@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-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 = "0581-5738",
ISSN-L = "0581-5738",
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 = "0581-5738",
ISSN-L = "0581-5738",
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 = "0581-5738",
ISSN-L = "0581-5738",
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{
