,
year = "2015",
ISSN = "2229-5518",
ISSN-L = "2229-5518",
bibdate = "Wed Jul 29 06:32:18 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ijser.org/onlineResearchPaperViewer.aspx?Benfords-Law-in-Scientific-Research.pdf",
abstract = "As departures from Benford's law have been observed in
many scientific data sets, there is a theoretical need
to understand such discrepancies. We argue that the use
of parametric extensions to Benford's law is
appropriate and demonstrate this for several first
significant digit distributions taken from theoretical
scientific laws or extracted from real-world data
sets.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Scientific and Engineering
Research",
journal-URL = "http://www.ijser.org/",
}
@Article{Hurlimann:2015:FDT,
author = "Werner H{\"u}rlimann",
title = "A first digit theorem for powerful integer powers",
journal = j-SPRINGERPLUS,
volume = "4",
number = "1",
pages = "576:1--576:??",
day = "6",
month = oct,
year = "2015",
CODEN = "SPRIFB",
DOI = "https://doi.org/10.1186/s40064-015-1370-3",
ISSN = "2193-1801",
ISSN-L = "2193-1801",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1186/s40064-015-1370-3",
acknowledgement = ack-nhfb,
fjournal = "SpringerPlus",
journal-URL = "http://link.springer.com/journal/40064",
keywords = "Benford's Law",
}
@Article{Hurlimann:2015:URU,
author = "Werner H{\"u}rlimann",
title = "On the uniform random upper bound family of first
significant digit distributions",
journal = j-J-INFORMETRICS,
volume = "9",
number = "2",
pages = "349--358",
year = "2015",
DOI = "https://doi.org/10.1016/j.joi.2015.02.007",
ISSN = "1751-1577 (print), 1875-5879 (electronic)",
ISSN-L = "1751-1577",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1751157715000255",
abstract = "The first significant digit patterns arising from a
mixture of uniform distributions with a random upper
bound are revisited. A closed-form formula for its
first significant digit distribution (FSD) is obtained.
The one-parameter model of Rodriguez is recovered for
an extended truncated Pareto mixing distribution.
Considering additionally the truncated Erlang, gamma
and Burr mixing distributions, and the generalized
Benford law, for which another probabilistic derivation
is offered, we study the fitting capabilities of the
FSD's for various Benford like data sets from
scientific research. Based on the results, we propose
the general use of a fine structure index for Benford's
law in case the data is well fitted by the truncated
Erlang member of the uniform random upper bound family
of FSD's.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informetrics",
journal-URL = "http://www.sciencedirect.com/science/journal/17511577",
keywords = "Benford's law; Erlang distribution; Extended truncated
Pareto; Simulation algorithm; Stigler's law; Uniform
distribution",
}
@Article{Iafrate:2015:EDN,
author = "Joseph R. Iafrate and Steven J. Miller and Frederick
W. Strauch",
title = "Equipartitions and a distribution for numbers: A
statistical model for {Benford's Law}",
journal = j-PHYS-REV-E,
volume = "91",
number = "6",
pages = "062138:1--062138:6",
month = jun,
year = "2015",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/PhysRevE.91.062138",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "60E99 (82B05)",
MRnumber = "3491369",
bibdate = "Tue Jan 26 11:15:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevE.91.062138",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
numpages = "6",
}
@Article{Khataei:2015:PPB,
author = "Amirsam Khataei and Ali Arya",
title = "Personalized presentation builder for persuasive
communication",
journal = j-COMMUN-DESIGN-Q-REVIEW,
volume = "3",
number = "3",
pages = "25--32",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2792989.2792993",
ISSN = "2166-1200 (print), 2166-1642 (electronic)",
ISSN-L = "2166-1200",
bibdate = "Wed Jun 17 19:00:11 MDT 2015",
bibsource = "http://dl.acm.org/citation.cfm?id=J1351;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/commundesignqreview.bib",
abstract = "Presentations are effective ways of communicating
information, especially in the field of education, but
they might not be equally or fully beneficial and
persuasive to all users. Each member of the audience
might be interested in a particular topic, come from a
different background and profession, and have his or
her own personality traits. In this conceptual paper,
we first describe our persuasive personalization model;
the Individualization Pyramid based on Yale Attitude
Change Approach. The model consists of the following
main sections: selecting contents by applying
segmentation, adjusting comprehensibility of the text,
tailoring the language of the text to fit with user's
personality and recommending content that is associated
with user's personal history within the related
subjects. We then propose an enhanced version of our
previously published presentation builder, which uses
users' digital traces such as those on social media to
personalize presentation content. Finally, we highlight
the available tools and algorithms to assist us with
developing the system.",
acknowledgement = ack-nhfb,
fjournal = "Communication Design Quarterly Review",
journal-URL = "http://dl.acm.org/citation.cfm?id=J1351",
}
@Article{Khosravani:2015:DBC,
author = "Azar Khosravani and Constantin Rasinariu",
title = "$n$-digit {Benford} converges to {Benford}",
journal = j-INT-J-MATH-MATH-SCI,
pages = "Art. ID 123816, 4",
year = "2015",
DOI = "https://doi.org/10.1155/2015/123816",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "60F25 (11K45)",
MRnumber = "3442627",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
journal-URL = "https://www.hindawi.com/journals/ijmms/",
}
@Book{Kossovsky:2015:BLT,
author = "Alex Ely Kossovsky",
title = "{Benford's Law}: theory, the general law of relative
quantities, and forensic fraud detection applications",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxi + 649",
year = "2015",
DOI = "https://doi.org/10.1142/9089",
ISBN = "981-4583-68-5 (hardcover), 981-4583-69-3 (e-book)",
ISBN-13 = "978-981-4583-68-8 (hardcover), 978-981-4583-69-5
(e-book)",
LCCN = "HV8079.F7 K67 2015",
bibdate = "Mon Feb 16 17:20:54 MST 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Contrary to common intuition that all digits should
occur randomly with equal chances in real data,
empirical examinations consistently show that not all
digits are created equal, but rather that low digits
such as {1, 2, 3} occur much more frequently than high
digits such as {7, 8, 9} in almost all data types, such
as those relating to geology, chemistry, astronomy,
physics, and engineering, as well as in accounting,
financial, econometrics, and demographics data sets.
This intriguing digital phenomenon is known as
Benford's Law. This book represents an attempt to give
a comprehensive and in-depth account of all the
theoretical aspects, results, causes and explanations
of Benford's Law, with a strong emphasis on the
connection to real-life data and the physical
manifestation of the law. In addition to such a bird's
eye view of the digital phenomenon, the conceptual
distinctions between digits, numbers, and quantities
are explored; leading to the key finding that the
phenomenon is actually quantitative in nature;
originating from the fact that in extreme generality,
nature creates many small quantities but very few big
quantities, corroborating the motto ``small is
beautiful'', and that therefore all this is applicable
just as well to data written in the ancient Roman,
Mayan, Egyptian, and other digit-less civilizations.
Fraudsters are typically not aware of this digital
pattern and tend to invent numbers with approximately
equal digital frequencies. The digital analyst can
easily check reported data for compliance with this
digital law, enabling the detection of tax evasion,
Ponzi schemes, and other financial scams. The forensic
fraud detection section in this book is written in a
very concise and reader-friendly style; gathering all
known methods and standards in the accounting and
auditing industry; summarizing and fusing them into a
singular coherent whole; and can be understood without
deep knowledge in statistical theory or advanced
mathematics. In addition, a digital algorithm is
presented, enabling the auditor to detect fraud even
when the sophisticated cheater is aware of the law and
invents numbers accordingly. The algorithm employs a
subtle inner digital pattern within the Benford's
pattern itself. This newly discovered pattern is deemed
to be nearly universal, being even more prevalent than
the Benford phenomenon, as it is found in all random
data sets, Benford as well as non-Benford types.",
acknowledgement = ack-nhfb,
subject = "Fraud investigation; Statistical methods; Fraud;
Distribution (Probability theory); Forensic statistics;
Forensic sciences",
tableofcontents = "1. Benford's law \\
2. Forensic digital analysis and fraud detection \\
3. Data compliance tests \\
4. Conceptual and mathematical foundations \\
5. Benford's law in the physical sciences \\
6. Topics in Benford's law \\
7. The law of Relative quantities",
}
@Article{Kozubowski:2015:DTP,
author = "Tomasz J. Kozubowski and Anna K. Panorska and Matthew
L. Forister",
title = "A discrete truncated {Pareto} distribution",
journal = j-STAT-METHODOL,
volume = "26",
number = "??",
pages = "135--150",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.stamet.2015.04.002",
ISSN = "1572-3127 (print), 1878-0954 (electronic)",
ISSN-L = "1572-3127",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1572312715000313",
abstract = "We propose a new discrete distribution with finite
support, which generalizes truncated Pareto and beta
distributions as well as uniform and Benford's laws.
Although our focus is on basic properties and
stochastic representations, we also consider parameter
estimation and include an illustration from ecology
showing potential applications of this new stochastic
model.",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methodology",
journal-URL = "http://www.sciencedirect.com/science/journal/15723127/",
keywords = "Benford's Law; Beta distribution; Discrete Pareto;
Ecology; First digit law; Heavy tail; Maximum
likelihood estimation; Power law; Truncated geometric;
Truncated Pareto",
}
@Article{Kramer:2015:MJE,
author = "Walter Kr{\"a}mer",
title = "{Miller, S. J. (ed.): \booktitle{Benford's law. Theory
and applications}}",
journal = j-STAT-PAPERS,
volume = "56",
number = "4",
pages = "1251--1252",
month = nov,
year = "2015",
CODEN = "STPAE4",
DOI = "https://doi.org/10.1007/s00362-015-0717-8",
ISSN = "0932-5026 (print), 1613-9798 (electronic)",
ISSN-L = "0932-5026",
bibdate = "Tue Nov 17 09:38:07 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s00362-015-0717-8",
acknowledgement = ack-nhfb,
fjournal = "Statistical Papers",
journal-URL = "http://link.springer.com/journal/362",
}
@Article{Kudryashov:2015:APE,
author = "Nikolay A. Kudryashov and Anastasia S. Zakharchenko",
title = "Analytical properties and exact solutions of the
{Lotka--Volterra} competition system",
journal = j-APPL-MATH-COMP,
volume = "254",
number = "??",
pages = "219--228",
day = "1",
month = mar,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Feb 23 08:51:11 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314017743",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Lafouge:2015:DTP,
author = "Thierry Lafouge and Abdellatif Agouzal and Genevieve
Lallich",
title = "The deconstruction of a text: the permanence of the
generalized {Zipf} law --- the inter-textual
relationship between entropy and effort amount",
journal = j-SCIENTOMETRICS,
volume = "104",
number = "1",
pages = "193--217",
month = jul,
year = "2015",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-015-1600-z",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Wed Sep 2 12:06:12 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-015-1600-z",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@InCollection{Lee:2015:GBL,
author = "Joanne Lee and Wendy K. Tam Cho and George Judge",
title = "Generalizing {Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "304--316",
year = "2015",
MRclass = "62P10",
MRnumber = "3411066",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Leemis:2015:BLG,
author = "Lawrence Leemis",
title = "{Benford's Law} geometry",
crossref = "Miller:2015:BLT",
pages = "109--118",
year = "2015",
MRclass = "62E17 (60E05)",
MRnumber = "3411059",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Lewis:2015:SDA,
author = "Peter R. Lewis and Lukas Esterle and Arjun Chandra and
Bernhard Rinner and Jim Torresen and Xin Yao",
title = "Static, Dynamic, and Adaptive Heterogeneity in
Distributed Smart Camera Networks",
journal = j-TAAS,
volume = "10",
number = "2",
pages = "8:1--8:??",
month = jun,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2764460",
ISSN = "1556-4665 (print), 1556-4703 (electronic)",
ISSN-L = "1556-4665",
bibdate = "Wed Jun 10 08:01:03 MDT 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/taas.bib",
abstract = "We study heterogeneity among nodes in self-organizing
smart camera networks, which use strategies based on
social and economic knowledge to target communication
activity efficiently. We compare homogeneous
configurations, when cameras use the same strategy,
with heterogeneous configurations, when cameras use
different strategies. Our first contribution is to
establish that static heterogeneity leads to new
outcomes that are more efficient than those possible
with homogeneity. Next, two forms of dynamic
heterogeneity are investigated: nonadaptive mixed
strategies and adaptive strategies, which learn online.
Our second contribution is to show that mixed
strategies offer Pareto efficiency consistently
comparable with the most efficient static heterogeneous
configurations. Since the particular configuration
required for high Pareto efficiency in a scenario will
not be known in advance, our third contribution is to
show how decentralized online learning can lead to more
efficient outcomes than the homogeneous case. In some
cases, outcomes from online learning were more
efficient than all other evaluated configuration types.
Our fourth contribution is to show that online learning
typically leads to outcomes more evenly spread over the
objective space. Our results provide insight into the
relationship between static, dynamic, and adaptive
heterogeneity, suggesting that all have a key role in
achieving efficient self-organization.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Autonomous and Adaptive Systems
(TAAS)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1010",
}
@Article{Li:2015:BBL,
author = "Qinglei Li and Zuntao Fu and Naiming Yuan",
title = "Beyond {Benford's Law}: Distinguishing Noise from
Chaos",
journal = j-PLOS-ONE,
volume = "10",
number = "6",
pages = "e0129161:1--e0129161:11",
day = "1",
month = jun,
year = "2015",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0129161",
ISSN = "1932-6203",
bibdate = "Wed Aug 12 08:58:10 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0129161",
abstract = "Determinism and randomness are two inherent aspects of
all physical processes. Time series from chaotic
systems share several features identical with those
generated from stochastic processes, which makes them
almost undistinguishable. In this paper, a new method
based on Benford's law is designed in order to
distinguish noise from chaos by only information from
the first digit of considered series. By applying this
method to discrete data, we confirm that chaotic data
indeed can be distinguished from noise data,
quantitatively and clearly.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{Lin:2015:DES,
author = "Cheng-Yen Lin and Chung-Wen Huang and Chi-Bang Kuan
and Shi-Yu Huang and Jenq-Kuen Lee",
title = "The Design and Experiments of a {SID}-Based
Power-Aware Simulator for Embedded Multicore Systems",
journal = j-TODAES,
volume = "20",
number = "2",
pages = "22:1--22:??",
month = feb,
year = "2015",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/2699834",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Tue Mar 3 14:46:37 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/todaes/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
abstract = "Embedded multicore systems are playing increasingly
important roles in the design of consumer electronics.
The objective of such systems is to optimize both
performance and power characteristics of mobile
devices. However, currently there are no power metrics
supporting popular application design platforms (such
as SID) that application developers use to develop
their applications. This hinders the ability of
application developers to optimize power consumption.
In this article we present the design and experiments
of a SID-based power-aware simulation framework for
embedded multicore systems. The proposed power
estimation flow includes two phases: IP-level power
modeling and power-aware system simulation. The first
phase employs PowerMixer$^{IP}$ to construct the power
model for the processor IP and other major IPs, while
the second phase involves a power abstract
interpretation method for summarizing the simulation
trace, then, with a CPE module, estimating the power
consumption based on the summarized trace information
and the input of IP power models. In addition, a
Manager component is devised to map each digital signal
processor (DSP) component to a host thread and maintain
the access to shared resources. The aim is to maintain
the simulation performance as the number of simulated
DSP components increases. A power-profiling API is also
supported that developers of embedded software can use
to tune the granularity of power-profiling for a
specific code section of the target application. We
demonstrate via case studies and experiments how
application developers can use our SID-based power
simulator for optimizing the power consumption of their
applications. We characterize the power consumption of
DSP applications with the DSPstone benchmark and
discuss how compiler optimization levels with SIMD
intrinsics influence the performance and power
consumption. A histogram application and an
augmented-reality application based on human-face-based
RMS (recognition, mining, and synthesis) application
are deployed as running examples on multicore systems
to demonstrate how our power simulator can be used by
developers in the optimization process to illustrate
different views of power dissipations of
applications.",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
}
@Article{Liu:2015:ASN,
author = "Qun Liu",
title = "Analysis of a stochastic non-autonomous food-limited
{Lotka--Volterra} cooperative model",
journal = j-APPL-MATH-COMP,
volume = "254",
number = "??",
pages = "1--8",
day = "1",
month = mar,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Feb 23 08:51:11 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314018037",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Liu:2015:DSD,
author = "Qun Liu and Qingmei Chen",
title = "Dynamics of stochastic delay {Lotka--Volterra} systems
with impulsive toxicant input and {L{\'e}vy} noise in
polluted environments",
journal = j-APPL-MATH-COMP,
volume = "256",
number = "??",
pages = "52--67",
day = "1",
month = apr,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Feb 27 06:15:38 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315000235",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Liu:2015:SPA,
author = "Si Liu and Qiang Chen and Shuicheng Yan and Changsheng
Xu and Hanqing Lu",
title = "{Snap \& Play}: Auto-Generated Personalized
Find-the-Difference Game",
journal = j-TIST,
volume = "5",
number = "4",
pages = "65:1--65:??",
month = jan,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2668109",
ISSN = "2157-6904 (print), 2157-6912 (electronic)",
ISSN-L = "2157-6904",
bibdate = "Wed Feb 11 12:29:09 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tist.bib",
abstract = "In this article, by taking a popular game, the
Find-the-Difference (FiDi) game, as a concrete example,
we explore how state-of-the-art image processing
techniques can assist in developing a personalized,
automatic, and dynamic game. Unlike the traditional
FiDi game, where image pairs (source image and target
image) with five different patches are manually
produced by professional game developers, the proposed
Personalized FiDi (P-FiDi) electronic game can be
played in a fully automatic Snap \& Play mode. Snap
means that players first take photos with their digital
cameras. The newly captured photos are used as source
images and fed into the P-FiDi system to autogenerate
the counterpart target images for users to play. Four
steps are adopted to autogenerate target images:
enhancing the visual quality of source images,
extracting some changeable patches from the source
image, selecting the most suitable combination of
changeable patches and difference styles for the image,
and generating the differences on the target image with
state-of-the-art image processing techniques. In
addition, the P-FiDi game can be easily redesigned for
the im-game advertising. Extensive experiments show
that the P-FiDi electronic game is satisfying in terms
of player experience, seamless advertisement, and
technical feasibility.",
acknowledgement = ack-nhfb,
articleno = "65",
fjournal = "ACM Transactions on Intelligent Systems and Technology
(TIST)",
journal-URL = "http://portal.acm.org/citation.cfm?id=J1318",
}
@Article{Llamocca:2015:DEP,
author = "Daniel Llamocca and Marios Pattichis",
title = "Dynamic Energy, Performance, and Accuracy Optimization
and Management Using Automatically Generated
Constraints for Separable {$2$D} {FIR} Filtering for
Digital Video Processing",
journal = j-TRETS,
volume = "7",
number = "4",
pages = "4:1--4:??",
month = jan,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2629623",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Fri Feb 13 07:24:19 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "There is strong interest in the development of
dynamically reconfigurable systems that can meet
real-time constraints on energy, performance, and
accuracy. The generation of real-time constraints will
significantly expand the applicability of dynamically
reconfigurable systems to new domains, such as digital
video processing. We develop a dynamically
reconfigurable 2D FIR filtering system that can meet
real-time constraints in energy, performance, and
accuracy (EPA). The real-time constraints are
automatically generated based on user input, image
types associated with video communications, and video
content. We first generate a set of Pareto-optimal
realizations, described by their EPA values and
associated 2D FIR hardware description bitstreams.
Dynamic management is then achieved by selecting
Pareto-optimal realizations that meet the automatically
generated time-varying EPA constraints. We validate our
approach using three different 2D Gaussian filters.
Filter realizations are evaluated in terms of the
required energy per frame, accuracy of the resulting
image, and performance in frames per second. We
demonstrate dynamic EPA management by applying a
Difference of Gaussians (DOG) filter to standard video
sequences. For video frame sizes that are equal to or
larger than the VGA resolution, compared to a static
implementation, our dynamic system provides significant
reduction in the total energy consumption
({$>$30}\%).",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{LoBuglio:2015:WDT,
author = "David {Lo Buglio} and Vanessa Lardinois and Livio {De
Luca}",
title = "What Do Thirty-One Columns Say about a ``Theoretical''
Thirty-Second?",
journal = j-JOCCH,
volume = "8",
number = "1",
pages = "6:1--6:??",
month = feb,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2700425",
ISSN = "1556-4673 (print), 1556-4711 (electronic)",
ISSN-L = "1556-4673",
bibdate = "Wed Feb 25 17:50:15 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/jocch/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jocch.bib",
abstract = "Over the past three decades, the introduction of
digital technologies in the field of architectural
documentation has profoundly changed tools and
acquisition techniques. Most of the developments
concern metrical and colorimetric characteristics of
the objects studied. These developments, surrounding
the practice of architectural survey, tend to respond
primarily to the requirements of completeness. In this
context, it seems necessary to assess the impact of
these instruments on the cognitive value of
architectural representation. With a strong
technological presence, the study of the built heritage
is facing a problem of ``information overload.''
Indeed, this strong technological presence fails to
strengthen representation in its role as a vehicle of
knowledge. Confronted with the intelligibility deficit,
this article proposes an original approach for reading
morphological features of an artifact by using a
bottom-up approach: the meaning of elements (i.e.,
their semantic layouts) come from a statistical
analysis of the major shape discontinuities of a
collection of instances. The idea is to rely on data
accumulation to render apparent high-level semantic
structures from the comparative analysis of common
low-level geometric features. The principles introduced
are illustrated by the study of 31 columns of the
cloister of the abbey of Saint-Michel-de-Cuxa. To
summarize, the first objective is to understand how
digital technologies can help us in the analysis of
artistic and technical production of Romanesque
columns. The second objective is to automatically
identify the common semantic articulations of the
entire collection to build a reference model for the
future assessment of each artifact.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "Journal on Computing and Cultural Heritage (JOCCH)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}
@Article{Luo:2015:IAD,
author = "Da Luo and Rui Yang and Jiwu Huang",
title = "Identification of {AMR} decompressed audio",
journal = "Digital Signal Processing",
volume = "37",
number = "0",
pages = "85--91",
year = "2015",
DOI = "https://doi.org/10.1016/j.dsp.2014.11.003",
ISSN = "1051-2004 (print), 1095-4333 (electronic)",
ISSN-L = "1051-2004",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1051200414003200",
abstract = "More and more conversation recordings from phone calls
are used as forensic evidence. To decide whether an
unknown speech recording comes from mobile phone or not
becomes an important issue in digital audio forensics.
The communicating conversation recorded by mobile
phones is encoded by Adaptive Multi-Rate (AMR) audio
codec, which was adopted as the standard speech codec
by 3GPP and widely used in {GSM} and UMTS. Therefore,
{AMR} decompressed audio detection can be used to
identify the source of the digital audio recording.
Furthermore, it is helpful to locate the forgery
position of the splicing {AMR} decompressed audio for
forensic purposes. In this article, we focus on the
identification of {AMR} decompressed audio, namely,
given the waveform of an audio, we wish to identify
whether it has been previously compressed by {AMR}
codec or not. The artifacts introduced by the {AMR}
codec will help to detect the source of the recordings.
Based on our analysis, we find that the sample
repetition rate of the {AMR} decompressed waveform is
significantly greater than the regular waveform.
Therefore, we employ the sample repetition rate as a
feature to identify the {AMR} decompressed audio. The
experimental results show that this feature is robust
and effective.",
acknowledgement = ack-nhfb,
keywords = "Audio forensics; Benford's Law; Decompression audio
identification; Sample repetition rate; {AMR}",
}
@Article{Manack:2015:LDL,
author = "Corey Manack and Steven J. Miller",
title = "Leading digit laws on linear {Lie} groups",
journal = "Research in Number Theory",
volume = "1",
number = "1",
pages = "22:1--22:19",
month = dec,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1007/s40993-015-0024-4",
ISSN = "2363-9555",
ISSN-L = "2363-9555",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s40993-015-0024-4",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/40993",
keywords = "Benford's Law; Digit laws; Haar measure; Matrix
groups",
}
@Article{Masse:2015:FGS,
author = "Bruno Mass{\'e} and Dominique Schneider",
title = "Fast growing sequences of numbers and the first digit
phenomenon",
journal = j-INT-J-NUMBER-THEORY,
volume = "11",
number = "3",
pages = "705--719",
month = may,
year = "2015",
DOI = "https://doi.org/10.1142/S1793042115500384",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11K31 (11K06)",
MRnumber = "3327839",
MRreviewer = "Steven Joel Miller",
bibdate = "Tue Jan 26 11:14:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042115500384",
abstract = "We consider a large class of fast growing sequences of
numbers $ U_n $ like the nth superfactorial, the $n$-th
hyperfactorial and similar ones. We show that their
mantissas are distributed following Benford's law in
the sense of the natural density. We prove that this is
also verified by, by and is passed down to all the
sequences obtained by iterating this design process. We
also consider the superprimorial numbers and the
products of logarithms of integers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McCartney:2015:TSD,
author = "Mark McCartney and David H. Glass",
title = "A three-state dynamical model for religious
affiliation",
journal = j-PHYSICA-A,
volume = "419",
number = "0",
pages = "145--152",
year = "2015",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2014.09.052",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437114008206",
abstract = "In the last century the western world has seen a rapid
increase in the number of people describing themselves
as affiliated with no religious group. We construct a
set of models using coupled differential equations in
which members of a society can be in one of three
groups; religiously committed, religiously affiliated
or religiously not affiliated. These models are then
used to analyse post World War {II} census data for
Northern Ireland.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Group behaviour; Nonlinear models;
Religion",
}
@InCollection{Mebane:2015:CVC,
author = "Walter R. {Mebane, Jr.}",
title = "Can vote counts' digits and {Benford's Law} diagnose
elections?",
crossref = "Miller:2015:BLT",
pages = "212--222",
year = "2015",
MRclass = "62P25 (91F10)",
MRnumber = "3411063",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Miller:2015:FAB,
author = "Steven J. Miller",
title = "{Fourier} analysis and {Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "68--105",
year = "2015",
DOI = "https://doi.org/10.1515/9781400866595",
MRclass = "60-02 (42B37 60B20 60F05 60J65 62G30 62N01 62N03)",
MRnumber = "3411058",
MRreviewer = "Rita Giuliano Antonini",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Miller:2015:HSOa,
author = "Steven J. Miller",
title = "How a Simple Observation from the 1800s about Patterns
in Big Data Sets Can Fight Fraud",
journal = "The Conversation",
volume = "??",
number = "??",
pages = "??--??",
day = "10",
month = dec,
year = "2015",
bibdate = "Mon Dec 14 09:36:50 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://theconversation.com/how-a-simple-observation-from-the-1800s-about-patterns-in-big-data-sets-can-fight-fraud-42683",
acknowledgement = ack-nhfb,
}
@Article{Miller:2015:HSOb,
author = "Steven J. Miller",
title = "How a Simple Observation from the 1800s about Patterns
in Big Data Sets Can Fight Fraud",
journal = j-SCI-COMPUT,
volume = "??",
number = "??",
pages = "??--??",
day = "10",
month = dec,
year = "2015",
CODEN = "SCHRCU",
ISSN = "1930-5753 (print), 1930-6156 (electronic)",
ISSN-L = "1930-5753",
bibdate = "Mon Dec 14 09:36:50 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.scientificcomputing.com/articles/2015/12/how-simple-observation-1800s-about-patterns-big-data-sets-can-fight-fraud",
acknowledgement = ack-nhfb,
fjournal = "Scientific Computing",
journal-URL = "http://digital.scientificcomputing.com/scientificcomputing/",
}
@InCollection{Miller:2015:QIB,
author = "Steven J. Miller",
title = "A quick introduction to {Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "3--22",
year = "2015",
DOI = "https://doi.org/10.1515/9781400866595",
MRclass = "60-02 (60E05 62-02)",
MRnumber = "3411056",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Mishra:2015:PGMa,
author = "Nikita Mishra and Huazhe Zhang and John D. Lafferty
and Henry Hoffmann",
title = "A Probabilistic Graphical Model-based Approach for
Minimizing Energy Under Performance Constraints",
journal = j-COMP-ARCH-NEWS,
volume = "43",
number = "1",
pages = "267--281",
month = mar,
year = "2015",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2786763.2694373",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Wed Jun 3 11:27:38 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "In many deployments, computer systems are
underutilized --- meaning that applications have
performance requirements that demand less than full
system capacity. Ideally, we would take advantage of
this under-utilization by allocating system resources
so that the performance requirements are met and energy
is minimized. This optimization problem is complicated
by the fact that the performance and power consumption
of various system configurations are often application
--- or even input --- dependent. Thus, practically,
minimizing energy for a performance constraint requires
fast, accurate estimations of application-dependent
performance and power tradeoffs. This paper
investigates machine learning techniques that enable
energy savings by learning Pareto-optimal power and
performance tradeoffs. Specifically, we propose LEO, a
probabilistic graphical model-based learning system
that provides accurate online estimates of an
application's power and performance as a function of
system configuration. We compare LEO to (1) offline
learning, (2) online learning, (3) a heuristic
approach, and (4) the true optimal solution. We find
that LEO produces the most accurate estimates and near
optimal energy savings.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "ASPLOS'15 conference proceedings.",
}
@Article{Mishra:2015:PGMb,
author = "Nikita Mishra and Huazhe Zhang and John D. Lafferty
and Henry Hoffmann",
title = "A Probabilistic Graphical Model-based Approach for
Minimizing Energy Under Performance Constraints",
journal = j-SIGPLAN,
volume = "50",
number = "4",
pages = "267--281",
month = apr,
year = "2015",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2775054.2694373",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue May 12 17:41:19 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "In many deployments, computer systems are
underutilized --- meaning that applications have
performance requirements that demand less than full
system capacity. Ideally, we would take advantage of
this under-utilization by allocating system resources
so that the performance requirements are met and energy
is minimized. This optimization problem is complicated
by the fact that the performance and power consumption
of various system configurations are often application
--- or even input --- dependent. Thus, practically,
minimizing energy for a performance constraint requires
fast, accurate estimations of application-dependent
performance and power tradeoffs. This paper
investigates machine learning techniques that enable
energy savings by learning Pareto-optimal power and
performance tradeoffs. Specifically, we propose LEO, a
probabilistic graphical model-based learning system
that provides accurate online estimates of an
application's power and performance as a function of
system configuration. We compare LEO to (1) offline
learning, (2) online learning, (3) a heuristic
approach, and (4) the true optimal solution. We find
that LEO produces the most accurate estimates and near
optimal energy savings.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "ASPLOS '15 conference proceedings.",
}
@InCollection{Nigrini:2015:DFE,
author = "Mark Nigrini",
title = "Detecting fraud and errors using {Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "191--211",
year = "2015",
MRclass = "62P20",
MRnumber = "3411062",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Noll:2015:FAO,
author = "Tobias N{\"o}ll and Johannes K{\"o}hler and Gerd Reis
and Didier Stricker",
title = "Fully Automatic, Omnidirectional Acquisition of
Geometry and Appearance in the Context of Cultural
Heritage Preservation",
journal = j-JOCCH,
volume = "8",
number = "1",
pages = "2:1--2:??",
month = feb,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2629693",
ISSN = "1556-4673 (print), 1556-4711 (electronic)",
ISSN-L = "1556-4673",
bibdate = "Wed Feb 25 17:50:15 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/jocch/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jocch.bib",
abstract = "Effective documentation and display of ancient objects
is an essential task in the field of cultural heritage
conservation. Digitization plays an important role in
the process of creating, preserving, and accessing
objects in digital space. Up to the present day,
industrial scanners are used for this task, which focus
mainly on the detailed reconstruction of the object's
geometry only. However, particularly important for a
faithful digital presentation of the object is the
appearance information-that is, a description of the
used materials and how they interact with incident
light. Using the world's first full-spherical scanner,
we propose a user-friendly reconstruction process that
is specifically tailored to the needs of digitizing and
representing cultural heritage artifacts. More
precisely, our hardware specifically addresses the
problem that invaluable or fragile artifacts may not be
turned over during acquisition. Nevertheless, we can
digitize the object completely, including its bottom.
Further, by integrating appearance information into our
digitization, we achieve a far more faithful digital
replica with a quality comparable to a real picture of
the object. But in contrast to a static picture, our
representation allows one to interactively change the
viewing and lighting directions freely. In addition,
the results are very memory efficient, consuming only
several megabytes per scanned object. In cooperation
with museums and a private collector, we digitized
several cultural heritage artifacts to demonstrate the
feasibility of the proposed process.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "Journal on Computing and Cultural Heritage (JOCCH)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}
@Article{Obradovic:2015:GFT,
author = "Marko Obradovi{\'c} and Milan Jovanovi{\'c} and Bojana
Milosevi{\'c}",
title = "Goodness-of-fit tests for {Pareto} distribution based
on a characterization and their asymptotics",
journal = j-STATISTICS,
volume = "49",
number = "5",
pages = "1026--1041",
year = "2015",
CODEN = "MOSSD5",
DOI = "https://doi.org/10.1080/02331888.2014.919297",
ISSN = "0233-1888 (print), 1029-4910 (electronic)",
ISSN-L = "0233-1888",
bibdate = "Wed Aug 19 08:16:20 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statistics.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistics: A Journal of Theoretical and Applied
Statistics",
journal-URL = "http://www.tandfonline.com/loi/gsta20",
}
@InCollection{Perez-Gonzalez:2015:ABL,
author = "Fernando P{\'e}rez-Gonz{\'a}lez and Tu-Thach Quach and
Chaouki T. Abdallah and Gregory L. Heileman and Steven
J. Miller",
title = "Application of {Benford's Law} to images",
crossref = "Miller:2015:BLT",
pages = "338--370",
year = "2015",
MRclass = "62H35",
MRnumber = "3411068",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Raman:2015:CSC,
author = "Raghu Raman and Smrithi Venkatasubramanian and
Krishnashree Achuthan and Prema Nedungadi",
title = "Computer Science {(CS)} Education in {Indian} Schools:
Situation Analysis using {Darmstadt} Model",
journal = j-TOCE,
volume = "15",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2716325",
ISSN = "1946-6226",
bibdate = "Tue May 12 06:10:11 MDT 2015",
bibsource = "http://www.acm.org/pubs/toce;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/toce.bib",
abstract = "Computer science (CS) and its enabling technologies
are at the heart of this information age, yet its
adoption as a core subject by senior secondary students
in Indian schools is low and has not reached critical
mass. Though there have been efforts to create core
curriculum standards for subjects like Physics,
Chemistry, Biology, and Math, CS seems to have been
kept outside the purview of such efforts leading to its
marginalization. As a first step, using the Darmstadt
model from the ITiCSE working group that provides a
systematic categorization approach to CS education in
schools, we coded and analyzed the CS situation for the
Indian schools. Next, we focused on the motivation
category of the Darmstadt model and investigated
behavioral intentions of secondary school students and
teachers from 332 schools in India. Considering the CS
subject as an educational innovation, using Rogers'
Theory of Diffusion of Innovations, we propose a
pedagogical framework for innovation attributes that
can significantly predict-adoption of the CS subject
among potential-adopter students and teachers. Data was
analyzed to answer research questions about student and
teacher intentions, influence of gender, school
management, and school location in adopting CS.
Interestingly, girls, urban students, teachers, and
private schools were seen favoring the adoption of CS.
An important issue that needed to be addressed,
however, was the interchangeable use of terms like CS,
Informatics, ICT, and digital literacy. Through our
article, we offer a promising picture of the
educational policy directives and the academic
environment in India that is rapidly growing and
embracing CS as a core subject of study in schools. We
also analyze the factors that influence the adoption of
CS by school students and teachers and conclude that
there is a very positive response for CS among
educators and students in India.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computing Education",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1193",
}
@Article{Ribeiro:2015:MPE,
author = "Marco Tulio Ribeiro and Nivio Ziviani and Edleno
{Silva De Moura} and Itamar Hata and Anisio Lacerda and
Adriano Veloso",
title = "Multiobjective {Pareto}-Efficient Approaches for
Recommender Systems",
journal = j-TIST,
volume = "5",
number = "4",
pages = "53:1--53:??",
month = jan,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2629350",
ISSN = "2157-6904 (print), 2157-6912 (electronic)",
ISSN-L = "2157-6904",
bibdate = "Wed Feb 11 12:29:09 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tist.bib",
abstract = "Recommender systems are quickly becoming ubiquitous in
applications such as e-commerce, social media channels,
and content providers, among others, acting as an
enabling mechanism designed to overcome the information
overload problem by improving browsing and consumption
experience. A typical task in many recommender systems
is to output a ranked list of items, so that items
placed higher in the rank are more likely to be
interesting to the users. Interestingness measures
include how accurate, novel, and diverse are the
suggested items, and the objective is usually to
produce ranked lists optimizing one of these measures.
Suggesting items that are simultaneously accurate,
novel, and diverse is much more challenging, since this
may lead to a conflicting-objective problem, in which
the attempt to improve a measure further may result in
worsening other measures. In this article, we propose
new approaches for multiobjective recommender systems
based on the concept of Pareto efficiency-a state
achieved when the system is devised in the most
efficient manner in the sense that there is no way to
improve one of the objectives without making any other
objective worse off. Given that existing multiobjective
recommendation algorithms differ in their level of
accuracy, diversity, and novelty, we exploit the
Pareto-efficiency concept in two distinct manners: (i)
the aggregation of ranked lists produced by existing
algorithms into a single one, which we call
Pareto-efficient ranking, and (ii) the weighted
combination of existing algorithms resulting in a
hybrid one, which we call Pareto-efficient
hybridization. Our evaluation involves two real
application scenarios: music recommendation with
implicit feedback (i.e., Last.fm) and movie
recommendation with explicit feedback (i.e.,
MovieLens). We show that the proposed Pareto-efficient
approaches are effective in suggesting items that are
likely to be simultaneously accurate, diverse, and
novel. We discuss scenarios where the system achieves
high levels of diversity and novelty without
compromising its accuracy. Further, comparison against
multiobjective baselines reveals improvements in terms
of accuracy (from 10.4\% to 10.9\%), novelty (from
5.7\% to 7.5\%), and diversity (from 1.6\% to 4.2\%).",
acknowledgement = ack-nhfb,
articleno = "53",
fjournal = "ACM Transactions on Intelligent Systems and Technology
(TIST)",
journal-URL = "http://portal.acm.org/citation.cfm?id=J1318",
}
@InCollection{Roukema:2015:CBL,
author = "Boudewijn F. Roukema",
title = "Complementing {Benford's Law} for small {$N$}: a local
bootstrap",
crossref = "Miller:2015:BLT",
pages = "223--232",
year = "2015",
MRclass = "62P25 (62G09)",
MRnumber = "3411064",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Rubino:2015:ILB,
author = "Irene Rubino and Claudia Barberis and Jetmir Xhembulla
and Giovanni Malnati",
title = "Integrating a Location-Based Mobile Game in the Museum
Visit: Evaluating Visitors' Behaviour and Learning",
journal = j-JOCCH,
volume = "8",
number = "3",
pages = "15:1--15:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2724723",
ISSN = "1556-4673 (print), 1556-4711 (electronic)",
ISSN-L = "1556-4673",
bibdate = "Tue May 12 07:01:13 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/jocch/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jocch.bib",
abstract = "Location-based systems currently represent a suitable
solution to enhance cultural experiences inside
museums, as they can satisfy visitors' needs through
the provision of contextualized contents and services.
In this framework, a promising approach to captivate
the attention of teenagers-a hard to please target
audience-is represented by mobile serious games, such
as playful activities aiming to primarily fulfil
educational purposes. The use of a mobile digital tool
during the visit definitely discloses new opportunities
for contextual learning scenarios; however, so far,
only a few studies have analysed the impact of
different communication approaches on visitors' degree
of exploration and acquisition of knowledge. This work
aims to enrich this field of research, presenting the
conceptual framework; the design principles; and the
evaluation results of ``Gossip at palace,'' a
location-based mobile game integrating a storytelling
approach. The game was developed for an Italian
historical residence to communicate its 18th-century
history to teenagers, capitalizing on narrative and
game mechanics to foster young visitors' motivations to
explore the museum and facilitate their meaning-making
process. Following a mixed-methods perspective, the
article firstly describes to what extent the components
of the application were appreciated by teenagers as
well as by other visitor segments. Secondly, it
provides an insight on the effectiveness of the game in
facilitating the acquisition of historical knowledge by
participants, enriched by considerations on the methods
to be adopted when evaluating mobile learning in
informal educational settings. Thirdly, players' degree
of use of the digital game throughout the visit is
compared to analogous patterns registered for people
using a multimedia mobile guide in the same venue. On
the one hand, the study pointed out that the game
facilitated a wider exploration of the museum; on the
other, it highlighted that players mainly gained a
superficial knowledge of the proposed contents.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "Journal on Computing and Cultural Heritage (JOCCH)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}
@InCollection{Schurger:2015:LPB,
author = "Klaus Sch{\"u}rger",
title = "{L{\'e}vy} processes and {Benford's Law}",
crossref = "Miller:2015:BLT",
pages = "135--173",
year = "2015",
MRclass = "60G51 (60F10 60F15 62G10)",
MRnumber = "3411061",
MRreviewer = "Sreenivasan Ravi",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Serra:2015:POA,
author = "Edoardo Serra and Sushil Jajodia and Andrea Pugliese
and Antonino Rullo and V. S. Subrahmanian",
title = "{Pareto}-Optimal Adversarial Defense of Enterprise
Systems",
journal = j-TISSEC,
volume = "17",
number = "3",
pages = "11:1--11:??",
month = mar,
year = "2015",
CODEN = "ATISBQ",
DOI = "https://doi.org/10.1145/2699907",
ISSN = "1094-9224 (print), 1557-7406 (electronic)",
ISSN-L = "1094-9224",
bibdate = "Fri Mar 27 17:03:46 MDT 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tissec.bib",
abstract = "The National Vulnerability Database (NVD) maintained
by the US National Institute of Standards and
Technology provides valuable information about
vulnerabilities in popular software, as well as any
patches available to address these vulnerabilities.
Most enterprise security managers today simply patch
the most dangerous vulnerabilities-an adversary can
thus easily compromise an enterprise by using less
important vulnerabilities to penetrate an enterprise.
In this article, we capture the vulnerabilities in an
enterprise as a Vulnerability Dependency Graph (VDG)
and show that attacks graphs can be expressed in them.
We first ask the question: What set of vulnerabilities
should an attacker exploit in order to maximize his
expected impact? We show that this problem can be
solved as an integer linear program. The defender would
obviously like to minimize the impact of the worst-case
attack mounted by the attacker-but the defender also
has an obligation to ensure a high productivity within
his enterprise. We propose an algorithm that finds a
Pareto-optimal solution for the defender that allows
him to simultaneously maximize productivity and
minimize the cost of patching products on the
enterprise network. We have implemented this framework
and show that runtimes of our computations are all
within acceptable time bounds even for large VDGs
containing 30K edges and that the balance between
productivity and impact of attacks is also
acceptable.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Information and System Security",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J789",
}
@InProceedings{Singh:2015:ABL,
author = "N. Singh and R. Bansal",
booktitle = "Signal Processing and Communication (ICSC), 2015
International Conference on",
title = "Analysis of {Benford's Law} in digital image
forensics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "413--418",
month = mar,
year = "2015",
DOI = "https://doi.org/10.1109/ICSPCom.2015.7150688",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford law; Benford's law; compression; data
compression; data detection; data recovery; digital
image forensics; Digital images; Discrete cosine
transforms; Discrete wavelet transforms; Forensics;
Image coding; image coding; image compression; image
forensics; image registration; JPEG2000; Q-factor;
tampering detection; Transform coding",
}
@Article{Slepkov:2015:BLT,
author = "Aaron D. Slepkov and Kevin B. Ironside and David
DiBattista",
title = "{Benford's Law}: Textbook Exercises and
Multiple-Choice Testbanks",
journal = j-PLOS-ONE,
volume = "10",
number = "2",
pages = "e0117972:1--e0117972:13",
day = "17",
month = feb,
year = "2015",
CODEN = "POLNCL",
DOI = "https://doi.org/10.1371/journal.pone.0117972",
ISSN = "1932-6203",
bibdate = "Wed Aug 12 08:59:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0117972",
abstract = "Benford's Law describes the finding that the
distribution of leading (or leftmost) digits of
innumerable datasets follows a well-defined logarithmic
trend, rather than an intuitive uniformity. In practice
this means that the most common leading digit is 1,
with an expected frequency of 30.1\%, and the least
common is 9, with an expected frequency of 4.6\%.
Currently, the most common application of Benford's Law
is in detecting number invention and tampering such as
found in accounting-, tax-, and voter-fraud. We
demonstrate that answers to end-of-chapter exercises in
physics and chemistry textbooks conform to Benford's
Law. Subsequently, we investigate whether this fact can
be used to gain advantage over random guessing in
multiple-choice tests, and find that while testbank
answers in introductory physics closely conform to
Benford's Law, the testbank is nonetheless secure
against such a Benford's attack for banal reasons.",
acknowledgement = ack-nhfb,
fjournal = "PLoS One",
journal-URL = "http://www.plosone.org/",
}
@Article{VanCaneghem:2015:NFSa,
author = "Tom {Van Caneghem}",
title = "{NPO} Financial Statement Quality: An Empirical
Analysis Based on {Benford's Law}",
journal = "VOLUNTAS: International Journal of Voluntary and
Nonprofit Organizations",
volume = "26",
number = "1",
pages = "1--24",
month = feb,
year = "2015",
DOI = "https://doi.org/10.1007/s11266-015-9629-4",
ISSN = "0957-8765 (print), 1573-7888 (electronic)",
ISSN-L = "0957-8765",
bibdate = "Wed Aug 12 10:03:53 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11266-015-9629-4",
acknowledgement = ack-nhfb,
journal-URL = "https://link.springer.com/journal/11266",
keywords = "Benford's Law; Digital analysis; Financial reporting;
Financial statements; Non-profit organizations",
}
@Article{VanCaneghem:2015:NFSb,
author = "Tom {Van Caneghem}",
title = "{NPO} Financial Statement Quality: An Empirical
Analysis Based on {Benford's Law}",
journal = "{VOLUNTAS}: International Journal of Voluntary and
Nonprofit Organizations",
volume = "27",
number = "6",
pages = "2685--2708",
month = aug,
year = "2015",
DOI = "https://doi.org/10.1007/s11266-015-9629-4",
ISSN = "0957-8765 (print), 1573-7888 (electronic)",
ISSN-L = "0957-8765",
bibdate = "Wed Jun 20 15:13:31 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "https://link.springer.com/journal/11266",
}
@Article{Wang:2015:SPW,
author = "Xiaohuan Wang",
title = "Stability of planar waves in a {Lotka--Volterra}
system",
journal = j-APPL-MATH-COMP,
volume = "259",
number = "??",
pages = "313--326",
day = "15",
month = may,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Apr 24 18:27:24 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315002398",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Whyman:2015:ICC,
author = "G. Whyman and E. Shulzinger and Ed. Bormashenko",
title = "Intuitive considerations clarifying the origin and
applicability of the {Benford Law}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "12",
day = "25",
month = oct,
year = "2015",
bibdate = "Tue Jan 26 09:53:36 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1510.07220v2",
acknowledgement = ack-nhfb,
}
@Article{Woods:2015:PDP,
author = "Louis Woods and Gustavo Alonso and Jens Teubner",
title = "Parallelizing Data Processing on {FPGAs} with Shifter
Lists",
journal = j-TRETS,
volume = "8",
number = "2",
pages = "7:1--7:??",
month = apr,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2629551",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue May 19 17:05:20 MDT 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "Parallelism is currently seen as a mechanism to
minimize the impact of the power and heat dissipation
problems encountered in modern hardware. Data
parallelism-based on partitioning the data-and pipeline
parallelism-based on partitioning the computation-are
the two main approaches to leverage parallelism on a
wide range of hardware platforms. Unfortunately, not
all data processing problems are susceptible to either
of those strategies. An example is the skyline operator
[B{\"o}rzs{\"o}nyi et al. 2001], which computes the set
of Pareto-optimal points within a multidimensional
dataset. Existing approaches to parallelize the skyline
operator are based on data parallelism. As a result,
they suffer from a high overhead when merging
intermediate results because of the lack of a global
view of the problem inherent to partitioning the input
data. In this article, we show how to combine pipeline
with data parallelism on a Field-Programmable Gate
Array (FPGA) for a more efficient utilization of the
available hardware parallelism. As we show in our
experiments, skyline computation using our proposed
technique scales linearly with the number of processing
elements, and the performance we achieve on a rather
small FPGA is comparable to that of a 64-core high-end
server running a state-of-the-art data parallel
implementation of skyline [Park et al. 2009]. The
proposed approach to parallelize the skyline operator
can be generalized to a wider range of data processing
problems. We demonstrate this through a novel, highly
parallel data structure, a shifter list, that can be
efficiently implemented on an FPGA. The resulting
template is easy to parametrize to implement a variety
of computationally intensive operators such as frequent
items, n -closest pairs, or K-means.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{Yang:2015:ERP,
author = "Ziyun Yang and Xiaobo Dong",
title = "Earnings roundup in private and public bank holding
companies",
journal = "Advances in Accounting",
volume = "31",
number = "1",
pages = "96--99",
year = "2015",
DOI = "https://doi.org/10.1016/j.adiac.2015.03.004",
ISSN = "0882-6110",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S088261101500005X",
abstract = "In this study, we compare the relative tendencies of
public versus private firms to round up earnings in a
setting of the banking industry. This industry consists
of a large number of public and private bank holding
companies (BHCs) that face the same regulation
environment. In both the full sample and the
size-matched sample, we find evidence that public BHCs
show a greater tendency to round up the second digit of
earnings than do private BHCs. Our study contributes to
the current debate on the financial reporting quality
of public versus private firms by providing evidence
supporting the opportunistic behavior hypothesis.",
acknowledgement = ack-nhfb,
keywords = "Benford's law; Earnings roundup; Reporting quality",
}
@Article{Zhao:2015:UCA,
author = "Peng Zhao and Engui Fan",
title = "A unified construction for the algebro-geometric
quasiperiodic solutions of the {Lotka--Volterra} and
relativistic {Lotka--Volterra} hierarchy",
journal = j-J-MATH-PHYS,
volume = "56",
number = "4",
pages = "043501",
month = apr,
year = "2015",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.4916676",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Aug 4 09:20:02 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Zornig:2015:ZLR,
author = "Peter Z{\"o}rnig",
title = "{Zipf}'s law for randomly generated frequencies:
explicit tests for the goodness-of-fit",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "85",
number = "11",
pages = "2202--2213",
year = "2015",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949655.2014.925113",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Jun 9 05:53:26 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Alves:2016:ABI,
author = "Alexandre Donizeti Alves and Horacio Hideki Yanasse
and Nei Yoshihiro Soma",
title = "An analysis of bibliometric indicators to {JCR}
according to {Benford's Law}",
journal = j-SCIENTOMETRICS,
volume = "107",
number = "3",
pages = "1489--1499",
month = jun,
year = "2016",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-016-1908-3",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Mon May 16 16:03:17 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/content/pdf/10.1007/s11192-016-1908-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
keywords = "Journal Citation Reports (JCR)",
}
@Article{Amir:2016:SNE,
author = "Ariel Amir and Mikhail Lemeshko and Tadashi Tokieda",
title = "Surprises in Numerical Expressions of Physical
Constants",
journal = j-AMER-MATH-MONTHLY,
volume = "123",
number = "6",
pages = "609--612",
month = jun,
year = "2016",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.123.6.609",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 20 14:16:05 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.609",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
keywords = "Benford's Law; experimental mathematics",
remark = "This paper looks at the probability that a particular
numerical physical constant is generated by a simple
expression involving a few mathematical constants. It
also discusses Benford's Law.",
}
@Article{Ausloos:2016:QQP,
author = "Marcel Ausloos and Olgica Nedic and Agata Fronczak and
Piotr Fronczak",
title = "Quantifying the quality of peer reviewers through
{Zipf}'s law",
journal = j-SCIENTOMETRICS,
volume = "106",
number = "1",
pages = "347--368",
month = jan,
year = "2016",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-015-1704-5",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Sat Jan 16 07:09:36 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/article/10.1007/s11192-015-1704-5",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Ausloos:2016:RDC,
author = "Marcel Ausloos and Rosella Castellano and Roy
Cerqueti",
title = "Regularities and discrepancies of credit default
swaps: a data science approach through {Benford}'s
law",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "90",
pages = "8--17",
month = sep,
year = "2016",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2016.03.002",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
bibdate = "Tue May 22 16:45:20 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
}
@Article{Berger:2016:CBL,
author = "Arno Berger and Gideon Eshun",
title = "A characterization of {Benford's Law} in discrete-time
linear systems",
journal = j-J-DYN-DIFFER-EQU,
volume = "28",
number = "2",
pages = "431--469",
year = "2016",
CODEN = "JDDEEH",
DOI = "https://doi.org/10.1007/s10884-014-9393-y",
ISSN = "1040-7294 (print), 1572-9222 (electronic)",
ISSN-L = "1040-7294",
MRclass = "37A45 (11J71 37A05)",
MRnumber = "3500397",
MRreviewer = "Joseph Andrew Vandehey",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Dynamics and Differential Equations",
}
@Article{Bormashenko:2016:BLA,
author = "Ed. Bormashenko and E. Shulzinger and G. Whyman and
Ye. Bormashenko",
title = "{Benford's Law}, its applicability and breakdown in
the {IR} spectra of polymers",
journal = j-PHYSICA-A,
volume = "444",
number = "??",
pages = "524--529",
year = "2016",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2015.10.090",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437115009498",
abstract = "Infrared spectra of various polymers were treated
statistically. It was established that for the
absorbance spectra the Benford distribution of leading
digits takes place, whereas the distribution of leading
digits for transmittance spectra is random. This
observation may be explained by the fact that the value
of transmittance $ T_r $ is restricted $ 0 < T_r < 1 $,
due to the physical reasons, whereas the value of
absorbance is not. Moreover, the transmittance and
absorbance $A$ are interrelated by the logarithmic
dependence $ A = \log T_r$. This observation supplies
the idea that the Benford law is valid in the
situations, when logarithmic dependencies take place.
Amalgamation of spectral data obtained for various
polymers brings the distribution of the leading digits
in the absorbance domain into proximity to the Benford
Law.",
acknowledgement = ack-nhfb,
fjournal = "Physica A",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Absorbance; Benford's Law; Infrared spectra of
polymers; Transmittance",
}
@Article{Chen:2016:LBS,
author = "Evan Chen and Peter S. Park and Ashvin A.
Swaminathan",
title = "On logarithmically {Benford} sequences",
journal = j-PROC-AM-MATH-SOC,
volume = "144",
number = "11",
pages = "4599--4608",
year = "2016",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/proc/13112",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "11F11 (11N05)",
MRnumber = "3544512",
MRreviewer = "Ping Xi",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Friar:2016:UBL,
author = "J. L. Friar and T. Goldman and J. P{\'e}rez-Mercader",
title = "Ubiquity of {Benford's Law} and emergence of the
reciprocal distribution",
journal = j-PHYS-LET-A,
volume = "380",
number = "22--23",
pages = "1895--1899",
year = "2016",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/j.physleta.2016.03.045",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
MRclass = "60E05 (94A15)",
MRnumber = "3489018",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters. A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
}
@InCollection{Frunza:2016:CBL,
author = "Marius-Christian Frunza",
editor = "Marius-Christian Frunza",
booktitle = "Solving Modern Crime in Financial Markets",
title = "{Benford's Law}",
chapter = "2K",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "528",
pages = "233--245",
year = "2016",
DOI = "https://doi.org/10.1016/B978-0-12-804494-0.00017-6",
ISBN = "0-12-804494-2 (hardcover), 0-12-804532-9 (e-book)",
ISBN-13 = "978-0-12-804494-0 (hardcover), 978-0-12-804532-9
(e-book)",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780128044940000176",
abstract = "Since the seminal work published by Nigrini in 1992,
Benford's Law has been employed as a forensic
accounting tool that is currently used as evidence in
many courts. The application to cases of fraud on
financial markets is still new, but successful
applications have been illustrated, in particular in
the case of the LIBOR manipulation. The field of
application for Benford's Law in the financial markets
is growing as many data sets can be the target of
manipulation or misrepresentation. Therefore, the test
assessing conformity with Benford's Law can emphasize
fictitious figures resulting from manual handling of
data in areas like fund performance metrics,
benchmarks, and index values or prices of niche
commodity markets.",
acknowledgement = ack-nhfb,
keywords = "Chi-square test; Digit manipulation; First digit;
Second digit",
}
@InCollection{Garrabrant:2016:ALU,
author = "Scott Garrabrant and Tsvi Benson-Tilsen and Siddharth
Bhaskar and Abram Demski and Joanna Garrabrant and
George Koleszarik and Evan Lloyd",
booktitle = "Artificial General Intelligence ({AGI 2016})",
title = "Asymptotic Logical Uncertainty and the {Benford}
Test",
volume = "9782",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "202--211",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-41649-6_20",
ISBN = "3-319-41648-0 (print), 3-319-41649-9 (e-book)",
ISBN-13 = "978-3-319-41648-9 (print), 978-3-319-41649-6
(e-book)",
bibdate = "Wed Jun 20 15:26:46 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Article{Goodman:2016:PPB,
author = "William Goodman",
title = "The promises and pitfalls of {Benford}'s law",
journal = j-SIGNIF,
volume = "13",
number = "3",
pages = "38--41",
month = jun,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1111/j.1740-9713.2016.00919.x",
ISSN = "1740-9705 (print), 1740-9713 (electronic)",
ISSN-L = "1740-9705",
bibdate = "Thu Aug 13 12:04:02 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/significance.bib",
acknowledgement = ack-nhfb,
ajournal = "Signif.",
fjournal = "Significance",
journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713",
onlinedate = "06 June 2016",
}
@Book{Guttag:2016:ICP,
author = "John Guttag",
title = "Introduction to Computation and Programming Using
{Python}: with Application to Understanding Data",
publisher = pub-MIT,
address = pub-MIT:adr,
edition = "Second",
pages = "xvii + 447",
year = "2016",
ISBN = "0-262-52962-9 (paperback), 0-262-33738-X (e-book)",
ISBN-13 = "978-0-262-52962-4 (paperback), 978-0-262-33738-0
(e-book)",
LCCN = "QA76.73.P98 G88 2016",
bibdate = "Tue Jun 5 11:01:20 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib;
z3950.loc.gov:7090/Voyager",
abstract = "This book introduces students with little or no prior
programming experience to the art of computational
problem solving using Python and various Python
libraries, including PyLab. It provides students with
skills that will enable them to make productive use of
computational techniques, including some of the tools
and techniques of data science for using computation to
model and interpret data. The book is based on an MIT
course (which became the most popular course offered
through MIT's OpenCourseWare) and was developed for use
not only in a conventional classroom but in a massive
open online course (MOOC). This new edition has been
updated for Python 3, reorganized to make it easier to
use for courses that cover only a subset of the
material, and offers additional material including five
new chapters. Students are introduced to Python and the
basics of programming in the context of such
computational concepts and techniques as exhaustive
enumeration, bisection search, and efficient
approximation algorithms. Although it covers such
traditional topics as computational complexity and
simple algorithms, the book focuses on a wide range of
topics not found in most introductory texts, including
information visualization, simulations to model
randomness, computational techniques to understand
data, and statistical techniques that inform (and
misinform) as well as two related but relatively
advanced topics: optimization problems and dynamic
programming. This edition offers expanded material on
statistics and machine learning and new chapters on
Frequentist and Bayesian statistics.",
acknowledgement = ack-nhfb,
subject = "Python (Computer program language); Textbooks;
Computer programming",
tableofcontents = "Preface \\
1. Introduction \\
2: Introduction to Python: The basic elements of Python
\\
Objects, expressions, and numerical types \\
Variables and assignment \\
Python IDE's \\
Branching programs \\
Strings and input \\
Input \\
A digression about character encoding \\
Iteration \\
3: Some simple numerical programs: Exhaustive
enumeration \\
For loops \\
Approximate solutions and bisection search \\
Few words about using floats \\
Newton--Raphson \\
4: Functions, scoping, and abstraction: Functions and
scoping \\
Function definitions \\
Keyword arguments and default values \\
Scoping \\
Specifications \\
Recursion \\
Fibonacci numbers \\
Palindromes \\
Global variables \\
Modules \\
Files \\
5: Structured types, mutability, and higher-order
functions: Tuples \\
Sequences and multiple assignment \\
Ranges \\
Lists and mutability \\
Cloning \\
List comprehension \\
Functions as objects \\
Strings, tuples, ranges, and lists \\
Dictionaries \\
6: Testing and debugging: Testing \\
Black-box testing \\
Glass-box testing \\
Conducting tests \\
Debugging \\
Learning to debug \\
Designing the experiment \\
When the going gets tough \\
When you have found ``the'' bug \\
7: Exceptions and assertions: Handling exceptions \\
Exceptions as a control flow mechanism \\
Assertions \\
8: Classes and object-oriented programming: Abstract
data types and classes \\
Designing programs using abstract data types \\
Using classes to keep track of students and faculty \\
Inheritance \\
Multiple levels of inheritance \\
Substitution principle \\
Encapsulation and information hiding \\
Generators \\
Mortgages, an extended example \\
9: A simplistic introduction to algorithmic complexity:
Thinking about computational complexity \\
Asymptotic notation \\
Some important complexity classes \\
Constant complexity \\
Logarithmic complexity \\
Linear complexity \\
Log-linear complexity \\
Polynomial complexity \\
Exponential complexity \\
Comparisons of complexity classes \\
10: Some simple algorithms and data structures: Search
algorithms \\
Linear search and using indirection to access elements
\\
Binary search and exploiting assumptions \\
Sorting algorithms \\
Merge sort \\
Exploiting functions as parameters \\
Sorting in Python \\
Hash tables \\
11: Plotting and more about classes: Plotting using
PyLab \\
Plotting mortgages, an extended example \\
12: Knapsack and graph optimization problems: Knapsack
problems \\
Greedy algorithms \\
Optimal solution to the 0/1 Knapsack problem \\
Graph optimization problems \\
Some classic graph-theoretic problems \\
Shortest path: depth-first search and breadth-first
search \\
13: Dynamic programming: Fibonacci sequences, revisited
\\
Dynamic programming and the 0/1 Knapsack problem \\
Dynamic programming and divide-and-conquer \\
14: Random walks and more about data visualization:
Random walks \\
The drunkard's walk \\
Biased random walks \\
Treacherous fields \\
15: Stochastic programs, probability, and
distributions: Stochastic programs \\
Calculating simple probabilities \\
Inferential statistics \\
Distributions \\
Probability distributions \\
Normal distributions \\
Continuous and discrete uniform distributions \\
Binomial and multinomial distributions \\
Exponential and geometric distributions \\
Benford's distribution \\
Hashing and collisions \\
How often does the better team win? \\
16: Monte Carlo stimulation: Pascal's problem \\
Pass or don't pass? \\
Using table lookup to improve performance \\
Finding pi \\
Some closing remarks about simulation models \\
17: Sampling and confidence intervals: Sampling the
Boston Marathon \\
Central limit theorem \\
Standard error of the mean \\
18: Understanding experimental data: The behavior of
springs \\
Using linear regression to find a fit \\
The behavior of projectiles \\
Coefficient of determination \\
Using a computational model \\
Fitting exponentially distributed data \\
When theory is missing \\
19: Randomized trials and hypothesis checking: Checking
significance \\
Beware of P-values \\
One-tail and one-sample tests \\
Significant or not? \\
Which N? \\
Multiple hypotheses \\
20: Conditional probability and Bayesian statistics. :
Conditional probabilities \\
Bayes' theorem \\
Bayesian updating \\
21: Lies, damned lies, and statistics: Garbage in
garbage out (GIGO) \\
Tests are imperfect \\
Pictures can be deceiving \\
Cum hoc ergo propter hoc \\
Statistical measures don't tell the whole story \\
Sampling bias \\
Context matters \\
Beware of extrapolation \\
Texas sharpshooter fallacy \\
Percentages can confuse \\
Statistically significant differences can be
insignificant \\
Regressive fallacy \\
Just beware \\
22: A quick look at machine learning: Feature vectors
\\
Distance metrics \\
23: Clustering: Class cluster \\
K-means clustering \\
A contrived example \\
A less contrived example \\
24: Classification methods: Evaluating classifiers \\
Predicting the gender of runners \\
K-nearest neighbors \\
Regression-based classifiers \\
Surviving the Titanic \\
Wrapping up \\
Python 3.5 quick reference",
}
@Article{Hill:2016:HLI,
author = "Theodore P. Hill and Ronald F. Fox",
title = "{Hubble's Law} Implies {Benford's Law} for Distances
to Galaxies",
journal = j-J-ASTROPHYS-ASTRON,
volume = "37",
number = "1",
pages = "??--??",
month = feb,
year = "2016",
CODEN = "JASRD7",
DOI = "https://doi.org/10.1007/s12036-016-9373-1",
ISSN = "0250-6335 (print), 0973-7758 (electronic)",
ISSN-L = "0250-6335",
bibdate = "Wed Jun 20 15:21:17 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Alexopoulos:2014:BLA}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Astrophysics and Astronomy",
journal-URL = "http://www.springerlink.com/content/0250-6335",
pagecount = "4",
}
@Article{Hoppe:2016:BLD,
author = "Fred M. Hoppe",
title = "{Benford's Law} and distractors in multiple choice
exams",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "47",
number = "4",
pages = "606--612",
year = "2016",
CODEN = "IJMEBM",
DOI = "https://doi.org/10.1080/0020739X.2015.1091515",
ISSN = "0020-739x (print), 1464-5211 (electronic)",
ISSN-L = "0020-739X",
MRclass = "60C05",
MRnumber = "3484057",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematical Education in
Science and Technology",
journal-URL = "http://www.tandfonline.com/loi/tmes20",
}
@Article{Jameson:2016:BLC,
author = "Marie Jameson and Jesse Thorner and Lynnelle Ye",
title = "{Benford's Law} for coefficients of newforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "12",
number = "2",
pages = "483--494",
month = mar,
year = "2016",
DOI = "https://doi.org/10.1142/S1793042116500299",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11F11 (11F30 11K06)",
MRnumber = "3461444",
MRreviewer = "Bingrong Huang",
bibdate = "Sat Mar 25 08:28:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042116500299",
abstract = "Let $ f(z) = \sum_{n = 1}^\infty \lambda_f(n) e^P{2
\pi i n z} \in S_k^{\mathrm {new}}(\Gamma_0 (N)) $ be a
newform of even weight $ k \geq 2 $ on $ \Gamma_0 (N) $
without complex multiplication. Let $P$ denote the set
of all primes. We prove that the sequence $ \{
\lambda_f(p) \}_{p \in P}$ does not satisfy Benford s
Law in any integer base $ b \geq 2$. However, given a
base $ b \geq 2$ and a string of digits $S$ in base
$b$, the set $ A_{\lambda_f}(b, S) \coloneq \{ p
\mathrm {prime : the first digits of } \lambda_f(p)
\mathrm {in base} b \mathrm {are given by} S \} $ has
logarithmic density equal to $ \log_b(1 + S^{ 1})$.
Thus, $ \{ \lambda_f(p) \}_{p \in P}$ follows Benford's
Law with respect to logarithmic density. Both results
rely on the now-proven Sato -Tate Conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Karthik:2016:ETS,
author = "Deepak Karthik and Gil Stelzer and Sivan Gershanov and
Danny Baranes and Mali Salmon-Divon",
title = "Elucidating tissue specific genes using the {Benford}
distribution",
journal = "{BMC} Genomics",
volume = "17",
number = "1",
month = aug,
year = "2016",
DOI = "https://doi.org/10.1186/s12864-016-2921-x",
ISSN = "1471-2164",
ISSN-L = "1471-2164",
bibdate = "Wed Jun 20 15:15:23 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
journal-URL = "https://link.springer.com/journal/12864",
}
@Article{Li:2016:QNS,
author = "Qinglei Li and Zuntao Fu",
title = "Quantifying non-stationarity effects on organization
of atmospheric turbulent eddy motion by {Benford}'s
law",
journal = j-COMM-NONLIN-SCI-NUM-SIM,
volume = "33",
number = "??",
pages = "91--98",
month = apr,
year = "2016",
DOI = "https://doi.org/10.1016/j.cnsns.2015.09.006",
ISSN = "1007-5704 (print), 1878-7274 (electronic)",
ISSN-L = "1007-5704",
MRclass = "86A10 (62M10)",
MRnumber = "3417171",
bibdate = "Tue Jan 26 11:05:08 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Commun. Nonlinear Sci. Numer. Simul.",
fjournal = "Communications in Nonlinear Science and Numerical
Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/10075704",
}
@Article{Mir:2016:CAC,
author = "Tariq Ahmad Mir",
title = "Citations to articles citing {Benford}'s law: a
{Benford} analysis",
journal = "CoRR",
volume = "abs/1602.01205",
number = "??",
pages = "??--??",
month = "????",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.48550/arXiv.1602.01205",
ISSN = "????",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1602.01205;
https://dblp.org/db/journals/corr/corr1602.html#Mir16",
abstract = "The occurrence of first significant digits of numbers
in large data is often governed by a logarithmically
decreasing distribution called Benford's law (BL),
reported first by S. Newcomb (SN) and many decades
later independently by F. Benford (FB). Due to its
counter-intuitiveness the law was ignored for decades
as a mere curious observation. However, an indication
of its remarkable resurgence is the huge swell in the
number of citations received by the papers of SN/FB.
The law has come a long way, from obscurity to now
being a regular subject of books, peer reviewed papers,
patents, blogs and news. Here, we use Google Scholar
(GS) to collect the data on the number of citations
received by the articles citing the original paper of
SN/FB and then investigate whether the leading digits
of this citations data are distributed according to the
law they discovered. We find that the citations data of
literature on BL is in remarkable agreement with the
predictions of the law.",
acknowledgement = ack-nhfb,
dblp-key = "journals/corr/Mir16",
dblp-mdate = "2018-08-13",
}
@Article{Mir:2016:LDD,
author = "T. A. Mir",
title = "The leading digit distribution of the worldwide
illicit financial flows",
journal = j-QUAL-QUANT,
volume = "50",
number = "1",
pages = "271--281",
month = jan,
year = "2016",
CODEN = "QQEJAV",
DOI = "https://doi.org/10.1007/s11135-014-0147-z",
ISSN = "0033-5177 (print), 1573-7845 (electronic)",
ISSN-L = "0033-5177",
bibdate = "Tue Jan 26 07:28:33 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer.com/article/10.1007/s11135-014-0147-z",
acknowledgement = ack-nhfb,
fjournal = "Quality \& Quantity",
journal-URL = "http://www.springer.com/social+sciences/journal/11135",
keywords = "Benford's Law",
}
@InProceedings{Neubert:2016:IPP,
author = "T. Neubert and M. Hildebrandt and J. Dittmann",
booktitle = "2016 First International Workshop on Sensing,
Processing and Learning for Intelligent Machines
(SPLINE)",
title = "Image pre-processing detection: Evaluation of
{Benford's Law}, spatial and frequency domain feature
performance",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
month = jul,
year = "2016",
DOI = "https://doi.org/10.1109/SPLIM.2016.7528405",
bibdate = "Sat Sep 10 11:43:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's law; Computer science; data integrity; Data
models; Feature extraction; frequency domain feature
performance; Frequency-domain analysis; image data
integrity; image filtering; image forensics; image
preprocessing blind detection; image preprocessing
filters; learning (artificial intelligence); Pattern
recognition; sensor intrinsic preprocessing; spatial
domain feature performance; statistical analysis;
statistical pattern recognition; supervised learning;
Transform coding",
}
@Article{Sheng:2016:DCA,
author = "Guorui Sheng and Tao Li and Qingtang Su and Beijing
Chen and Yi Tang",
title = "Detection of content-aware image resizing based on
{Benford}'s law",
journal = j-SOFT-COMP,
volume = "21",
number = "19",
pages = "5693--5701",
month = apr,
year = "2016",
DOI = "https://doi.org/10.1007/s00500-016-2146-6",
ISSN = "1432-7643 (print), 1433-7479 (electronic)",
ISSN-L = "1432-7643",
bibdate = "Wed Jun 20 15:03:09 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soft computing: newsletter of the {Canadian Society
for Fuzzy Information and Neural Systems}",
}
@Article{Sheng:2016:DSC,
author = "Guorui Sheng and Tiegang Gao",
title = "Detection of Seam-Carving Image Based on {Benford's
Law} for Forensic Applications",
journal = "International Journal of Digital Crime and Forensics",
volume = "8",
number = "1",
pages = "51--61",
month = "????",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.4018/IJDCF.2016010104",
ISSN = "1941-6210 (print), 1941-6229 (electronic)",
ISSN-L = "1941-6210",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/ijdcf/ijdcf8.html#ShengG16",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Digit. Crime Forensics",
dblp-key = "journals/ijdcf/ShengG16",
dblp-mdate = "2020-08-12",
fjournal = "International Journal of Digital Crime and Forensics",
journal-URL = "https://www.igi-global.com/gateway/journal/1112",
}
@Article{Stoerk:2016:SCB,
author = "Thomas Stoerk",
title = "Statistical corruption in {Beijing}'s air quality data
has likely ended in 2012",
journal = j-ATMOS-ENV,
volume = "127",
number = "??",
pages = "365--371",
year = "2016",
CODEN = "ATENBP",
DOI = "https://doi.org/10.1016/j.atmosenv.2015.12.055",
ISSN = "1352-2310 (print), 1873-2844 (electronic)",
ISSN-L = "1352-2310",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1352231015306336",
abstract = "This research documents changes in likely misreporting
in official air quality data from Beijing for the years
2008--2013. It is shown that, consistent with prior
research, the official Chinese data report suspiciously
few observations that exceed the politically important
Blue Sky Day threshold, a particular air pollution
level used to evaluate local officials, and an excess
of observations just below that threshold. Similar
data, measured by the US Embassy in Beijing, do not
show this irregularity. To document likely
misreporting, this analysis proposes a new way of
comparing air quality data via Benford's Law, a
statistical regularity known to fit air pollution data.
Using this method to compare the official data to the
US Embassy data for the first time, I find that the
Chinese data fit Benford's Law poorly until a change in
air quality measurements at the end of 2012. From 2013
onwards, the Chinese data fit Benford's Law closely.
The US Embassy data, by contrast, exhibit no variation
over time in the fit with Benford's Law, implying that
the underlying pollution processes remain unchanged.
These findings suggest that misreporting of air quality
data for Beijing has likely ended in 2012.
Additionally, I use aerosol optical density data to
show the general applicability of this method of
detecting likely misreporting in air pollution data.",
acknowledgement = ack-nhfb,
fjournal = "Atmospheric Environment",
keywords = "Air pollution; Air quality data; Beijing; Benford's
Law; Misreporting; PM10; PM2.5",
}
@Article{Whyman:2016:ICC,
author = "G. Whyman and E. Shulzinger and Ed. Bormashenko",
title = "Intuitive considerations clarifying the origin and
applicability of the {Benford Law}",
journal = "Results in Physics",
volume = "6",
number = "??",
pages = "3--6",
year = "2016",
DOI = "https://doi.org/10.1016/j.rinp.2015.11.010",
ISSN = "2211-3797",
bibdate = "Tue Jan 26 09:03:59 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S2211379715000728",
abstract = "The diverse applications of the Benford law attract
investigators working in various fields of physics,
biology and sociology. At the same time, the groundings
of the Benford law remain obscure. Our paper
demonstrates that the Benford law arises from the
positional (place-value) notation accepted for
representing various sets of data. An alternative to
Benford formulae to predict the distribution of digits
in statistical data is derived. Application of these
formulae to the statistical analysis of infrared
spectra of polymers is presented. Violations of the
Benford Law are discussed.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Infrared spectra; Leading digit
phenomenon; Positional notation; Statistical data",
}
@Article{Yang:2016:WSZ,
author = "Yue Yang and Jianwen Zhu",
title = "Write Skew and {Zipf} Distribution: Evidence and
Implications",
journal = j-TOS,
volume = "12",
number = "4",
pages = "21:1--21:??",
month = aug,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2908557",
ISSN = "1553-3077 (print), 1553-3093 (electronic)",
ISSN-L = "1553-3077",
bibdate = "Sat Mar 25 07:00:07 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/tos/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/tos.bib",
abstract = "Understanding workload characteristics is essential to
storage systems design and performance optimization.
With the emergence of flash memory as a new viable
storage medium, the new design concern of flash
endurance arises, necessitating a revisit of workload
characteristics, in particular, of the write behavior.
Inspired by Web caching studies where a Zipf-like
access pattern is commonly found, we hypothesize that
write count distribution at the block level may also
follow Zipf's Law. To validate this hypothesis, we
study 48 block I/O traces collected from a wide variety
of real and benchmark applications. Through extensive
analysis, we demonstrate that the Zipf-like pattern
indeed widely exists in write traffic provided its
disguises are removed by statistical processing. This
finding implies that write skew in a large class of
applications could be analytically expressed and, thus,
facilitates design tradeoff explorations adaptive to
workload characteristics.",
acknowledgement = ack-nhfb,
articleno = "21",
fjournal = "ACM Transactions on Storage",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J960",
}
@Article{Berger:2017:WLB,
author = "Arno Berger and Theodore P. Hill",
title = "What is \ldots{} {Benford's Law}?",
journal = j-NAMS,
volume = "64",
number = "2",
pages = "132--134",
month = feb,
year = "2017",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1477",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "60C05 (60E05)",
MRnumber = "3587717",
bibdate = "Mon Jan 30 16:18:54 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/nams2010.bib",
URL = "http://www.ams.org/publications/journals/notices/201702/rnoti-p132.pdf",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@InCollection{Best:2017:BBG,
author = "Andrew Best and Patrick Dynes and Xixi Edelsbrunner
and Brian McDonald and Steven J. Miller and Kimsy Tor
and Caroline Turnage-Butterbaugh and Madeleine
Weinstein",
editor = "M. Nathanson",
booktitle = "Springer Proceedings in Mathematics \& Statistics",
title = "{Benford} Behavior of Generalized {Zeckendorf}
Decompositions",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "25--37",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-68032-3_3",
MRclass = "11B39 (11B05 11K06 60F05 62E20)",
MRnumber = "3754894",
MRreviewer = "Vilius Stakenas",
bibdate = "Wed Jun 20 15:07:06 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Corazza:2017:LET,
author = "Marco Corazza and Andrea Ellero and Alberto Zorzi",
title = "L'importanza di Essere ``{UNO}'' (ovvero la legge di
{Benford}). ({Italian}) [The importance of Being
``one'' (i.e., the {Benford} law)]",
journal = "Lettera Matematica Pristem",
volume = "103",
number = "1",
pages = "31--38",
month = dec,
year = "2017",
DOI = "https://doi.org/10.1007/s10031-017-0051-5",
ISSN = "1593-5884 (print), 1970-6820 (electronic)",
ISSN-L = "1593-5884",
bibdate = "Wed Jun 20 15:01:02 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Daniels:2017:BLQ,
author = "Jeremy Daniels and Samantha-Jo Caetano and Dirk Huyer
and Andrew Stephen and John Fernandes and Alice Lytwyn
and Fred M. Hoppe",
title = "{Benford's Law} for Quality Assurance of Manner of
Death Counts in Small and Large Databases",
journal = "Journal of Forensic Sciences",
volume = "62",
number = "5",
pages = "1326--1331",
month = jun,
year = "2017",
DOI = "https://doi.org/10.1111/1556-4029.13437",
ISSN = "0022-1198 (print), 1556-4029 (electronic)",
ISSN-L = "0022-1198",
bibdate = "Wed Jun 20 14:41:06 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Fellman:2017:BP,
author = "Johan Fellman",
title = "{Benford} paradox",
journal = j-ARKHIMEDES,
volume = "??",
number = "4",
pages = "26--33",
year = "2017",
CODEN = "AKMDA5",
ISSN = "0004-1920",
MRclass = "60E99",
MRnumber = "3931184",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Arkhimedes",
}
@Article{Hullemann:2017:ABL,
author = "S. H{\"u}llemann and G. Sch{\"u}pfer and J. Mauch",
title = "Application of {Benford}'s law: a valuable tool for
detecting scientific papers with fabricated data?",
journal = "Der Anaesthesist",
volume = "66",
number = "10",
pages = "795--802",
month = jun,
year = "2017",
DOI = "https://doi.org/10.1007/s00101-017-0333-1",
ISSN = "0003-2417 (print), 1432-055X (electronic)",
ISSN-L = "0003-2417",
bibdate = "Wed Jun 20 14:24:42 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Iorliam:2017:UBL,
author = "Aamo Iorliam and Anthony T. S. Ho and Adrian Waller
and Xi Zhao",
editor = "Y. Shi and H. Kim and F. Perez-Gonzalez and F. Liu",
booktitle = "Digital Forensics and Watermarking (IWDW 2016)",
title = "Using {Benford's Law} Divergence and Neural Networks
for Classification and Source Identification of
Biometric Images",
volume = "10082",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "88--105",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-53465-7_7",
bibdate = "Wed Jun 20 15:08:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@InCollection{Klepac:2017:CDS,
author = "Goran Klepac",
editor = "A. Sangaiah and A. Thangavelu and Sundaram V.
Meenakshi",
booktitle = "Cognitive Computing for Big Data Systems Over {IoT}",
title = "Cognitive Data Science Automatic Fraud Detection
Solution, Based on {Benford's Law}, Fuzzy Logic with
Elements of Machine Learning",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "79--95",
month = dec,
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-70688-7_4",
ISBN = "3-319-70687-X (print), 3-319-70688-8 (electronic)",
ISBN-13 = "978-3-319-70687-0 (print), 978-3-319-70688-7
(electronic)",
bibdate = "Wed Jun 20 14:57:48 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes on Data Engineering and Communications
Technologies",
acknowledgement = ack-nhfb,
}
@InCollection{Mochty:2017:ABL,
author = "Ludwig Mochty",
editor = "B. Kaluza and K. Braun and H. Beschorner and B.
Rolfes",
booktitle = "Betriebswirtschaftliche Fragen zu Steuern,
Finanzierung, Banken und Management",
title = "{Die Achillesferse des Benford's Law: KMUs}.
({German}) [{The} {Achilles} heel of {Benford's Law}:
{SMEs}]",
publisher = "Springer Fachmedien Wiesbaden",
address = "Wiesbaden, Germany",
pages = "39--55",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-658-16730-1_3",
bibdate = "Wed Jun 20 15:11:20 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Misc{Oransky:2017:TCT,
author = "Ivar Oransky",
title = "Two in 100 clinical trials in eight major journals
likely contain inaccurate data: Study",
howpublished = "Web site article.",
day = "5",
month = jun,
year = "2017",
bibdate = "Wed Jun 20 14:31:24 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://retractionwatch.com/2017/06/05/two-100-clinical-trials-eight-major-journals-likely-contain-inaccurate-data-study/",
acknowledgement = ack-nhfb,
}
@Article{Shukla:2017:BDE,
author = "Abhishek Shukla and Ankit Kumar Pandey and Anirban
Pathak",
title = "{Benford}'s Distribution in Extrasolar World: Do the
Exoplanets Follow {Benford}'s Distribution?",
journal = j-J-ASTROPHYS-ASTRON,
volume = "38",
number = "1",
month = mar,
year = "2017",
CODEN = "JASRD7",
DOI = "https://doi.org/10.1007/s12036-017-9427-z",
ISSN = "0250-6335 (print), 0973-7758 (electronic)",
ISSN-L = "0250-6335",
bibdate = "Wed Jun 20 15:05:03 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Astrophysics and Astronomy",
journal-URL = "http://www.springerlink.com/content/0250-6335",
}
@Article{Tseng:2017:MBL,
author = "Hsiang-chi Tseng and Wei-neng Huang and Ding-wei
Huang",
title = "Modified {Benford's Law} for two-exponent
distributions",
journal = j-SCIENTOMETRICS,
volume = "110",
number = "3",
pages = "1403--1413",
month = mar,
year = "2017",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-016-2217-6",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Tue Feb 21 09:16:43 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s11192-016-2217-6",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Barabesi:2018:GFT,
author = "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli
and Domenico Perrotta",
title = "Goodness-of-Fit Testing for the {Newcomb--Benford Law}
With Application to the Detection of Customs Fraud",
journal = j-J-BUS-ECON-STAT,
volume = "36",
number = "2",
pages = "346--358",
year = "2018",
DOI = "https://doi.org/10.1080/07350015.2016.1172014",
ISSN = "0735-0015 (print), 1537-2707 (electronic)",
ISSN-L = "0735-0015",
MRclass = "62G10",
MRnumber = "3790219",
bibdate = "Mon Jun 15 17:20:33 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jbuseconstat.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/07350015.2016.1172014",
acknowledgement = ack-nhfb,
fjournal = "Journal of Business \& Economic Statistics",
journal-URL = "https://amstat.tandfonline.com/loi/ubes20",
onlinedate = "28 Apr 2017",
}
@Article{Becker:2018:BLC,
author = "Thealexa Becker and David Burt and Taylor C. Corcoran
and Alec Greaves-Tunnell and Joseph R. Iafrate and Joy
Jing and Steven J. Miller and Jaclyn D. Porfilio and
Ryan Ronan and Jirapat Samranvedhya and Frederick W.
Strauch and Blaine Talbut",
title = "{Benford}'s law and continuous dependent random
variables",
journal = j-ANN-PHYS,
volume = "388",
pages = "350--381",
year = "2018",
CODEN = "APNYA6",
DOI = "https://doi.org/10.1016/j.aop.2017.11.013",
ISSN = "0003-4916 (print), 1096-035x (electronic)",
ISSN-L = "0003-4916",
MRclass = "60A10 (11K06 60E10)",
MRnumber = "3759655",
MRreviewer = "Ad Ridder",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00034916",
}
@Article{Berger:2018:BFA,
author = "Arno Berger and Chuang Xu",
title = "Best Finite Approximations of {Benford's Law}",
journal = j-J-THEOR-PROBAB,
volume = "??",
number = "??",
pages = "??--??",
month = apr,
year = "2018",
CODEN = "JTPREO",
DOI = "https://doi.org/10.1007/s10959-018-0827-z",
ISSN = "0894-9840 (print), 1572-9230 (electronic)",
ISSN-L = "0894-9840",
bibdate = "Wed Jun 20 14:46:04 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Probability",
journal-URL = "http://link.springer.com/journal/10959",
xxnote = "Check; not yet assigned volume / number / pages
data.",
}
@Article{Berger:2018:SUR,
author = "Arno Berger and Isaac Twelves",
title = "On the significands of uniform random variables",
journal = j-J-APPL-PROBAB,
volume = "55",
number = "2",
pages = "353--367",
month = jun,
year = "2018",
CODEN = "JPRBAM",
DOI = "https://doi.org/10.1017/jpr.2018.23",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
bibdate = "Sat Mar 16 09:23:51 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/japplprobab.bib",
URL = "https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-the-significands-of-uniform-random-variables/0D08D0EEC38F52E431CF41290651603A",
abstract = "For all $ \alpha > 0 $ and real random variables $X$,
we establish sharp bounds for the smallest and the
largest deviation of $ \alpha X$ from the logarithmic
distribution also known as Benford's law. In the case
of uniform $X$, the value of the smallest possible
deviation is determined explicitly. Our elementary
calculation puts into perspective the recurring claims
that a random variable conforms to Benford's law, at
least approximately, whenever it has large spread.",
acknowledgement = ack-nhfb,
ajournal = "J. Appl. Probab.",
fjournal = "Journal of Applied Probability",
journal-URL = "https://www.cambridge.org/core/journals/journal-of-applied-probability",
onlinedate = "26 July 2018",
}
@Article{Corazza:2018:IBO,
author = "Marco Corazza and Andrea Ellero and Alberto Zorzi",
title = "The importance of being ``one'' (or {Benford}'s law)",
journal = "Lettera Matematica",
volume = "6",
number = "1",
pages = "33--39",
day = "01",
month = mar,
year = "2018",
DOI = "https://doi.org/10.1007/s40329-018-0218-4",
ISSN = "2281-5937 (print), 2281-6917 (electronic)",
ISSN-L = "2281-6917",
MRclass = "60E05 (62P99)",
MRnumber = "3775303",
bibdate = "Wed Jun 20 14:53:18 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translated from the Italian.",
acknowledgement = ack-nhfb,
keywords = "Benford's law; First significant digit; Power
sequences; Tax evasion; Vote rigging",
}
@Article{Ferrer-i-Cancho:2018:OZM,
author = "Ramon Ferrer-i-Cancho and Michael S. Vitevitch",
title = "The origins of {Zipf}'s meaning-frequency law",
journal = j-J-ASSOC-INF-SCI-TECHNOL,
volume = "69",
number = "11",
pages = "1369--1379",
month = nov,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1002/asi.24057",
ISSN = "2330-1643 (print), 2330-1643 (electronic)",
ISSN-L = "2330-1643",
bibdate = "Thu Mar 28 08:58:20 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jaist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Information Science and
Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "30 July 2018",
}
@Article{Hartmann:2018:AVK,
author = "Sandro Hartmann and Daniel Brinkert",
title = "{Aufdeckung von Versicherungsbetrug bei
Kfz-Sch{\"a}den mit Hilfe des Benford-Tests}.
({German}) [{Detection} of insurance fraud for vehicle
damage using the {Benford} test]",
journal = "{Zeitschrift f{\"u}r die gesamte
Versicherungswissenschaft}",
volume = "107",
number = "1",
pages = "41--59",
month = jan,
year = "2018",
DOI = "https://doi.org/10.1007/s12297-017-0396-8",
ISSN = "0044-2585 (print), 1865-9748 (electronic)",
ISSN-L = "0044-2585",
bibdate = "Wed Jun 20 14:52:07 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Book{Holt:2018:WEW,
author = "Jim Holt",
title = "When {Einstein} walked with {G{\"o}del}: excursions to
the edge of thought",
publisher = pub-FARRAR,
address = pub-FARRAR:adr,
pages = "xi + 368",
year = "2018",
ISBN = "0-374-14670-5 (hardcover), 0-374-71784-2 (e-book)",
ISBN-13 = "978-0-374-14670-2 (hardcover), 978-0-374-71784-1
(e-book)",
LCCN = "PS3608.O4943595 A6 2018",
bibdate = "Fri May 18 13:58:57 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
abstract = "A collection of essays on philosophy, mathematics, and
science, and the people who pursue them.",
acknowledgement = ack-nhfb,
author-dates = "1954--",
remark = "Chapter 8 discusses the influence of Zipf's Law on
Mandelbrot's discovery of fractals.",
shorttableofcontents = "Part I: The moving image of eternity \\
Part II: Numbers in the brain, in platonic heaven, and
in society \\
Part III: Mathematics, pure and impure \\
Part IV: Higher dimensions, abstract maps \\
Part V: Infinity, large and small \\
Part VI: Heroism, tragedy, and the computer age \\
Part VII: The cosmos reconsidered \\
Part VIII: Quick studies: A selection of shorter essays
\\
Part IX: God, sainthood, truth and bullshit",
tableofcontents = "Part I: The moving image of eternity \\
1: When Einstein walked with G{\"o}del \\
2: Time --- the grand illusion? \\
Part II: Numbers in the brain, in platonic heaven, and
in society \\
3: Numbers guy: the neuroscience of math \\
4: The Riemann Zeta conjecture and the laughter of the
primes \\
5: Sir Francis Galton, the father of
statistics\ldots{}and eugenics \\
Part III: Mathematics, pure and impure \\
6: A mathematical romance \\
7: The avatars of higher mathematics \\
8: Beno{\^\i}t Mandelbrot and the discovery of fractals
\\
Part IV: Higher dimensions, abstract maps \\
9: Geometrical creatures \\
10: A comedy of colors \\
Part V: Infinity, large and small \\
11: Infinite visions: Georg Cantor v. David Foster
Wallace \\
12: Worshipping infinity: why the Russians do and the
French don't \\
13: The dangerous idea of the infinitesimal \\
Part VI: Heroism, tragedy, and the computer age \\
14: The Ada perplex: was Byron's daughter the first
coder? \\
15: Alan Turing in life, logic, and death \\
16: Dr. Strangelove makes a thinking machine \\
17: Smarter, happier, more productive \\
Part VII: The cosmos reconsidered \\
18: The string theory wars: is beauty truth? \\
19: Einstein, ``Spooky action,'' and the reality of
space \\
20: How will the Universe end? \\
Part VII: Quick studies: a selection of shorter essays
\\
Little big man \\
Doom soon \\
Death: bad? \\
The looking-glass war \\
Astrology and the demarcation problem \\
G{\"o}del takes on the U.S. Constitution \\
The law of least action \\
Emmy Noether's beautiful theorem \\
Is logic coercive? \\
Newcomb's problem and the paradox of choice \\
The right not to exist \\
Can't anyone get Heisenberg right? \\
Overconfidence and the Monty Hall problem \\
The cruel law of eponymy \\
The mind of a rock \\
Part IX: God, sainthood, truth, and bullshit \\
21: Dawkins and the deity \\
22: On moral sainthood \\
23: Truth and reference: a philosophical feud \\
24: Say anything \\
Further Reading \\
Acknowledgments \\
Index",
}
@InCollection{Humenberger:2018:BGW,
author = "Hans Humenberger",
editor = "Hans-Stefan Siller and Gilbert Greefrath and Werner
Blum",
booktitle = "Neue Materialien f{\"u}r einen realit{\"a}tsbezogenen
Mathematikunterricht 4: 25 Jahre ISTRON-Gruppe - eine
Best-of-Auswahl aus der ISTRON-Schriftenreihe",
title = "{Das Benford-Gesetz`` --- warum ist die Eins als
f{\"u}hrende Ziffer von Zahlen bevorzugt?}. ({German})
[{The} ``{Benford Law}'' --- why is one preferred as
the leading digit of numbers?]",
chapter = "12",
publisher = "Springer Fachmedien Wiesbaden",
address = "Wiesbaden",
pages = "161--176",
year = "2018",
DOI = "https://doi.org/10.1007/978-3-658-17599-3_12",
ISBN = "978-36581-7-5-9-9-3",
ISBN-13 = "978-3-658-17599-3",
bibdate = "Wed Jun 20 14:56:18 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Lacasa:2018:NBL,
author = "Lucas Lacasa",
title = "{Newcomb--Benford} law helps customs officers to
detect fraud in international trade",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "116",
number = "1",
pages = "11--13",
month = dec,
year = "2018",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.1819470116",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Wed Aug 28 15:42:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.pnas.org/cgi/doi/10.1073/pnas.1819470116",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Lee:2018:PIB,
author = "Edward D. Lee",
title = "Partisan Intuition Belies Strong, Institutional
Consensus and Wide {Zipf's Law} for Voting Blocs in {US
Supreme Court}",
journal = j-J-STAT-PHYS,
volume = "173",
number = "6",
pages = "1722--1733",
month = dec,
year = "2018",
CODEN = "JSTPSB",
DOI = "https://doi.org/10.1007/s10955-018-2156-0",
ISSN = "0022-4715 (print), 1572-9613 (electronic)",
ISSN-L = "0022-4715",
bibdate = "Fri Mar 1 07:23:36 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jstatphys2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Physics",
journal-URL = "http://link.springer.com/journal/10955",
}
@Article{Mir:2018:BLS,
author = "Tariq Ahmad Mir and Marcel Ausloos",
title = "{Benford}'s law: a ``sleeping beauty'' sleeping in the
dirty pages of logarithmic tables",
journal = j-J-ASSOC-INF-SCI-TECHNOL,
volume = "69",
number = "3",
pages = "349--358",
month = mar,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1002/asi.23845",
ISSN = "2330-1643 (print), 2330-1643 (electronic)",
ISSN-L = "2330-1643",
bibdate = "Tue May 22 14:36:54 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jaist.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Information Science and
Technology",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
onlinedate = "17 September 2017",
}
@Article{Riccioni:2018:RPF,
author = "Jessica Riccioni and Roy Cerqueti",
title = "Regular paths in financial markets: investigating the
{Benford}'s law",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "107",
pages = "186--194",
year = "2018",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2018.01.008",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
MRclass = "91B24",
MRnumber = "3759502",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
}
@Article{Aleksandrova:2019:BLD,
author = "Elena B. Aleksandrova and Daria S. Lavrova and A. V.
Yarmak",
title = "{Benford's Law} in the Detection of {DoS} Attacks on
Industrial Systems",
journal = "Automatic Control and Computer Sciences",
volume = "53",
number = "8",
pages = "954--962",
month = "????",
year = "2019",
CODEN = "ACCSCE",
DOI = "https://doi.org/10.3103/S0146411619080030",
ISSN = "0146-4116 (print), 1558-108X (electronic)",
ISSN-L = "0146-4116",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/accs/accs53.html#AleksandrovaLY19",
acknowledgement = ack-nhfb,
ajournal = "Autom. Control. Comput. Sci.",
dblp-key = "journals/accs/AleksandrovaLY19",
dblp-mdate = "2021-10-14",
fjournal = "Automatic Control and Computer Sciences",
}
@Article{Benjamin:2019:LSB,
author = "Arthur T. Benjamin",
title = "The long and the short of {Benford}'s law",
journal = "Math Horizons",
volume = "26",
number = "4",
pages = "8--9",
year = "2019",
DOI = "https://doi.org/10.1080/10724117.2019.1568086",
ISSN = "1072-4117",
MRclass = "60E05",
MRnumber = "3925688",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Math Horiz.",
fjournal = "Math Horizons",
}
@Article{Berger:2019:BFA,
author = "Arno Berger and Chuang Xu",
title = "Best Finite Approximations of {Benford's Law}",
journal = j-J-THEOR-PROBAB,
volume = "32",
number = "3",
pages = "1525--1553",
month = sep,
year = "2019",
CODEN = "JTPREO",
DOI = "https://doi.org/10.1007/s10959-018-0827-z",
ISSN = "0894-9840 (print), 1572-9230 (electronic)",
ISSN-L = "0894-9840",
MRclass = "60B10 (60E15 62E15)",
MRnumber = "3979679",
bibdate = "Tue Jul 9 09:42:45 MDT 2019",
bibsource = "http://link.springer.com/journal/10959/32/3;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Probability",
journal-URL = "http://link.springer.com/journal/10959",
}
@Article{Cai:2019:LBL,
author = "Zhaodong Cai and A. J. Hildebrand and Junxian Li",
title = "A local {Benford Law} for a class of arithmetic
sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "15",
number = "3",
pages = "613--638",
month = apr,
year = "2019",
DOI = "https://doi.org/10.1142/S1793042119500325",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11K31 (11B05 11K06 11N05)",
MRnumber = "3925756",
MRreviewer = "Vilius Stakenas",
bibdate = "Tue Jul 21 10:35:38 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042119500325",
abstract = "It is well known that sequences such as the Fibonacci
numbers and the factorials satisfy Benford's Law; that
is, leading digits in these sequences occur with
frequencies given by $ P(d) = \log_{10} (1 + 1 / d) $,
$ d = 1, 2, \ldots, 9 $. In this paper, we investigate
leading digit distributions of arithmetic sequences
from a local point of view. We call a sequence locally
Benford distributed of order $k$ if, roughly speaking,
$k$-tuples of consecutive leading digits behave like
$k$ independent Benford-distributed digits. This notion
refines that of a Benford distributed sequence, and it
provides a way to quantify the extent to which the
Benford distribution persists at the local level.
Surprisingly, most sequences known to satisfy Benford's
Law have rather poor local distribution properties. In
our main result we establish, for a large class of
arithmetic sequences, a ``best-possible'' local Benford
Law; that is, we determine the maximal value k such
that the sequence is locally Benford distributed of
order k. The result applies, in particular, to
sequences of the form $ \{ a^n \} $, $ \{ a^{n^d} \} $,
and $ \{ n^\beta a^{n^\alpha } \} $, as well as the
sequence of factorials $ \{ n! \} $ and similar
iterated product sequences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cerioli:2019:NBL,
author = "Andrea Cerioli and Lucio Barabesi and Andrea Cerasa
and Mario Menegatti and Domenico Perrotta",
title = "{Newcomb--Benford} law and the detection of frauds in
international trade",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "116",
number = "1",
pages = "106--115",
year = "2019",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.1806617115",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
MRclass = "91B60 (62P99 91B24)",
MRnumber = "3900205",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Durst:2019:BLB,
author = "Rebecca F. Durst and Steven J. Miller",
title = "{Benford}'s law beyond independence: tracking
{Benford} behavior in copula models",
journal = "Involve",
volume = "12",
number = "7",
pages = "1193--1218",
year = "2019",
DOI = "https://doi.org/10.2140/involve.2019.12.1193",
ISSN = "1944-4176",
MRclass = "60E99",
MRnumber = "4023347",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Involve. A Journal of Mathematics",
}
@Article{Ruankong:2019:CTB,
author = "Pongpol Ruankong and Songkiat Sumetkijakan",
title = "Chains of truncated beta distributions and {Benford}'s
law",
journal = "Unif. Distrib. Theory",
volume = "14",
number = "2",
pages = "27--32",
year = "2019",
ISSN = "1336-913X",
MRclass = "60A10",
MRnumber = "4063899",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Uniform Distribution Theory",
}
@Article{Zunini:2019:BL,
author = "Mar{\'{}\i}a Caputi Zunini",
title = "{Benford}'s law",
journal = "Publ. Mat. Urug.",
volume = "17",
pages = "285--290",
year = "2019",
ISSN = "0797-1443",
MRclass = "62E99",
MRnumber = "4018784",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Publicaciones Matem\'{a}ticas del Uruguay",
}
@Article{Barabesi:2020:GBL,
author = "Lucio Barabesi and Luca Pratelli",
title = "On the {Generalized Benford law}",
journal = j-STAT-PROB-LETT,
volume = "160",
number = "??",
pages = "Article 108702",
month = may,
year = "2020",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2020.108702",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60E05 (60F05 62E15)",
MRnumber = "4058264",
bibdate = "Mon Aug 3 15:37:29 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715220300055",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
}
@Article{Cai:2020:SAB,
author = "Zhaodong Cai and Matthew Faust and A. J. Hildebrand
and Junxian Li and Yuan Zhang",
title = "The surprising accuracy of {Benford}'s law in
mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "127",
number = "3",
pages = "217--237",
year = "2020",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2020.1690387",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K31 (11K38 11Y55 60F99)",
MRnumber = "4067893",
MRreviewer = "Russell Jay Hendel",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
}
@Article{DAlessandro:2020:BLM,
author = "Angelo D'Alessandro",
title = "{Benford}'s law and metabolomics: A tale of numbers
and blood",
journal = "Transfusion and Apheresis Science",
volume = "59",
number = "6",
pages = "103019",
month = dec,
year = "2020",
DOI = "https://doi.org/10.1016/j.transci.2020.103019",
ISSN = "1473-0502 (print), 1878-1683 (electronic)",
ISSN-L = "1473-0502",
bibdate = "Thu May 20 15:42:53 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{DaSilva:2020:BBS,
author = "St{\'e}phane Blondeau {Da Silva}",
title = "{Benford} or Not {Benford}: A Systematic But Not
Always Well-Founded Use of an Elegant Law in
Experimental Fields",
journal = j-COMMUN-MATH-STAT,
volume = "8",
number = "2",
pages = "167--201",
month = jun,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1007/s40304-018-00172-1",
ISSN = "2194-6701 (print), 2194-671X (electronic)",
ISSN-L = "2194-6701",
MRclass = "60E05",
MRnumber = "4102358",
bibdate = "Fri Jul 24 15:51:38 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communmathstat.bib",
URL = "http://link.springer.com/article/10.1007/s40304-018-00172-1",
acknowledgement = ack-nhfb,
fjournal = "Communications in Mathematics and Statistics",
journal-URL = "http://link.springer.com/journal/40304",
}
@Article{daSilva:2020:VNB,
author = "A. J. da Silva and S. Floquet and D. O. C. Santos and
R. F. Lima",
title = "On the validation of the {Newcomb--Benford} law and
the {Weibull} distribution in neuromuscular
transmission",
journal = j-PHYSICA-A,
volume = "553",
pages = "124606, 15",
year = "2020",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2020.124606",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "92C42 (62P10 92C37)",
MRnumber = "4096745",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Durst:2020:IGD,
author = "R. F. Durst and C. Huynh and A. Lott and S. J. Miller
and E. A. Palsson and W. Touw and G. Vriend",
title = "The inverse gamma distribution and {Benford}'s law",
journal = "PUMP J. Undergrad. Res.",
volume = "3",
pages = "95--109",
year = "2020",
ISSN = "2765-8724",
MRclass = "60F05 (42A16 60E10 62E15)",
MRnumber = "4143770",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "The PUMP Journal of Undergraduate Research",
}
@Article{Ectors:2020:ZPL,
author = "Wim Ectors and Bruno Kochan and Davy Janssens and Tom
Bellemans and Geert Wets",
title = "{Zipf}'s power law in activity schedules and the
effect of aggregation",
journal = j-FUT-GEN-COMP-SYS,
volume = "107",
number = "??",
pages = "1014--1025",
month = jun,
year = "2020",
CODEN = "FGSEVI",
DOI = "https://doi.org/10.1016/j.future.2018.04.095",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Fri Jun 19 07:44:14 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/futgencompsys.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167739X17321891",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
}
@Article{Fang:2020:SCP,
author = "Guojun Fang and Qihong Chen",
title = "Several common probability distributions obey
{Benford}'s law",
journal = j-PHYSICA-A,
volume = "540",
pages = "123129, 8",
year = "2020",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2019.123129",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "60E05",
MRnumber = "4041619",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Huang:2020:TFL,
author = "Yasheng Huang and Zhiyong Niu and Clair Yang",
title = "Testing firm-level data quality in {China} against
{Benford}'s law",
journal = j-ECONOM-LETT,
volume = "192",
pages = "109182, 4",
year = "2020",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/j.econlet.2020.109182",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "91G70",
MRnumber = "4095772",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01651765",
}
@Article{Kazemitabar:2020:MCD,
author = "Jalil Kazemitabar and Javad Kazemitabar",
title = "Measuring the conformity of distributions to
{Benford's Law}",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "49",
number = "14",
pages = "3530--3536",
year = "2020",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610926.2019.1590599",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
MRclass = "60E05",
MRnumber = "4107617",
bibdate = "Fri Jul 24 10:15:17 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/03610926.2019.1590599",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
onlinedate = "28 Mar 2019",
}
@Article{Koch:2020:BLC,
author = "Christoffer Koch and Ken Okamura",
title = "{Benford's Law} and {COVID-19} reporting",
journal = j-ECONOM-LETT,
volume = "196",
pages = "109573",
month = nov,
year = "2020",
CODEN = "ECLEDS",
DOI = "https://doi.org/10.1016/j.econlet.2020.109573",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "92B10 (92D30)",
MRnumber = "4150786",
bibdate = "Thu May 20 15:46:14 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01651765",
}
@Article{Lee:2020:CFC,
author = "Kang-Bok Lee and Sumin Han and Yeasung Jeong",
title = "{COVID-19}, flattening the curve, and {Benford}'s
law",
journal = j-PHYSICA-A,
volume = "559",
pages = "125090",
month = dec,
year = "2020",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2020.125090",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "92D30 (62P10)",
MRnumber = "4138406",
bibdate = "Thu May 20 15:48:54 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@InProceedings{Lindstrom:2020:VRC,
author = "Peter Lindstrom",
title = "Variable-Radix Coding of the Reals",
crossref = "Cornea:2020:ISC",
pages = "111--116",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00024",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently proposed real number systems like Posits and
Elias codes make use of tapered accuracy resulting from
variable-length coding of exponents and significands.
Several quite different interpretations of these number
systems have been provided, though most often these
rely on some combination of fixed- and variable-length
codes for exponent and significand. We provide a new
perspective on these number systems that unifies known
representations while suggesting new ones. Our
framework is based on multibit radix representations
that encode the exponent in unary, the leading nonzero
digit in a variable-length code, and the remaining
digits in fixed-length binary code. We show how Posits,
the various Elias codes, and IEEE 754 like
representations can be expressed in this framework.
Moreover, we show that Posits and the Elias and codes
represent the leading digit using the canonical Huffman
code for a probability distribution given by Benford's
law, which governs the probability of leading digits.
We further show that Posits correspond to the use of a
fixed radix while Elias and codes are based on simple
sequences of increasing radix. Our approach provides
for an intuitive and uniform framework for representing
numbers that reveals a visual mapping between codewords
and the binary representation of real numbers obscured
by prior frameworks. This new interpretation suggests a
generalization of Posits and other number systems and
provides simple rules for designing
information-theoretically optimal codes.",
acknowledgement = ack-nhfb,
keywords = "Benford's law; Binary codes; Digital arithmetic; Elias
codes; Encoding; floating point; Huffman code; Indexes;
posits; Probability distribution; Proposals; real
number systems; tapered accuracy; Visualization",
}
@Article{Ma:2020:ERD,
author = "Chengcheng Ma and Baoyuan Wu and Shibiao Xu and Yanbo
Fan and Yong Zhang and Xiaopeng Zhang and Zhifeng Li",
title = "Effective and Robust Detection of Adversarial Examples
via {Benford--Fourier} Coefficients",
journal = "CoRR",
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.48550/arXiv.2005.05552",
ISSN = "????",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://arxiv.org/abs/2005.05552 [;]
db/journals/corr/corr2005.html#abs-2005-05552",
abstract = "Adversarial examples have been well known as a serious
threat to deep neural networks (DNNs). In this work, we
study the detection of adversarial examples, based on
the assumption that the output and internal responses
of one DNN model for both adversarial and benign
examples follow the generalized Gaussian distribution
(GGD), but with different parameters (i.e., shape
factor, mean, and variance). GGD is a general
distribution family to cover many popular distributions
(e.g., Laplacian, Gaussian, or uniform). It is more
likely to approximate the intrinsic distributions of
internal responses than any specific
distribution. Besides, since the shape factor is more
robust to different databases rather than the other two
parameters, we propose to construct discriminative
features via the shape factor for adversarial
detection, employing the magnitude of Benford-Fourier
coefficients (MBF), which can be easily estimated using
responses. Finally, a support vector machine is trained
as the adversarial detector through leveraging the MBF
features. Extensive experiments in terms of image
classification demonstrate that the proposed detector
is much more effective and robust on detecting
adversarial examples of different crafting methods and
different sources, compared to state-of-the-art
adversarial detection methods.",
acknowledgement = ack-nhfb,
dblp-key = "journals/corr/abs-2005-05552",
dblp-mdate = "2022-04-22",
}
@Article{Volcic:2020:UDB,
author = "Aljo{\v{s}}a Vol{\v{c}}i{\v{c}}",
title = "Uniform distribution, {Benford}'s law and
scale-invariance",
journal = j-BOLL-UNIONE-MAT-ITAL,
volume = "13",
number = "4",
pages = "539--543",
year = "2020",
CODEN = "BLUMAM",
DOI = "https://doi.org/10.1007/s40574-020-00245-6",
ISSN = "1972-6724",
MRclass = "60A10 (28D05)",
MRnumber = "4172954",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bollettino dell'Unione Matematica Italiana",
}
@Article{Barabesi:2021:FBL,
author = "Lucio Barabesi and Andrea Cerioli and Domenico
Perrotta",
title = "Forum on {Benford}'s law and statistical methods for
the detection of frauds [{Editorial}]",
journal = "Stat. Methods Appl.",
volume = "30",
number = "3",
pages = "767--778",
year = "2021",
DOI = "https://doi.org/10.1007/s10260-021-00588-0",
ISSN = "1618-2510",
MRclass = "Expansion",
MRnumber = "4308363",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methods \& Applications. Journal of the
Italian Statistical Society",
}
@Article{Berger:2021:MBL,
author = "Arno Berger and Theodore P. Hill",
title = "The mathematics of {Benford}'s law: a primer",
journal = "Stat. Methods Appl.",
volume = "30",
number = "3",
pages = "779--795",
year = "2021",
DOI = "https://doi.org/10.1007/s10260-020-00532-8",
ISSN = "1618-2510",
MRclass = "Expansion",
MRnumber = "4308364",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methods \& Applications. Journal of the
Italian Statistical Society",
}
@Article{Cerqueti:2021:DVS,
author = "Roy Cerqueti and Mario Maggi",
title = "Data validity and statistical conformity with
{Benford}'s {Law}",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "144",
pages = "Paper No. 110740, 7",
year = "2021",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2021.110740",
ISSN = "0960-0779 (print), 1873-2887 (electronic)",
ISSN-L = "0960-0779",
MRclass = "62R07",
MRnumber = "4220694",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Chaos, Solitons \& Fractals",
}
@Article{daSilvaAzevedo:2021:BLB,
author = "Caio {da Silva Azevedo} and Rodrigo Franco
Gon{\c{c}}alves and Vagner Luiz Gava and Mauro {de
Mesquita Spinola}",
title = "A {Benford's Law} based methodology for fraud
detection in social welfare programs: {Bolsa Familia}
analysis",
journal = j-PHYSICA-A,
volume = "567",
pages = "125626",
month = apr,
year = "2021",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/j.physa.2020.125626",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu May 20 15:52:27 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
}
@Article{Farris:2021:RRB,
author = "Madeleine Farris and Noah Luntzlara and Steven J.
Miller and Lily Shao and Mengxi Wang",
title = "Recurrence relations and {Benford}'s law",
journal = "Stat. Methods Appl.",
volume = "30",
number = "3",
pages = "797--817",
year = "2021",
DOI = "https://doi.org/10.1007/s10260-020-00547-1",
ISSN = "1618-2510",
MRclass = "11K06 (60F05 65Q30)",
MRnumber = "4308365",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methods \& Applications. Journal of the
Italian Statistical Society",
}
@Article{Galveas:2021:FAS,
author = "Daniel Galv{\^e}as and Fernando Barros and Carlos
Alessandro Fuzo",
title = "A forensic analysis of {SARS-CoV-2} cases and
{COVID-19} mortality misreporting in the {Brazilian}
population",
journal = "Public Health",
month = may,
year = "2021",
CODEN = "PUHEAE",
DOI = "https://doi.org/10.1016/j.puhe.2021.05.010",
ISSN = "0033-3506 (print), 1476-5616 (electronic)",
ISSN-L = "0033-3506",
bibdate = "Thu May 20 15:54:19 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Jianu:2021:RFI,
author = "Ionel Jianu and Iulia Jianu",
title = "Reliability of Financial Information from the
Perspective of {Benford's Law}",
journal = j-ENTROPY,
volume = "23",
number = "5",
pages = "557--??",
month = may,
year = "2021",
CODEN = "ENTRFG",
DOI = "https://doi.org/10.3390/e23050557",
ISSN = "????",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/entropy/entropy23.html#JianuJ21",
acknowledgement = ack-nhfb,
dblp-key = "journals/entropy/JianuJ21",
dblp-mdate = "2021-06-01",
fjournal = "Entropy",
journal-URL = "https://www.mdpi.com/journal/entropy/",
}
@Article{Marchand:2021:BLC,
author = "Chase Marchand and Dalton Maahs",
title = "{Benford's Law} and {COVID-19} Data",
journal = j-CHANCE,
volume = "34",
number = "2",
pages = "31--38",
year = "2021",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.2021.1915031",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Mon May 17 16:10:57 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/chance.bib",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
onlinedate = "26 Apr 2021",
}
@Article{Mocnik:2021:BLG,
author = "Franz-Benjamin Mocnik",
title = "{Benford}'s law and geographical information --- the
example of {OpenStreetMap}",
journal = "International Journal of Geographical Information
Science",
volume = "35",
number = "9",
pages = "1746--1772",
month = "????",
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1080/13658816.2020.1829627",
ISSN = "1365-8816 (print), 1365-8824 (electronic)",
ISSN-L = "1365-8816",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/gis/gis35.html#Mocnik21",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Geogr. Inf. Sci.",
dblp-key = "journals/gis/Mocnik21",
dblp-mdate = "2021-09-16",
fjournal = "International Journal of Geographical Information
Science",
}
@Article{Mumic:2021:MTD,
author = "Nermina Mumic and Peter Filzmoser",
title = "A multivariate test for detecting fraud based on
{Benford}'s law, with application to music streaming
data",
journal = "Stat. Methods Appl.",
volume = "30",
number = "3",
pages = "819--840",
year = "2021",
DOI = "https://doi.org/10.1007/s10260-021-00582-6",
ISSN = "1618-2510",
MRclass = "Expansion",
MRnumber = "4308366",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Methods \& Applications. Journal of the
Italian Statistical Society",
}
@Article{Tosic:2021:UBL,
author = "Aleksandar To{\v{s}}i{\'c} and Jernej
Vi{\v{c}}i{\v{c}}",
title = "Use of {Benford}'s law on academic publishing
networks",
journal = j-J-INFORMETRICS,
volume = "15",
number = "3",
pages = "Article 101163",
month = aug,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.joi.2021.101163",
ISSN = "1751-1577 (print), 1875-5879 (electronic)",
ISSN-L = "1751-1577",
bibdate = "Thu May 20 15:50:31 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jinformetrics.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1751157721000341",
acknowledgement = ack-nhfb,
fjournal = "Journal of Informetrics",
journal-URL = "http://www.sciencedirect.com/science/journal/17511577/",
}
@Article{Wase:2021:BLB,
author = "Viktor Wase",
title = "{Benford's Law} in the {Beale} ciphers",
journal = j-CRYPTOLOGIA,
volume = "45",
number = "3",
pages = "282--286",
year = "2021",
CODEN = "CRYPE6",
DOI = "https://doi.org/10.1080/01611194.2020.1821409",
ISSN = "0161-1194 (print), 1558-1586 (electronic)",
ISSN-L = "0161-1194",
bibdate = "Wed Jun 9 08:58:59 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/01611194.2020.1821409",
acknowledgement = ack-nhfb,
fjournal = "Cryptologia",
journal-URL = "https://www.tandfonline.com/loi/ucry20",
}
@Article{Barabesi:2022:CTB,
author = "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli
and Domenico Perrotta",
title = "On Characterizations and Tests of {Benford's Law}",
journal = j-J-AM-STAT-ASSOC,
volume = "117",
number = "540",
pages = "1887--1903",
year = "2022",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1080/01621459.2021.1891927",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Mar 22 07:55:40 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc2020.bib;
http://www.tandfonline.com/toc/uasa20/117/540",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
onlinedate = "06 Apr 2021",
}
@InCollection{Neves:2021:ABL,
author = "Gilberto A. Neves and Catarina S. Nunes and Paula
Odete Fernandes",
booktitle = "Optimization, Learning Algorithms and Applications:
First International Conference, {OL2A 2021},
Bragan{\c{c}}a, Portugal, July 19--21, 2021, Revised
Selected Papers",
title = "Application of {Benford}'s law to the tourism demand:
the case of the {Island of Sal, Cape Verde}",
volume = "1488",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "587--598",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-91885-9_43",
ISBN = "3-030-91884-X; 3-030-91885-8",
ISBN-13 = "978-3-030-91884-2; 978-3-030-91885-9",
MRnumber = "4432720",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Commun. Comput. Inf. Sci.",
URL = "https://doi.org/10.1007/978-3-030-91885-9_43",
acknowledgement = ack-nhfb,
}
@Article{Cangiotti:2022:BLN,
author = "Nicol{\`o} Cangiotti and Mattia Sensi",
title = "{Benford}'s law: a number-theoretical perspective",
journal = "Palestine Journal of Mathematics",
volume = "11",
number = "3",
pages = "379--385",
year = "2022",
ISSN = "2219-5688",
ISSN-L = "2219-5688",
MRclass = "62E10 (11K06 11K16 62A99)",
MRnumber = "4447060",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Palest. J. Math.",
fjournal = "Palestine Journal of Mathematics",
}
@Article{Chen:2022:ASU,
author = "Tianyi Chen and Charalampos E. Tsourakakis",
title = "{AntiBenford} Subgraphs: Unsupervised Anomaly
Detection in Financial Networks",
journal = "CoRR",
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.48550/arXiv.2205.13426",
ISSN = "????",
bibdate = "Wed Mar 29 09:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/corr/corr2205.html#abs-2205-13426",
acknowledgement = ack-nhfb,
DBLP-key = "journals/corr/abs-2205-13426",
DBLP-mdate = "2022-10-02",
}
@Article{DaSilva:2022:AOB,
author = "St{\'e}phane Blondeau {Da Silva}",
title = "An alternative to the oversimplifying {Benford}'s law
in experimental fields",
journal = j-SANKHYA-B,
volume = "84",
number = "2",
pages = "778--808",
year = "2022",
CODEN = "SANBBV",
DOI = "https://doi.org/10.1007/s13571-022-00287-0",
ISSN = "0976-8386 (print), 0976-8394 (electronic)",
ISSN-L = "0976-8394",
MRclass = "99-01",
MRnumber = "4502751",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://doi.org/10.1007/s13571-022-00287-0",
acknowledgement = ack-nhfb,
fjournal = "Sankhya B. The Indian Journal of Statistics",
}
@Article{Groharing:2022:BLC,
author = "Brooks Groharing and David McCune",
title = "{Benford's Law} and County-Level Votes in {US}
{Presidential} Elections",
journal = j-CHANCE,
volume = "35",
number = "2",
pages = "4--10",
year = "2022",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.2022.2066408",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Sat Jun 4 14:19:58 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/chance.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066408",
acknowledgement = ack-nhfb,
fjournal = "Chance",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
}
@Article{Mbona:2022:FSU,
author = "Innocent Mbona and Jan H. P. Eloff",
title = "Feature selection using {Benford}'s law to support
detection of malicious social media bots",
journal = j-INFO-SCI,
volume = "582",
pages = "369--381",
month = jan,
year = "2022",
CODEN = "ISIJBC",
DOI = "https://doi.org/10.1016/j.ins.2021.09.038",
ISSN = "0020-0255 (print), 1872-6291 (electronic)",
ISSN-L = "0020-0255",
MRclass = "62H25 (91D30)",
MRnumber = "4318332",
bibdate = "Tue Feb 22 14:31:21 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://dblp.org/db/journals/isci/isci582.html#MbonaE22",
acknowledgement = ack-nhfb,
DBLP-key = "journals/isci/MbonaE22",
DBLP-mdate = "2021-12-01",
fjournal = "Information Sciences. An International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/00200255",
}
@Article{Miraglia:2022:AIC,
author = "Jorge E. Miraglia and Maria Silvia Gravielle",
title = "Atomic ionization, capture, and stopping cross
sections by ion impact examined with the {Benford
law}",
journal = j-ADV-QUANTUM-CHEM,
volume = "85",
pages = "??--??",
year = "2022",
CODEN = "AQCHA9",
DOI = "https://doi.org/10.1016/bs.aiq.2022.04.006",
ISSN = "0065-3276",
ISSN-L = "0065-3276",
bibdate = "Wed Sep 21 07:26:09 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0065327622000107",
acknowledgement = ack-nhfb,
ajournal = "Adv. Quantum Chem.",
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276/",
}
@InCollection{Nelson:2022:BLM,
author = "Sybil Prince Nelson and Brian Wickman and Jack Null
and Eric Gazin",
booktitle = "Mathematics and computation in music",
title = "{Benford}'s law and music note frequencies",
volume = "13267",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "383--389",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-07015-0\_34",
ISBN = "978-30310-7-0-1-4-3; 978-30310-7-0-1-5-0",
ISBN-13 = "978-3-031-07014-3; 978-3-031-07015-0",
MRclass = "00A65",
MRnumber = "4485599",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Comput. Sci.",
URL = "https://doi.org/10.1007/978-3-031-07015-0_34",
acknowledgement = ack-nhfb,
}
@Article{Pollack:2022:DSB,
author = "Paul Pollack and Akash Singha Roy",
title = "{Dirichlet}, {Sierpi{\'n}ski}, and {Benford}",
journal = j-J-NUMBER-THEORY,
volume = "239",
number = "??",
pages = "352--364",
month = oct,
year = "2022",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2021.12.010",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Fri Jun 3 11:42:55 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X22000099",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Velleman:2022:ECD,
author = "Paul Velleman and Howard Wainer",
title = "Exploring {COVID} Data with {Benford}'s and {Zipf}'s
Laws",
journal = j-CHANCE,
volume = "35",
number = "2",
pages = "11--15",
year = "2022",
CODEN = "CNDCE4",
DOI = "https://doi.org/10.1080/09332480.2022.2066410",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
ISSN-L = "0933-2480",
bibdate = "Sat Jun 4 14:19:58 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/chance.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066410",
acknowledgement = ack-nhfb,
fjournal = "Chance",
journal-URL = "http://chance.amstat.org/;
http://link.springer.com/journal/144;
http://www.tandfonline.com/loi/ucha20",
}
@Article{Barabesi:2023:SMB,
author = "Lucio Barabesi and Andrea Cerioli and Marco {Di
Marzio}",
title = "Statistical models and the {Benford} hypothesis: a
unified framework",
journal = j-TEST,
volume = "32",
number = "4",
pages = "1479--1507",
month = dec,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11749-023-00881-y",
ISSN = "1133-0686 (print), 1863-8260 (electronic)",
ISSN-L = "1133-0686",
bibdate = "Wed Aug 14 12:02:10 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/test.bib",
URL = "https://link.springer.com/article/10.1007/s11749-023-00881-y",
acknowledgement = ack-nhfb,
ajournal = "TEST",
fjournal = "TEST: An Official Journal of the Spanish Society of
Statistics and Operations Research",
journal-URL = "http://link.springer.com/journal/11749",
}
@Article{Cerqueti:2023:BLE,
author = "Roy Cerqueti and Davide Provenzano",
title = "{Benford}'s law for economic data reliability: the
case of tourism flows in {Sicily}",
journal = j-CHAOS-SOLITONS-FRACTALS,
volume = "173",
pages = "1--10",
year = "2023",
CODEN = "CSFOEH",
DOI = "https://doi.org/10.1016/j.chaos.2023.113635",
ISSN = "0960-0779,1873-2887",
ISSN-L = "0960-0779",
MRclass = "62R07 (62P20)",
MRnumber = "4598410",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://doi.org/10.1016/j.chaos.2023.113635",
acknowledgement = ack-nhfb,
articleno = "113635",
fjournal = "Chaos, Solitons \& Fractals",
pagecount = "10",
}
@Article{Cerqueti:2023:STB,
author = "Roy Cerqueti and Claudio Lupi",
title = "Severe testing of {Benford}'s law",
journal = j-TEST,
volume = "32",
number = "2",
pages = "677--694",
month = jun,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11749-023-00848-z",
ISSN = "1133-0686 (print), 1863-8260 (electronic)",
ISSN-L = "1133-0686",
bibdate = "Wed Oct 11 15:13:55 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/test.bib",
URL = "https://link.springer.com/article/10.1007/s11749-023-00848-z",
acknowledgement = ack-nhfb,
ajournal = "TEST",
fjournal = "TEST: An Official Journal of the Spanish Society of
Statistics and Operations Research",
journal-URL = "http://link.springer.com/journal/11749",
}
@Article{Chandee:2023:BLM,
author = "Vorrapan Chandee and Xiannan Li and Paul Pollack and
Akash Singha Roy",
title = "On {Benford}'s law for multiplicative functions",
journal = j-PROC-AM-MATH-SOC,
volume = "151",
number = "11",
pages = "4607--4619",
year = "2023",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/proc/16480",
ISSN = "0002-9939,1088-6826",
ISSN-L = "0002-9939",
MRclass = "11N60 (11K65)",
MRnumber = "4634867",
MRreviewer = "Christoph Aistleitner",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://doi.org/10.1090/proc/16480",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Kazemitabar:2023:GFC,
author = "Javad Kazemitabar",
title = "A general framework for constructing distributions
satisfying {Benford}'s law",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "52",
number = "12",
pages = "6160--6167",
year = "2023",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1080/03610918.2022.2032153",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
bibdate = "Sat May 18 14:28:31 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput2020.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
onlinedate = "18 May 2022",
}
@Article{Kim:2023:EFA,
author = "Phuoc Nguyen Kim and Jonatan Contreras and Martine
Ceberio and Nguyen Ngoc Thach",
title = "Economic and financial applications of {Benford's
Law}: from traditional use in audits to help in deep
learning",
journal = "Internat. J. Uncertain. Fuzziness Knowledge-Based
Systems",
volume = "31",
pages = "197--207",
year = "2023",
DOI = "https://doi.org/10.1142/S0218488523400111",
ISSN = "0218-4885,1793-6411",
MRclass = "91B99 (68T07)",
MRnumber = "4700940",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://doi.org/10.1142/S0218488523400111",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Uncertainty, Fuzziness and
Knowledge-Based Systems",
}
@Article{Kondo:2023:HTZ,
author = "Illenin O. Kondo and Logan T. Lewis and Andrea
Stella",
title = "Heavy tailed but not {Zipf}: Firm and establishment
size in the {United States}",
journal = j-J-APPL-ECONOMETRICS,
volume = "38",
number = "5",
pages = "767--785",
month = aug,
year = "2023",
CODEN = "JAECET",
DOI = "https://doi.org/10.1002/jae.2976",
ISSN = "0883-7252 (print), 1099-1255 (electronic)",
ISSN-L = "0883-7252",
bibdate = "Mon Oct 16 14:44:43 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jappleconometrics.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Appl. Econometrics",
fjournal = "Journal of Applied Econometrics",
journal-URL = "https://onlinelibrary.wiley.com/journal/10991255;
https://www.jstor.org/journal/japplecon",
onlinedate = "23 April 2023",
}
@Article{Murtagh:2023:WBL,
author = "Jack Murtagh",
title = "What is {Benford's Law}? {Why} This Unexpected Pattern
of Numbers is Everywhere",
journal = j-SCI-AMER,
volume = "??",
number = "??",
pages = "??--??",
day = "8",
month = may,
year = "2023",
CODEN = "SCAMAC",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Mon May 08 09:47:36 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Campanelli:2024:EDS,
author = "Leonardo Campanelli",
title = "On the {Euclidean} distance statistic of {Benford}'s
law",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "53",
number = "2",
pages = "451--474",
year = "2024",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610926.2022.2082480",
ISSN = "0361-0926,1532-415X",
ISSN-L = "0361-0926",
MRclass = "99-01",
MRnumber = "4669200",
bibdate = "Tue May 21 16:59:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib",
URL = "https://doi.org/10.1080/03610926.2022.2082480",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics. Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
}
@Article{Fang:2024:BLR,
author = "Xinyu Fang and Steven J. Miller and Maxwell Sun and
Amanda Verga",
title = "{Benford}'s law and random integer decomposition with
congruence stopping condition",
journal = j-J-NUMBER-THEORY,
volume = "264",
number = "??",
pages = "307--356",
month = nov,
year = "2024",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2024.05.005",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Tue Aug 6 14:07:34 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X24001367",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Gupta:2024:ADQ,
author = "Solanki Gupta and Vivek Kumar Singh and Sumit Kumar
Banshal",
title = "Altmetric data quality analysis using {Benford}'s
law",
journal = j-SCIENTOMETRICS,
volume = "129",
number = "7",
pages = "4597--4621",
month = jul,
year = "2024",
CODEN = "SCNTDX",
DOI = "https://doi.org/10.1007/s11192-024-05061-9",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Mon Aug 5 13:03:44 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/scientometrics2020.bib",
URL = "https://link.springer.com/article/10.1007/s11192-024-05061-9",
acknowledgement = ack-nhfb,
ajournal = "Scientometrics",
fjournal = "Scientometrics",
journal-URL = "http://link.springer.com/journal/11192",
}
@Article{Kossler:2024:SNI,
author = "Wolfgang K{\"o}ssler and Hans-J. Lenz and Xing D.
Wang",
title = "Some new invariant sum tests and {MAD} tests for the
assessment of {Benford}'s law",
journal = j-COMP-STAT,
volume = "39",
number = "7",
pages = "3779--3800",
month = dec,
year = "2024",
CODEN = "CSTAEB",
DOI = "https://doi.org/10.1007/s00180-024-01463-8",
ISSN = "0943-4062 (print), 1613-9658 (electronic)",
ISSN-L = "0943-4062",
bibdate = "Thu Nov 21 06:02:05 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/compstat.bib",
URL = "https://link.springer.com/article/10.1007/s00180-024-01463-8",
acknowledgement = ack-nhfb,
ajournal = "Comp. Stat.",
fjournal = "Computational Statistics",
journal-URL = "http://link.springer.com/journal/180",
}
@Book{Mebane:20xx:EF,
author = "Walter R. {Mebane, Jr.}",
title = "Election Forensics",
publisher = "????",
address = "????",
pages = "????",
year = "20xx",
bibdate = "Sat Sep 10 14:28:31 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Book in preparation.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
}
@Proceedings{Apers:1989:VLD,
editor = "P. M. G. (Petrus Maria Gerardus) Apers and Gio
Wiederhold",
booktitle = "Very large data bases: proceedings: proceedings of the
Fifteenth International Conference on Very Large Data
Bases, August 22--25, 1989, Amsterdam, The
Netherlands",
title = "Very large data bases: proceedings: proceedings of the
Fifteenth International Conference on Very Large Data
Bases, August 22--25, 1989, Amsterdam, The
Netherlands",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xii + 467",
year = "1989",
ISBN = "1-55860-101-5",
ISBN-13 = "978-1-55860-101-7",
LCCN = "QA 76.9 D3 I61 1989",
bibdate = "Sat Dec 7 13:05:35 MST 1996",
bibsource = "DBLP; http://dblp.uni-trier.de;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "database management -- congresses",
}
@Book{Gell-Mann:1997:QJA,
author = "Murray Gell-Mann",
booktitle = "The quark and the jaguar: adventures in the simple and
the complex",
title = "The quark and the jaguar: adventures in the simple and
the complex",
publisher = pub-W-H-FREEMAN,
address = pub-W-H-FREEMAN:adr,
pages = "xviii + 392",
year = "1997",
ISBN = "0-7167-2725-0 (paperback)",
ISBN-13 = "978-0-7167-2725-5 (paperback)",
LCCN = "QC774.G45 A3 1994",
bibdate = "Fri Aug 8 06:26:36 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.gbv.de/dms/bowker/toc/9780716725817.pdf;
http://www.zentralblattmath.org/zmath/en/search/?an=0833.00011",
abstract = "From one of the architects of the new science of
simplicity and complexity comes a highly personal,
unifying vision of the natural world. As a theoretical
physicist, Murray Gell-Mann has explored nature at its
most fundamental level. His achievements include the
1969 Nobel Prize for work leading up to his discovery
of the quark --- the basic building block of all atomic
nuclei throughout the universe. But Gell-Mann is a man
of many intellectual passions, with lifelong interests
in fields that seek to understand existence at its most
complex: natural history, biological evolution, the
history of language, and the study of creative
thinking. These seemingly disparate pursuits come
together in Gell-Mann's current work at the Santa Fe
Institute, where scientists are investigating the
similarities and differences among complex adaptive
systems --- systems that learn or evolve by utilizing
acquired information. They include a child learning his
or her native language, a strain of bacteria becoming
resistant to an antibiotic, the scientific community
testing new theories, or an artist implementing a
creative idea. The Quark and the Jaguar is Gell-Mann's
own story of finding the connections between the basic
laws of physics and the complexity and diversity of the
natural world. The simple: a quark inside an atom. The
complex: a jaguar prowling its jungle territory in the
night. Exploring the relationship between them becomes
a series of exciting intellectual adventures.",
acknowledgement = ack-nhfb,
subject = "Gell-Mann, Murray; Travel; Ecuador; Particles (Nuclear
physics); Nuclear physicists; United States; Biography;
Description and travel",
tableofcontents = "Part 1. The Simple and the Complex \\
1. Prologue: An Encounter in the Jungle \\
2. Early Light \\
3. Information and Crude Complexity \\
4. RANDomness \\
5. A Child Learning a Language \\
6. Bacteria Developing Drug Resistance \\
7. The Scientific Enterprise \\
8. The Power of Theory \\
9. What Is Fundamental? \\
Part 2. The Quantum Universe \\
10. Simplicity and Randomness in the Quantum Mechanics
Universe \\
11. A Contemporary View of Quantum Mechanics \\
12. Quantum Mechanics and Flapdoodle \\
13. Quarks and All That: The Standard Model \\
14. Superstring Theory: Unification at Last? \\
15. Time's Arrow's: Forward and Backward Time \\
Part 3. Selection and Fitness \\
16. Selection at Work in Biological Evolution and
Elsewhere \\
17. From Learning to Creative Thinking \\
18. Superstition and Skepticism \\
19. Adaptive and Maladaptive Schema \\
20. Machines That Learn or Simulate Learning \\
Part 4. Diversity and Sustainability \\
21. Diversities Under Threat \\
22. Transitions to a More Sustainable World \\
23. Afterword \\
Index",
}
@Proceedings{ACM:2000:PIC,
editor = "{ACM}",
booktitle = "{Proceedings of the 2000 International Conference on
Software Engineering: ICSE 2000, the new millennium:
June 4--11, 2000, Limerick, Ireland}",
title = "{Proceedings of the 2000 International Conference on
Software Engineering: ICSE 2000, the new millennium:
June 4--11, 2000, Limerick, Ireland}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xviii + 843",
year = "2000",
ISBN = "1-58113-206-9, 0-7803-6325-6 (casebound),
0-7803-6326-4 (microfiche)",
ISBN-13 = "978-1-58113-206-9, 978-0-7803-6325-0 (casebound),
978-0-7803-6326-7 (microfiche)",
LCCN = "QA76 N271 2000",
bibdate = "Sun Feb 17 08:56:25 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{Raidl:2003:AEC,
editor = "Gunther Raidl",
booktitle = "{Applications of evolutionary computing: EvoWorkshops
2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and
EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}",
title = "{Applications of evolutionary computing: EvoWorkshops
2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and
EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}",
volume = "2611",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxi + 708",
year = "2003",
CODEN = "LNCSD9",
DOI = "????",
ISBN = "3-540-00976-0 (softcover)",
ISBN-13 = "978-3-540-00976-4 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.618 .E899 2003",
bibdate = "Thu Aug 21 09:09:03 MDT 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2611.htm;
http://www.springerlink.com/content/978-3-540-00976-4;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2611",
acknowledgement = ack-nhfb,
keywords = "evolutionary computation --- congresses; evolutionary
programming (computer science) --- congresses",
}
@Article{Rybski:2023:ALZ,
author = "Diego Rybski and Antonio Ciccone",
title = "{Auerbach}, {Lotka}, and {Zipf}: pioneers of power-law
city-size distributions",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "77",
number = "6",
pages = "601--613",
month = nov,
year = "2023",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/s00407-023-00314-0",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
bibdate = "Wed Mar 27 09:47:28 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "https://link.springer.com/article/10.1007/s00407-023-00314-0",
acknowledgement = ack-nhfb,
ajournal = "Arch. Hist. Exact Sci.",
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
}
@Book{Warren:2003:HD,
author = "Henry S. Warren",
booktitle = "Hacker's delight",
title = "Hacker's delight",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xiv + 306",
year = "2003",
ISBN = "0-201-91465-4",
ISBN-13 = "978-0-201-91465-8",
LCCN = "QA76.6 .W375 2003",
bibdate = "Tue Jan 03 18:20:34 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "While this book does not specifically address
computational aspects of floating-point arithmetic
(apart from the nine-page Chapter 15), it has extensive
coverage of, and clever algorithms for, integer
arithmetic operations that are fundamental for
implementing hardware floating-arithmetic and software
multiple-precision arithmetic.",
URL = "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
http://www.hackersdelight.org/;
http://www.hackersdelight.org/hackerTOC.pdf;
http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
acknowledgement = ack-nhfb,
keywords = "DEC PDP-10; division by constants; Gray code; Hilbert
curves; IEEE 754 floating-point arithmetic; integer
cube root; integer division; integer exponentiation;
integer logarithm; integer square root; prime numbers;
unusual number bases",
remark = "Foreword by Guy L. Steele, Jr., who begins ``When I
first got a summer job at MIT's Project MAC almost 30
years ago, I was delighted to be able to work with the
DEC PDP-10 computer, which was more fun to program in
assembly language than any other computer, bar none,
because of its rich yet tractable set of instructions
for performing bit tests, bit masking, field
manipulation, and operations on integers. Though the
PDP-10 has not been manufactured for quite some years,
there remains a thriving cult of enthusiasts who keep
old PDP-10 hardware running and who run old PDP-10
software---entire operating systems and their
applications---by using personal computers to simulate
the PDP-10 instruction set.''",
subject = "Computer programming; Computer hackers",
tableofcontents = "Preface\par
1. Introduction\par
Notation\par
Instruction Set and Execution Time Model\par
2. Basis\par
Manipulating Rightmost Bits \\
Addition Combined with Logical Operations \\
Inequalities among Logical and Arithmetic Expressions
\\
Absolute Value Function \\
Sign Extension \\
Shift Right Signed from Unsigned \\
Sign Function \\
Three-Valued Compare \\
Transfer of Sign \\
Decoding a `Zero Means 2**n' Field \\
Comparison Predicates \\
Overflow Detection \\
Condition Code Result of Add, Subtract, and Multiply
\\
Rotate Shifts \\
Double-Length Add/Subtract \\
Double-Length Shifts \\
Multibyte Add, Subtract, Absolute Value \\
Doz, Max, Min \\
Exchanging Registers \\
Alternating among Two or More Values\par
3. Power-of-2 Boundaries\par
Rounding Up/Down to a Multiple of a Known Power of 2
\\
Rounding Up/Down to the Next Power of 2 \\
Detecting a Power-of-2 Boundary Crossing\par
4. Arithmetic Bounds\par
Checking Bounds of Integers \\
Propagating Bounds through Adds and Subtracts \\
Propagating Bounds through Logical Operations \\
Signed Bounds\par
5. Counting Bits\par
Counting 1-bits \\
Parity \\
Counting Leading 0's \\
Counting Trailing 0's\par
6. Searching Words\par
Find First 0-Byte \\
Find First String of 1-Bits of a Given Length\par
7. Rearranging Bits and Bytes\par
Reversing Bits and Bytes \\
Shuffling Bits \\
Transposing a Bit Matrix \\
Compress, or Generalized Extract \\
General Permutations, Sheep and Goats Operation \\
Rearrangements and Index Transformations\par
8. Multiplication\par
Multiword Multiplication \\
High-Order Half of 64-Bit Product \\
High-Order Product Signed from/to Unsigned \\
Multiplication by Constants\par
9. Integer Division\par
Preliminaries \\
Multiword Division \\
Unsigned Short Division from Signed Division \\
Unsigned Long Division\par
10. Integer Division by Constants\par
Signed Division by a Known Power of 2 \\
Signed Remainder from Division by a Known Power of 2
\\
Signed Division and Remainder by Non-powers of 2 \\
Signed Division by Divisors >= 2 \\
Signed Division by Divisors <= -2 \\
Incorporation into a Compiler \\
Miscellaneous Topics \\
Unsigned Division \\
Unsigned Division by Divisors >= 1 \\
Incorporation into a Compiler (Unsigned) \\
Miscellaneous Topics (Unsigned) \\
Applicability to Modulus and Floor Division \\
Similar Methods \\
Sample Magic Numbers \\
Exact Division by Constants \\
Test for Zero Remainder after Division by a
Constant\par
11. Some Elementary Functions\par
Integer Square Root \\
Integer Cube Root \\
Integer Exponentiation \\
Integer Logarithm\par
12. Unusual Bases for Number Systems\par
Base -2 \\
Base -1 + i \\
Other Bases \\
What is the Most Efficient Base?\par
13. Gray Code \\
Gray Code \\
Incrementing a Gray Coded Integer \\
Negabinary Gray Code \\
Brief History and Applications\par
14. Hilbert's Curve\par
A Recursive Algorithm for Generating the Hilbert Curve
\\
Coordinates from Distance along the Hilbert Curve \\
Distance from Coordinates on the Hilbert Curve \\
Incrementing the Coordinates on the Hilbert Curve \\
Non-recursive Generating Algorithms \\
Other Space-Filling Curves \\
Applications\par
15. Floating-Point\par
IEEE Format \\
Comparing Floating-Point Numbers Using Integer
Operations \\
The Distribution of Leading Digits \\
Table of Miscellaneous Values\par
16. Formulas for Primes\par
Introduction \\
Willans's Formulas \\
Wormell's Formula \\
Formulas for Other Difficult Functions\par
Appendix A. Arithmetic Tables for a 4-Bit
Machine\par
Appendix B. Newton's Method\par
Bibliography.",
}
@Proceedings{Gama:2005:MLE,
editor = "Jo{\~a}ao Gama and Rui Camacho and Pavel Brazdil and
Al{\'\i}pio M{\'a}rio Jorge and Lu{\'\i}s Torgo",
booktitle = "{Machine learning --- ECML 2005: 16th European
Conference on Machine Learning, Porto, Portugal,
October 3--7, 2005: proceedings}",
title = "{Machine learning --- ECML 2005: 16th European
Conference on Machine Learning, Porto, Portugal,
October 3--7, 2005: proceedings}",
volume = "3720",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiii + 769",
year = "2005",
ISBN = "3-540-29243-8",
ISBN-13 = "978-3-540-29243-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "Q325.5 .E26 2005",
bibdate = "Tue Nov 15 08:57:03 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS # " and " # ser-LNAI,
URL = "http://www.loc.gov/catdir/enhancements/fy0663/2005933045-d.html;
http://www.springerlink.com/openurl.asp?genre=issue\%26issn=0302-9743\%26volume=3720",
acknowledgement = ack-nhfb,
meetingname = "ECML 2005 (2005: Porto, Portugal)",
subject = "Machine learning; Congresses",
}
@Proceedings{Neumann:2005:CAE,
editor = "L{\'a}szl{\'o} Neumann and Mateu Sbert and Bruce Gooch
and Werner Purgathofer",
booktitle = "{Computational aesthetics 2005: Eurographics Workshop
on Computational Aesthetics in Graphics, Visualization
and Imaging, Girona, Spain, 18--20 May 2005}",
title = "{Computational aesthetics 2005: Eurographics Workshop
on Computational Aesthetics in Graphics, Visualization
and Imaging, Girona, Spain, 18--20 May 2005}",
publisher = "Eurographics Association",
address = "Aire-la-Ville, Switzerland",
pages = "245",
year = "2005",
ISBN = "3-905673-27-4",
ISBN-13 = "978-3-905673-27-2",
ISSN = "1816-0859",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Computational aesthetics",
acknowledgement = ack-nhfb,
}
@Book{Alvarez:2008:EFD,
editor = "R. Michael Alvarez and Thad E. (Thad Edward) Hall and
Susan D. Hyde",
booktitle = "Election Fraud: Detecting and Deterring Electoral
Manipulation",
title = "Election Fraud: Detecting and Deterring Electoral
Manipulation",
publisher = "Brookings Institution Press",
address = "Washington, DC, USA",
pages = "xiii + 255",
year = "2008",
ISBN = "0-8157-0138-1 (hardcover), 0-8157-0139-X (paperback)",
ISBN-13 = "978-0-8157-0138-5 (hardcover), 978-0-8157-0139-2
(paperback)",
LCCN = "JK1994 .E43 2008",
bibdate = "Sat Sep 10 14:23:39 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/toc/ecip0810/2008005719.html",
abstract = "Brings together experts on election law, election
administration, and U.S. and comparative politics to
examine the U.S. understanding of election fraud. With
survey data, incident reports, and state-collected
fraud allegations, measures the extent and nature of
election fraud in U.S. Analyzes techniques for
detecting and potentially deterring fraud..",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
subject = "Elections; Corrupt practices; United States;
Prevention; Ballot; Security measures; Case studies",
tableofcontents = "Corruption of the election process under U.S.
federal law / Craig C. Donsanto \\
International principles for election integrity / Thad
E. Hall and Tova Andrea Wang \\
Beyond election fraud: manipulation, violence, and
foreign power intervention / Gamze {\eth}Cavdar \\
Measuring perceptions of election threats: survey data
from voters and elites / R. Michael Alvarez and Thad E.
Hall \\
Caught in the act: recent federal election fraud cases
/ Delia Bailey \\
Correlates of fraud: studying state election fraud
allegations / R. Michael Alvarez and Frederick J.
Boehmke \\
Fraud or failure? what incident reports reveal about
election anomalies and irregularities / D. Roderick
Kiewiet \ldots{} [et al.] \\
Identifying and preventing signature fraud on ballot
measure petitions / Todd Donovan and Daniel A. Smith
\\
The case of the 2002 general election / R. Michael
Alvarez and Jonathan N. Katz \\
Election forensics: the second-digit Benford's law test
and recent American presidential elections / Walter R.
Mebane, Jr. \\
On the trail of fraud: estimating the flow of votes
between Russia's elections / Mikhail Myagkov, Peter C.
Ordeshook, and Dimitry Shaikin \\
How international election observers detect and deter
fraud / Susan D. Hyde \\
Unintended consequences of election monitoring /
Alberto Simpser",
}
@Book{Horgan:2009:PRI,
author = "Jane M. Horgan",
booktitle = "Probability with {R}: an introduction with computer
science applications",
title = "Probability with {R}: an introduction with computer
science applications",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xviii + 393",
year = "2009",
ISBN = "0-470-28073-5 (cloth)",
ISBN-13 = "978-0-470-28073-7 (cloth)",
LCCN = "QA76.9.M35 H863 2009",
bibdate = "Wed Sep 15 09:37:35 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/toc/ecip0819/2008022817.html;
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470280735.html",
acknowledgement = ack-nhfb,
subject = "computer science; mathematics; probabilities; R
(computer programming language)",
}
@Proceedings{Paredaens:2009:PTE,
editor = "Jan Paredaens and Jianwen Su",
booktitle = "{Proceedings of the twenty-eighth ACM
SIGMOD-SIGACT-SIGART symposium on Principles of
database systems: PODS'09, Providence, Rhode Island,
June 29--July 1, 2009}",
title = "{Proceedings of the twenty-eighth ACM
SIGMOD-SIGACT-SIGART symposium on Principles of
database systems, PODS'09, Providence, Rhode Island,
June 29--July 1, 2009}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 288",
year = "2009",
ISBN = "1-60558-553-X",
ISBN-13 = "978-1-60558-553-6",
LCCN = "????",
bibdate = "Thu Jul 02 12:41:14 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Nigrini:2011:FAM,
author = "Mark J. (Mark John) Nigrini",
booktitle = "Forensic analytics: methods and techniques for
forensic accounting investigations",
title = "Forensic analytics: methods and techniques for
forensic accounting investigations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 463",
year = "2011",
DOI = "https://doi.org/10.1002/9781118386798",
ISBN = "0-470-89046-0, 1-118-08763-1 (e-book), 1-118-08766-6
(e-book), 1-118-08768-2 (e-book), 1-118-38679-5
(e-book)",
ISBN-13 = "978-0-470-89046-2, 978-1-118-08763-3 (e-book),
978-1-118-08766-4 (e-book), 978-1-118-08768-8 (e-book),
978-1-118-38679-8 (e-book)",
LCCN = "HV6768 .N54 2011",
bibdate = "Sat Feb 23 17:38:11 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley corporate F and A",
URL = "http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-t.html;
http://catdir.loc.gov/catdir/enhancements/fy1109/2011007210-b.html",
abstract = "The book will review and discuss (with Access and
Excel examples) the methods and techniques that
investigators can use to uncover anomalies in corporate
and public sector data. These anomalies would include
errors, biases, duplicates, number rounding, and
omissions. The focus will be the detection of fraud,
intentional errors, and unintentional errors using data
analytics. Despite the quantitative and computing bias,
the book will still be interesting to read with
interesting vignettes and illustrations. Most chapters
will be understandable by accountants and auditors that
usually are lacking in the rigors of mathematics and
statistics. The data interrogation methods are based on
(a) known statistical techniques, and (b) the author's
own published research in the field.",
acknowledgement = ack-nhfb,
subject = "Forensic accounting; Fraud; Misleading financial
statements; LAW / Forensic Science",
tableofcontents = "Front Matter \\
Using Access in Forensic Investigations \\
Using Excel in Forensic Investigations \\
Using PowerPoint in Forensic Presentations \\
High-Level Data Overview Tests \\
Benford's Law: The Basics \\
Benford's Law: Assessing Conformity \\
Benford's Law: The Second-Order and Summation Tests \\
Benford's Law: The Number Duplication and Last-Two
Digits Tests \\
Testing the Internal Diagnostics of Current Period and
Prior Period Data \\
Identifying Fraud Using the Largest Subsets and Largest
Growth Tests \\
Identifying Anomalies Using the Relative Size Factor
Test \\
Identifying Fraud Using Abnormal Duplications within
Subsets \\
Identifying Fraud Using Correlation \\
Identifying Fraud Using Time-Series Analysis \\
Fraud Risk Assessments of Forensic Units \\
Examples of Risk Scoring with Access Queries \\
The Detection of Financial Statement Fraud \\
Using Analytics on Purchasing Card Transactions \\
References \\
Index",
}
@Book{Zenil:2011:RTC,
editor = "Hector Zenil",
booktitle = "Randomness through computation: some answers, more
questions",
title = "Randomness through computation: some answers, more
questions",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xviii + 419",
year = "2011",
ISBN = "981-4327-74-3",
ISBN-13 = "978-981-4327-74-9",
LCCN = "QA274 .R363 2011",
bibdate = "Mon Feb 18 18:30:30 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
subject = "Stochastic processes; Computational complexity; Random
polynomials",
tableofcontents = "Is randomness necessary? / R. Graham \\
Probability is a lot of logic at once: if you don't
know which one to pick, take 'em all / T. Toffoli \\
Statistical testing of randomness: new and old
procedures / A. L. Rukhin \\
Scatter and regularity imply Benford's law\ldots{} and
more / N. Gauvrit, J.-P. Delahaye \\
Some bridging results and challenges in classical,
quantum and computational randomness / G. Longo, C.
Palamidessi, T. Paul \\
Metaphysics, metamathematics and metabiology / G.
Chaitin \\
Uncertainty in physics and computation / M. A. Stay \\
Indeterminism and randomness through physics / K.
Svozil \\
The Martin-L{\"o}f--Chaitin thesis: the identification
by recursion theory of the mathematical notion of
random sequence / J.-P. Delahaye \\
The road to intrinsic randomness / S. Wolfram \\
Algorithmic probability its discovery, it's properties
and application to strong AI / R. J. Solomonoff \\
Algorithmic randomness as foundation of inductive
reasoning and artificial intelligence / M. Hutter \\
Randomness, Occam's razor, AI, creativity and digital
physics / J. Schmidhuber \\
Randomness everywhere: my path to algorithmic
information theory / C. S. Calude \\
The impact of algorithmic information theory on our
current views on complexity, randomness, information
and prediction / P. G\'acs \\
Randomness, computability and information / J. S.
Miller \\
Studying randomness through computation / A. Nies \\
Computability, algorithmic randomness and complexity /
R. G. Downey \\
Is randomness native to computer science? Ten years
after / M. Ferbus-Zanda, S. Grigorieff \\
Randomness as circuit complexity (and the connection to
pseudorandomness) / E. Allender \\
Randomness: a tool for constructing and analyzing
computer programs / A. Ku{\v{c}}era \\
Connecting randomness to computation / M. Li \\
From error-correcting codes to algorithmic
informational theory / L. Staiger \\
Randomness in algorithms / O. Watanabe \\
Is the universe random? / C. S. Calude, J. L. Casti, G.
J. Chaitin, P. C. W. Davies, K. Svozil, S. Wolfram \\
What is computation? (How) Does nature computer? / C.
S. Calude, G. J. Chaitin, E. Fredkin, A. J. Leggett, R.
de Ruyter, T. Toffoli, S. Wolfram",
}
@Book{Gorroochurn:2012:CPP,
author = "Prakash Gorroochurn",
booktitle = "Classic Problems of Probability",
title = "Classic Problems of Probability",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 314",
year = "2012",
DOI = "https://doi.org/10.1002/9781118314340",
ISBN = "1-118-06325-2 (paperback), 1-118-31432-8,
1-118-31433-6 (e-book), 1-118-31434-4 (e-book),
1-118-31431-X (e-book)",
ISBN-13 = "978-1-118-06325-5 (paperback), 978-1-118-31432-6,
978-1-118-31433-3 (e-book), 978-1-118-31434-0 (e-book),
978-1-118-31431-9 (e-book)",
LCCN = "QA273.A4",
bibdate = "Mon Feb 25 05:50:42 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter / i?-xi \\
Chapter 1: Cardano and Games of Chance (1564) / 1--8
\\
Chapter 2: Galileo and a Discovery Concerning Dice
(1620) / 9--12 \\
Chapter 3: The Chevalier de M{\'e}r{\'e} Problem I: The
Problem of Dice (1654) / 13--19 \\
Chapter 4: The Chevalier de M{\'e}r{\'e} Problem II:
The Problem of Points (1654) / 20--38 \\
Chapter 5: Huygens and the Gambler's Ruin (1657) /
39--48 \\
Chapter 6: The Pepys--Newton Connection (1693) / 49--53
\\
Chapter 7: Rencontres with Montmort (1708) / 54--61 \\
Chapter 8: Jacob Bernoulli and his Golden Theorem
(1713) / 62--80 \\
Chapter 9: De Moivre's Problem (1730) / 81--88 \\
Chapter 10: De Moivre, Gauss, and the Normal Curve
(1730, 1809) / 89--107 \\
Chapter 11: Daniel Bernoulli and the St. Petersburg
Problem (1738) / 108--118 \\
Chapter 12: d'Alembert and the ?Croix ou Pile? Article
(1754) / 119--123 \\
Chapter 13: d'Alembert and the Gambler's Fallacy (1761)
/ 124--128 \\
Chapter 14: Bayes, Laplace, and Philosophies of
Probability (1764, 1774) / 129--155 \\
Chapter 15: Leibniz's Error (1768) / 156--158 \\
Chapter 16: The Buffon Needle Problem (1777) / 159--168
\\
Chapter 17: Bertrand's Ballot Problem (1887) / 169--174
\\
Chapter 18: Bertrand's Strange Three Boxes (1889) /
175--178 \\
Chapter 19: Bertrand's Chords (1889) / 179--185 \\
Chapter 20: Three Coins and a Puzzle from Galton (1894)
/ 186--188 \\
Chapter 21: Lewis Carroll's Pillow Problem No. 72
(1894) / 189--193 \\
Chapter 22: Borel and a Different Kind of Normality
(1909) / 194--198 \\
Chapter 23: Borel's Paradox and Kolmogorov's Axioms
(1909, 1933) / 199--207 \\
Chapter 24: Of Borel, Monkeys, and the New Creationism
(1913) / 208--214 \\
Chapter 25: Kraitchik's Neckties and Newcomb's Problem
(1930, 1960) / 215--223 \\
Chapter 26: Fisher and the Lady Tasting Tea (1935) /
224--232 \\
Chapter 27: Benford and the Peculiar Behavior of the
First Significant Digit (1938) / 233--239 \\
Chapter 28: Coinciding Birthdays (1939) / 240--246 \\
Chapter 29: L{\'e}vy and the Arc Sine Law (1939) /
247--252 \\
Chapter 30: Simpson's Paradox (1951) / 253--259 \\
Chapter 31: Gamow, Stern, and Elevators (1958) /
260--263 \\
Chapter 32: Monty Hall, Cars, and Goats (1975) /
264--270 \\
Chapter 33: Parrondo's Perplexing Paradox (1996) /
271--276 \\
Bibliography / 277--295 \\
Photo Credits / 296--298 \\
Index / 299--314",
}
@Proceedings{Niola:2012:RRA,
editor = "Vincenzo Niola and Michel Kadoch and Alexander
Zemliak",
booktitle = "{Recent researches in automatic control and
electronics: proceedings of the 14th International
conference on automatic control, modelling and
simulation (ACMOS '12): proceedings of the 11th
International conference on microelectronics,
nanoelectronics, optoelectronics (MINO '12): Saint Malo
and Mont Saint-Michel, France, April 2--4, 2012}",
title = "{Recent researches in automatic control and
electronics: proceedings of the 14th International
conference on automatic control, modelling and
simulation (ACMOS '12): proceedings of the 11th
International conference on microelectronics,
nanoelectronics, optoelectronics (MINO '12): Saint Malo
and Mont Saint-Michel, France, April 2--4, 2012}",
publisher = "WSEAS",
address = "???, Greece",
pages = "209",
year = "2012",
ISBN = "1-61804-080-4 (paperback)",
ISBN-13 = "978-1-61804-080-0 (paperback)",
LCCN = "????",
bibdate = "Tue Feb 19 06:02:11 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Tijms:2012:UPC,
author = "Henk C. Tijms",
booktitle = "Understanding probability: chance rules in everyday
life",
title = "Understanding probability: chance rules in everyday
life",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "x + 562",
year = "2012",
ISBN = "1-107-65856-X",
ISBN-13 = "978-1-107-65856-1",
LCCN = "QA273",
bibdate = "Mon Feb 18 06:48:08 MST 2013",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
Introduction \\
Part I. Probability in Action \\
1. Probability questions \\
2. The law of large numbers and simulation \\
3. Probabilities in everyday life \\
4. Rare events and lotteries \\
5. Probability and statistics \\
6. Chance trees and Bayes' rule \\
Part II. Essentials of Probability \\
7. Foundations of probability theory \\
8. Conditional probability and Bayes \\
9. Basic rules for discrete random variables \\
10. Continuous random variables \\
11. Jointly distributed random variables \\
12. Multivariate normal distribution \\
13. Conditioning by random variables \\
14. Generating functions \\
15. Discrete-time Markov chains \\
16. Continuous-time Markov chains \\
Appendix \\
Counting methods and ex \\
Recommended reading \\
Answers to odd-numbered problems \\
Bibliography \\
Index",
}
@Book{Abergel:2013:ESR,
editor = "Fr{\'e}d{\'e}ric Abergel and Bikas K. Chakrabarti and
Anirban Chakraborti and Asim Ghosh",
booktitle = "Econophysics of systemic risk and network dynamics",
title = "Econophysics of systemic risk and network dynamics",
publisher = "Springer Italia",
address = "Milan, Italy",
bookpages = "????",
pages = "119--129",
year = "2013",
DOI = "https://doi.org/10.1007/978-88-470-2553-0",
ISBN = "88-470-2553-2, 88-470-2552-4",
ISBN-13 = "978-88-470-2553-0, 978-88-470-2552-3",
bibdate = "Mon Feb 18 16:48:12 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "New Econ. Windows",
acknowledgement = ack-nhfb,
tableofcontents = "Part 1. Systemic risk, network dynamics and other
empirical studies \\
Diffusion of Defaults Among Financial Institutions /
Gabrielle Demange \\
Systemic Risk and Complex Systems: A Graph-Theory
Analysis / Delphine Lautier and Franck Raynaud \\
Omori Law After Exogenous Shocks on Supplier-Customer
Network / Yoshi Fujiwara \\
Aftershock Prediction for High-Frequency Financial
Markets' Dynamics / Fulvio Baldovin, Francesco Camana,
Michele Caraglio, Attilio L. Stella and Marco Zamparo
\\
How Unstable Are Complex Financial Systems? Analyzing
an Inter-bank Network of Credit Relations / Sitabhra
Sinha, Maximilian Thess and Sheri Markose \\
Study of Statistical Correlations in Intraday and Daily
Financial Return Time Series / Gayatri Tilak, Tam{\'a}s
Sz{\'e}ll, R{\'e}my Chicheportiche and Anirban
Chakraborti \\
A Robust Measure of Investor Contrarian Behaviour /
Damien Challet and David Morton de Lachapelle \\
Evolution of Zipf's Law for Indian Urban Agglomerations
Vis-{\`a}-Vis Chinese Urban Agglomerations / Kausik
Gangopadhyay and Banasri Basu \\
Part 2. Model-based studies \\
Reaction to Extreme Events in a Minimal Agent Based
Model / Andrea Zaccaria, Matthieu Cristelli and Luciano
Pietronero \\
Predatory Trading and Risk Minimisation: How to (B)Eat
the Competition / Anita Mehta \\
Statistical Mechanics of Labor Markets / He Chen and
Jun-ichi Inoue \\
Kolkata Paise Restaurant Problem: An Introduction /
Asim Ghosh, Soumyajyoti Biswas, Arnab Chatterjee,
Anindya Sundar Chakrabarti and Tapan Naskar, et al. \\
Kolkata Paise Restaurant Problem and the Cyclically
Fair Norm / Priyodorshi Banerjee, Manipushpak Mitra and
Conan Mukherjee \\
An Introduction to Multi-player, Multi-choice Quantum
Games: Quantum Minority Games and Kolkata Restaurant
Problems / Puya Sharif and Hoshang Heydari \\
Part 3. Miscellaneous reports \\
Cluster Analysis and Gaussian Mixture Estimation of
Correlated Time-Series by Means of Multi-dimensional
Scaling / Takero Ibuki, Sei Suzuki and Jun-ichi Inoue
\\
Analyzing Crisis in Global Financial Indices / Sunil
Kumar and Nivedita Deo \\
Study of Systemic Risk Involved in Mutual Funds /
Kishore C. Dash and Monika Dash \\
Characterizing Price Index Behavior Through Fluctuation
Dynamics / Prasanta K. Panigrahi, Sayantan Ghosh, Arjun
Banerjee, Jainendra Bahadur and P. Manimaran",
}
@Book{Miller:2015:BLT,
editor = "Steven J. Miller",
booktitle = "{Benford's Law}: theory and applications",
title = "{Benford's Law}: theory and applications",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xxvi + 438",
year = "2015",
DOI = "https://doi.org/10.1515/9781400866595",
ISBN = "0-691-14761-2 (hardcover), 1-4008-6659-6 (e-book)",
ISBN-13 = "978-0-691-14761-1 (hardcover), 978-1-4008-6659-5
(e-book)",
LCCN = "QA273.6 .B46 2015",
MRclass = "60-06 (62-06)",
MRnumber = "3408774",
bibdate = "Tue Nov 17 09:41:52 MST 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
URL = "http://press.princeton.edu/titles/10527.html",
acknowledgement = ack-nhfb,
subject = "Distribution (Probability theory); Probability
measures; MATHEMATICS / Applied; MATHEMATICS /
Probability and Statistics / General; Distribution
(Probability theory); Probability measures.",
tableofcontents = "Foreword / xiii \\
Preface / xvii \\
Notation / xxiii \\
Part I. General Theory I: Basis of Benford's Law / 1
\\
Chapter 1. A Quick Introduction to Benford's Law / 3
\\
Chapter 2. A Short Introduction to the Mathematical
Theory of Benford's Law / 23 \\
Chapter 3. Fourier Analysis and Benford's Law / 68 \\
Part II. General Theory II: Distributions and Rates of
Convergence / 107 \\
Chapter 4. Benford's Law Geometry / 109 \\
Chapter 5. Explicit Error Bounds via Total Variation /
119 \\
Chapter 6. L{\'e}vy Processes and Benford's Law / 135
\\
Part III. Applications I: Accounting and Vote Fraud /
175 \\
Chapter 7. Benford's Law as a Bridge between Statistics
and Accounting / 177 \\
Chapter 8. Detecting Fraud and Errors Using Benford's
Law / 191 \\
Chapter 9. Can Vote Counts Digits and Benford's Law
Diagnose Elections? Chapter 10. Complementing Benford's
Law for Small N: A Local Bootstrap Bootstrap Model /
227 \\
Part IV. Applications II: Economics / 233 \\
Chapter 11. Measuring the Quality of European
Statistics / 235 \\
Chapter 12. Benford's Law and Fraud in Economic
Research / 244 \\
Chapter 13. Testing for Strategic Manipulation of
Economic and Financial Data / 257 \\
Part V. Applications III: Sciences / 265 \\
Chapter 14. Psychology and Benford's Law / 267 \\
Chapter 15. Managing Risk in Numbers Games: Benford's
Law and the Small-Number Phenomenon / 276 \\
Chapter 16. Benford's Law in the Natural Sciences / 290
\\
Chapter 17. Generalizing Benford's Law: A Reexamination
of Falsified Clinical Data / 304 \\
Part VI. Applications IV: Images / 317 \\
Chapter 18. Partial Volume Modeling of Medical Imaging
Systems Using the Benford Distribution / 319 \\
Chapter 19. Application of Benford's Law to Images /
338 \\
Part VII. Exercises / 371 \\
Chapter 20. Exercises / 373 \\
Phenomenon / 399 \\
Distribution / 401 \\
Bibliography / 402 \\
Index / 433",
}
@Proceedings{Cornea:2020:ISC,
editor = "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
booktitle = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
title = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020",
ISBN = "1-72817-120-2, 1-72817-121-0",
ISBN-13 = "978-1-72817-120-3, 978-1-72817-121-0",
LCCN = "????",
bibdate = "Wed Jul 7 06:24:52 2021",
bibdate = "Wed Jul 7 06:23:45 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
acknowledgement = ack-nhfb,
}
