Pinkham, RS (1961). On the Distribution of First Significant Digits. Annals of Mathematical Statistics 32(4), 1223-1230. ISSN: 0003-4851.
This paper is cited by the following items of the Benford Online Bibliography:
Note that this list may be incomplete, and is currently being updated. Please check back at a later date.
Adhikari, AK
(1969).
Some Results on Distribution of Most Significant Digit.
Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), 413-420. ISSN: 0581-5738. |
|
|
|
|
Barlow, JL and Bareiss, EH
(1985).
On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic.
Computing 34(4), 325-347. ISSN: 0010-485X. |
|
|
|
|
Berger, A and Hill, TP
(2010).
Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law.
University of Alberta preprint. |
|
|
|
|
Brooks, D
(2002).
Naked-Eye Quantum Mechanics:
Practical Applications of Benford's Law for Integer Quantities.
Frequencies - The Journal of Size Law Applications, Special Paper #1, 1-8. |
|
|
|
|
Bumby, R and Ellentuck, E
(1969).
Finitely additive measures and the first digit problem.
Fundamenta Mathematicae 65, 33-42. |
|
|
|
|
Ciofalo, M
(2009).
Entropy, Benford’s first digit law, and the distribution of everything.
Dipartimento di Ingegneria Nucleare, Università degli Studi di Palermo, Italy. |
|
|
|
|
Clenshaw, CV, Olver, FWJ and Turner, PR
(1989).
Level-Index Arithmetic - An Introductory Survey.
Lecture Notes in Mathematics 1397, pp 95-168. ISSN: 0075-8434. |
|
|
|
|
Cohen, DIA
(1976).
An Explanation of First Digit Phenomenon.
Journal of Combinatorial Theory Series A 20(3), 367-370. ISSN: 0097-3165. |
|
|
|
|
Davis, BS and Davis, TA
(1989).
Fibonacci numbers and the golden mean in nature.
The Mathematical Scientist 14, 89-100. |
|
|
|
|
De Ceuster, MJK, Dhaene, G and Schatteman, T
(1998).
On the hypothesis of psychological barriers in stock markets and Benford’s law.
Journal of Empirical Finance 5(3), 263-279. |
|
|
|
|
De Marchi, S and Hamilton, JT
(2006).
Assessing the accuracy of self-reported data: An evaluation of the toxics release inventory.
Journal of Risk and Uncertainty 32(1), 57-76. ISSN: 0895-5646. |
|
|
|
|
Dickinson, JR
(2002).
A universal mathematical law criterion for algorithmic validity.
Developments in Business Simulation and Experiential Learning 29, 26-33. |
|
|
|
|
Drake, PD and Nigrini, MJ
(2000).
Computer assisted analytical procedures using Benford’s law.
Journal of Accounting Education 18, 127-146. |
|
|
|
|
Drmota, M and Tichy, RF
(1997).
Sequences, Discrepancies and Applications.
Lecture Notes in Mathematics 1651. |
|
|
|
|
Dümbgen, L and Leuenberger, C
(2008).
Explicit Bounds for the Approximation Error in Benford’s Law.
Electronic Communications in Probability 13, 99-112. ISSN: 1083-589X. |
|
|
|
|
Farnsworth, DF, Horan, KK and Galgon, RM
(2007).
A guide to Benford's law.
Mathematics and Computer Education 41, 230-243. ISSN: ISSN: 0730-8639. |
|
|
|
|
Filipponi, P and Menicocci, R
(1995).
Some Probabilistic Aspects of the Terminal Digits of Fibonacci Numbers.
Fibonacci Quarterly 33(4), 325-331. ISSN: 0015-0517. |
|
|
|
|
Flehinger, BJ
(1966).
On Probability that a Random Integer has Initial Digit A.
American Mathematical Monthly 73(10), 1056-1061. ISSN: 0002-9890. |
|
|
|
|
Gauvrit, N and Delahaye, JP
(2009).
Scatter and regularity imply Benford's Law ... and more.
arXive preprint. |
|
|
|
|
Good, IJ
(1965).
Letter to the Editor.
The American Statistician 19(3), 43. |
|
|
|
|
Günnel, S and Tödter, KH
(2009).
Does Benford's law hold in economic research and forecasting?.
Empirica 36, 273-292. |
|
|
|
|
Hafner, EM
(1979).
Circular slide roulette.
IEEE Communications Magazine 17(2), 29-32. |
|
|
|
|
Hamming, R
(1970).
On the distribution of numbers.
Bell Syst. Tech. J. 49(8), 1609-1625. |
|
|
|
|
Hassan, B
(2002).
Assessing data authenticity with Benford’s law.
Information Systems Control Journal 6. |
|
|
|
|
Havil, J
(2008).
Benford's Law.
pp 190-200 in: Impossible? Surprising solutions to counterintuitive conundrums, Princeton University Press, USA. ISSN: ISBN 978-0-691-13131. |
|
|
|
|
Hill, TP
(1995).
Base-Invariance Implies Benford's Law.
Proceedings of the American Mathematical Society 123(3), 887-895. ISSN: 0002-9939. |
|
|
|
|
Hill, TP
(2001).
Response to "Benfords Gesetz", Brief an die Herausgeber.
Mitteilungen der Deutschen Mathematiker Vereinigung, 3/2001, p 4. |
|
|
|
|
Hobza, T and Vajda, I
(2001).
On the Newcomb-Benford law in models of statistical data.
Revista Matematica Complutense XIV(2), 407-420. ISSN: 1139-1138. |
|
|
|
|
Humenberger, H
(1996).
Das Benford-Gesetz über die Verteilung der ersten Ziffer von Zahlen.
Stochastik in der Schule 16(3), 2–17. |
|
|
|
|
Hürlimann, W
(2009).
Generalizing Benford’s law using power laws: application to integer sequences.
International Journal of Mathematics and Mathematical Sciences, Article ID 970284, 10 p. |
|
|
|
|
Irmay, S
(1997).
The relationship between Zipf's law and the distribution of first digits.
Journal of Applied Statistics 24(4), 383-393. ISSN: 0266-4763. |
|
|
|
|
Iyengar, SS, Rajagopal, AK and Uppuluri, VRR
(1983).
String Patterns of Leading Digits.
Applied Mathematics and Computation 12(4), 321-337. ISSN: 0096-3003. |
|
|
|
|
Jamain, A
(2001).
Benford’s Law.
Master Thesis. Imperial College of London and ENSIMAG. |
|
|
|
|
Janvresse, E
(2009).
Quel est le début de ce nombre ? .
Images des Mathématiques, 26 December. |
|
|
|
|
Janvresse, E and de la Rue, T
(2004).
From Uniform Distributions to Benford’s Law.
Journal of Applied Probability 41(4), 1203-1210. ISSN: 0021-9002. |
|
|
|
|
Kak, SC
(1983).
Strings of first digits of powers of a number.
Indian J. Pure Appl. Math. 14(7), 896-907. |
|
|
|
|
Kontorovich, AV and Miller, SJ
(2005).
Benford's Law, Values of L-functions and the 3x+ 1 Problem.
Acta Arithmetica 120(3), 269-297. ISSN: 0065-1036. |
|
|
|
|
Kossovsky, AE
(2006).
Towards a Better Understanding of the Leading Digits Phenomena.
arXiv:math/0612627. |
|
|
|
|
Lemons, DS
(1986).
On the Numbers of Things and the Distribution of first Digits.
American Journal of Physics 54(9): 816-817. ISSN: 0002-9505. |
|
|
|
|
Ley, E
(1996).
On the Peculiar Distribution of the US Stock Indexes' Digits.
American Statistician 50(4), 311-313. ISSN: 0003-1305. |
|
|
|
|
Lipovetsky, S
(2008).
Comparison among different patterns of priority vectors estimation methods.
International Journal of Mathematical Education in Science 39(3), 301-311. |
|
|
|
|
Lolbert, T
(2006).
Digital Analysis: Theory and Applications in Auditing.
Hungarian Statistical Review 84, Special number 10. ISSN: 0039 0690. |
|
|
|
|
Lolbert, T
(2007).
Statisztikai eljárások alkalmazása az ellenőrzésben (Applications of statistical methods in monitoring).
PhD thesis, Corvinus University, Budapest, Hungary. |
|
|
|
|
Lu, F
(2007).
Uncovering Fraud in Direct Marketing Data with a Fraud Auditing Case Builder.
Lecture Notes in Computer Science 4702, 540-547. |
|
|
|
|
Lu, F, Boritz, JE and Covvey, D
(2006).
Adaptive fraud detection using Benford’s Law.
Lecture Notes in Computer Science 4013, 347-358. |
|
|
|
|
Lu, OF and Giles, DE
(2006).
Benford's Law and Psychological Barriers in Certain eBay Auctions.
Econometrics Working Paper EWP0606, University of Victoria. ISSN: 1485-6441. |
|
|
|
|
Luque, B and Lacasa, L
(2009).
The first-digit frequencies of prime numbers and Riemann zeta zeros.
Proc. Royal Soc. A, published online 22Apr09. |
|
|
|
|
Mardia, KV
(1972).
The distribution of first significant digits.
pp 92-93 in: Statistics of Directional Data, Academic Press. |
|
|
|
|
Martín, AB
(2003).
Sistematización del proceso de depuración de los datos en estudios con seguimientos.
PhD Thesis, Universitat Autònoma de Barcelona, Spain. |
|
|
|
|
Miller, SJ and Nigrini, MJ
(2006).
Order Statistics and Shifted Almost Benford Behavior.
Preprint. |
|
|
|
|
Miller, SJ and Nigrini, MJ
(2008).
Order Statistics and Benford's Law.
To appear in: International Journal of Mathematics and Mathematical Sciences. |
|
|
|
|
Mörters, P
(2001).
Benford’s Gesetz über die Verteilung der Ziffern. Habilitationsvorlesung.
Kaiserslauten und Bath. |
|
|
|
|
Nagasaka, K
(1984).
On Benford's Law.
Annals of the Institute of Statistical Mathematics 36(2), 337-352. ISSN: 0020-3157. |
|
|
|
|
Nelson, LS
(1984).
Display Tables and Significant Digits.
Journal of Quality Technology 16(3), 175-176. ISSN: 0022-4065. |
|
|
|
|
Ni, D, Wei, L and Ren, Z
(2009).
Benford's Law and β-Decay Half-Lives.
Commun. Theor. Phys. 51, 713-716. |
|
|
|
|
Nigrini, MJ
(1992).
The Detection of Income Tax Evasion Through an Analysis of Digital Frequencies.
PhD thesis, University of Cincinnati, OH, USA. |
|
|
|
|
Nigrini, MJ
(1996).
A taxpayer compliance application of Benford’s law.
Journal of the American Taxation Association 18(1), 72-91. |
|
|
|
|
Nigrini, MJ
(1999).
Peculiar patterns of first digits.
IEEE Potentials 18(2), 24-27. |
|
|
|
|
Nigrini, MJ and Miller, SJ
(2007).
Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data.
Mathematical Geology 39(5), 469-490. ISSN: 0882-8121. |
|
|
|
|
Nigrini, MJ and Mittermaier, LJ
(1997).
The use of Benford's Law as an aid in analytical procedures.
Auditing - A Journal of Practice & Theory 16(2), 52-67. ISSN: 0278-0380. |
|
|
|
|
Pavlov, AI
(1982).
On the distribution of fractional parts and Benford’s law.
Math. USSR Izvestija 19(1), 65-77. English translation of: Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45(4), 760–774. |
|
|
|
|
Pocheau, A
(2006).
The significant digit law: a paradigm of statistical scale symmetries .
European Physical Journal B 49(4), 491-511. ISSN: 1434-6028. |
|
|
|
|
Posch, PN
(2004).
Ziffernanalyse in der Fälschungsaufspürung. Benford’s Gesetz und Steuererklärungen in Theorie und Praxis.
unpublished manuscript. |
|
|
|
|
Raimi, RA
(1969).
On Distribution of First Significant Figures.
American Mathematical Monthly 76(4), 342-348. ISSN: 0002-9890. |
|
|
|
|
Raimi, RA
(1969).
The Peculiar Distribution of First Digits.
Scientific American 221(6), 109-119. ISSN: 0036-8733. |
|
|
|
|
Raimi, RA
(1976).
The First Digit Problem.
American Mathematical Monthly 83(7), 521-538. ISSN: 0002-9890. |
|
|
|
|
Rajagopal, AK, Uppuluri, VRR and Scott, DS, Iyengar, SS, Yellayi, M
(1984).
New structural properties of strings generated by leading digits of 2N.
Applied Mathematics and Computation 14(3), 221-244. |
|
|
|
|
Rieger, J
(1993).
Das Rätsel der ersten Ziffern.
Frankfurter Allgemeine Zeitung, Oktober 20. |
|
|
|
|
Robertson, JB, Uppuluri, VRR and Rajagopal, AK
(1983).
First digit phenomenon and ergodic theory.
Journal of Mathematical Analysis and Applications 95(2), 375-378. |
|
|
|
|
Rodriguez, RJ
(2004).
Reducing False Alarms in the Detection of Human Influence on Data.
Journal of Accounting, Auditing & Finance 19(2), 141-158. |
|
|
|
|
Rosenkrantz, RD
(1977).
Benford's Law.
Example 3.6.6, pp 67-68 in: Inference, Method and Decision: Towards a Bayesian Philosophy of Science, Reidel Publishing Company, USA. |
|
|
|
|
Ryder, P
(2009).
Multiple origins of the Newcomb-Benford law: rational numbers, exponential growth and random fragmentation.
Staats- und Universitätsbibliothek Bremen, Germany. |
|
|
|
|
Ryder, P
(2009).
The Relationship Between the Newcomb-Benford Law and the Distribution of Rational Numbers.
Zeitschrift für Naturforschung 64a, 615-617. |
|
|
|
|
Sarkar, BP
(1973).
An Observation on the Significant Digits of Binomial Coefficients and Factorials.
Sankhya - The Indian Journal of Statistics Series B 35(3), 363-364. ISSN: 0581-5738. |
|
|
|
|
Saville, A
(2003).
Using Benford's Law to predict data error and fraud. An examination of companies listed on the JSE securities exchange.
|
|
|
|
|
Schäfer, C, Schräpler, JP and Müller, KR
(2004).
Identification, Characteristics and Impact of Faked and Fraudulent Interviews in Surveys.
|
|
|
|
|
Schatte, P
(1988).
On mantissa distributions in computing and Benford’s law.
Journal of Information Processing and Cybernetics EIK 24(9), 443-455. |
|
|
|
|
Schatte, P
(1998).
On Benford's law to variable base.
Statistics & Probability Letters 37(4): 391-397. ISSN: 0167-7152. |
|
|
|
|
Schatte, P
(2001).
Briefe an die Herausgeber.
Mitteilungen der Deutschen Mathematiker Vereinigung, 2/2001, pp 6-7. |
|
|
|
|
Scheidt, JK and Schelin, CW
(1987).
Distributions of floating point numbers.
Computing 38(4), 315-324. ISSN: 0010-485X. |
|
|
|
|
Schilling, MF
(1992).
Sequential Partitioning.
American Mathematical Monthly 99(9), 846-855. ISSN: 0002-9890. |
|
|
|
|
Scott, PD and Fasli, M
(2001).
Benford’s law: an empirical investigation and a novel explanation.
CSM Technical Report 349, Department of Computer Science, University of Essex, UK. |
|
|
|
|
Scozzafava, R
(1981).
Un esempio concreto di probabilita non σ-additiva: la distribuzione della prima cifra significativa dei dati statistici.
Boll. Un. Mat. Ital. A(5) 18(3), 403-410. |
|
|
|
|
Shao, L and Ma, BQ
(2009).
First Digit Distribution of Hadron full width.
Modern Physics Letters A, 24(40), 3275-3282. |
|
|
|
|
Shao, L and Ma, BQ
(2010).
Empirical mantissa distributions of pulsars.
To appear in: Astroparticle Physics. |
|
|
|
|
Shenton, LR
(1968).
Periodicity and density of modified Fibonacci sequences.
Fibonacci Quarterly 6(2), 109-116. |
|
|
|
|
Stoschek, EP and Schönfeld, D
(2002).
Benford's Law - Places of interest near Benford`s Law.
Module 45 of: Workshop on Design of Algorithms. |
|
|
|
|
Tödter, KH
(2009).
Benford's Law as an Indicator of Fraud in Economics.
German Economic Review 10(3), p 339-351 (2009). |
|
|
|
|
Torres, J, Fernandez, S and Gamero, A, Sola, A
(2007).
How do numbers begin? (The first digit law).
European Journal of Physics 28(3), L17-L25. ISSN: 0143-0807. |
|
|
|
|
Tsao, NK
(1974).
On the Distributions of Significant Digits and Roundoff Errors.
Communications of the ACM 17(5), 269-271. ISSN: 0001-0782. |
|
|
|
|
Turner, PR
(1982).
The Distribution of Leading Significant Digits.
IMA Journal orf Numerical Analysis 2(4), 407-412. ISSN: 0272-4979. |
|
|
|
|
Turner, PR
(1984).
Further Revelations on LSD.
IMA Journal of Numerical Analysis 4(2), 225-231. ISSN: 0272-4979. |
|
|
|
|
Valk, G
(2004).
Benford’s Law and Faking Data.
The Pi, Volume 1, Spring 2004, Dept of Mathematics and Statistics, Georgia State University, Atlanta, USA. |
|
|
|
|
Wallace, WA
(2002).
Assessing the quality of data used for benchmarking and decision- making.
The Journal of Government Financial Management 51(3), 16-22. |
|
|
|
|
Watrin, C, Struffert, R and Ullmann, R
(2008).
Benford’s Law: an instrument for selecting tax audit targets?.
Review of Managerial Science 2(3), 219-237. |
|
|
|
|
Weaver, W
(1963).
The distribution of first significant digits.
pp 270-277 in: Lady Luck: The Theory of Probability, Doubleday Anchor Series, New York. Republished by Dover, 1982. |
|
|
|
|
Webb, W
(1975).
Distribution of the first digits of Fibonacci numbers.
Fibonacci Quarterly 13, 334-336. |
|
|
|
|
Whittaker, JV
(1983).
On scale-invariant distributions.
SIAM Journal on Applied Mathematics 43(2), 257-267. |
|
|
|
|