VIEW ALPHABETICAL
Abumrad, J and Krulwich, R
(2009).
From Benford to Erdős.
WNYC Radiolab, 9 October. |
|
|
|
|
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. |
|
|
|
|
Aggarwal, R and Lucey, BM
(2007).
Psychological barriers in gold prices?.
Review of Financial Economics 16, 217–230. |
|
|
|
|
Albers, DJ
(1995).
Professor of |
|
|
|
|
Albrecht, CC, Albrecht, WS and Dunn, JG
(2000).
Conducting a Pro-Active Fraud Audit: A Case Study.
The Journal of Forensic Accounting II: 203-218. |
|
|
|
|
Albrecht, J
(2000).
Die Eins vom Planet Zob.
Die Zeit, 28 September. |
|
|
|
|
Albrecht, WS and Albrecht, CC
(2002).
Root out financial deception.
Journal of Accountancy 193(4), 30-34. |
|
|
|
|
Aldous, D and Phan, T
(2009).
When Can One Test an Explanation? Compare
and Contrast Benford's Law and the Fuzzy CLT.
Class project report, Statistics Department, UC Berkeley. |
|
|
|
|
Aldous, D and Phan, T
(2010).
When Can One Test an Explanation? Compare and Contrast Benford's Law and the Fuzzy CLT.
Preprint, Statistics Department, UC Berkeley. |
|
|
|
|
Allaart, PC
(1997).
An invariant-sum characterization of Benford's law.
Journal of Applied Probability 34, 288-291. |
|
|
|
|
Altamirano, C and Robledo, A
(2009).
Generalized Thermodynamics underlying the laws of Zipf and Benford.
pp 2232-2237 in: J. Zhou (ed.), Complex Sciences 2009, Part II, LNICST 5. ISSN: 1867-8211. |
|
|
|
|
Anonymous
(1998).
Numerology for accountants.
Journal of Accountancy 186(5), 15. |
|
|
|
|
Arita, M
(2005).
Scale-freeness and biological networks.
Journal of Biochemistry, 138 (1): 1-4. ISSN: 0021-924X. |
|
|
|
|
Armstrong, JS
(2001).
Extrapolation for time-series and cross-sectional data. In: Principles of Forecasting: a Handbook for Researchers and Practitioners.
Kluwer Publishers. |
|
|
|
|
Ashcraft, MH
(1992).
Cognitive arithmetic: A review of data and theory.
Cognition 44 (Aug), 75-106. |
|
|
|
|
Ashcraft, MH and Christy, KS
(1995).
The Frequency of Arithmetic Facts in Elementary Texts: Addition and Multiplication in Grades 1-6.
Journal for Research in Mathematics Education 26, 396-421. |
|
|
|
|
Auffhammer, M and Carson, RT
(2006).
Offsetting Reductions From Kyoto And Then Some: Forecasts of China’s CO2 Emissions Using Province Level Data.
Draft 7 Sep 2006. |
|
|
|
|
Auffhammer, M and Carson, RT
(2008).
Forecasting the path of China's CO2 emissions using province-level information.
J. Environ. Econ. Manage. 55(3), 229-247. ISSN: 0095-0696. |
|
|
|
|
Bach, A
(2006).
Wenn sich Zahlen an Gesetze halten .../ Auf Verbrecherjagd mit Benford.
Quarks & Co, WDR science broadcast, 17 October 2006. |
|
|
|
|
Baer, MB
(2006).
Prefix coding under Siege.
(submitted to IEEE Trans. Inform. Theory). |
|
|
|
|
Baer, MB
(2006).
Rényi to Rényi - Source Coding under Siege.
(accepted to ISIT 2006). |
|
|
|
|
Baer, MB
(2007).
Bounds on Generalized Huffman Codes.
|
|
|
|
|
Baer, MB
(2007).
Reserved-Length Prefix Coding.
(submitted to ISIT 2008). |
|
|
|
|
Baiocchi, G
(2004).
Using Perl for Statistics: Data Processing and Statistical Computing.
Journal of Statistical Software, 2004 , Vol. 11, Issue 1. |
|
|
|
|
Baird, JC
(1975).
Psychophysical study of numbers: IV. Generalized Preferred State Theory.
Psychological Research 38 (Jun), 175-187. |
|
|
|
|
Baird, JC
(1975).
Psychophysical study of numbers: V. Preferred State Theory of Matching Functions.
Psychological Research 38 (Jun), 189-207. |
|
|
|
|
Baird, JC and Noma, E
(1975).
Psychophysical study of numbers: I. Generation of numerical responses.
Psychological Research 37 (Dec), 281-297. |
|
|
|
|
Banks, WP and Hill, DK
(1974).
The Apparent Magnitude of Number Scaled by Random Production.
Journal of Experimental Psychology 102 (2), 353-376. ISSN: 0022-1015. |
|
|
|
|
Barlow, JL and Bareiss, EH
(1985).
On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic.
Computing 34(4), 325-347. ISSN: 0010-485X. |
|
|
|
|
Barnard, PJ, Scott, SK and May, J
(2001).
When the central executive lets us down: Schemas, attention, and load in a generative working memory task.
Memory, 9 (4-6), 209-221. ISSN: 0965-8211. |
|
|
|
|
Battersby, S
(2009).
Statistics hint at fraud in Iranian election.
New Scientist 24 June. |
|
|
|
|
Beber, B and Scacco, A
(2009).
The Devil is in the Digits.
Washington Post, 20 June. |
|
|
|
|
Becker, PW
(1982).
Patterns in Listings of Failure-Rate and MTTF Values and Listings of Other Data.
IEEE Transactions on Reliability 31(2), 132-134. ISSN: 0018-9529. |
|
|
|
|
Becker, TJ
(2000).
Sorry, Wrong Number. Century-old math rule ferrets out modern-day digital deception.
Research Horizons, Fall 2000, Georgia Tech. |
|
|
|
|
Beeli, G, Esslen, M and Jäncke, L
(2007).
Frequency Correlates in Grapheme-Color Synaesthesia.
Psychological Science, 18(9), 788-792. ISSN: 0956-7976. |
|
|
|
|
Beer, TW
(2009).
Terminal digit preference: beware of Benford's law.
Journal of Clinical Pathology 62(2), 192. |
|
|
|
|
Benford, F
(1938).
The law of anomalous numbers.
Proceedings of the American Philosophical Society 78, 551-572. |
|
|
|
|
Bensmail, H and Haoudi, A
(2003).
Postgenomics: Proteomics and Bioinformatics in Cancer Research.
Journal of Biomedicine and Biotechnology (4), 217-230. ISSN: 1110-7243. |
|
|
|
|
Berger, A
(2001).
Chaos and Chance.
De Gruyter, Berlin and New York. |
|
|
|
|
Berger, A
(2005).
Benford’s Law in power-like dynamical systems.
Stoch. Dyn. 5, 587-607. ISSN: 0219-4937. |
|
|
|
|
Berger, A
(2005).
Multi-dimensional dynamical systems and Benford's law.
Discrete and Continuous Dynamical Systems 13(1), 219-237. ISSN: 1078-0947. |
|
|
|
|
Berger, A, Bunimovich, LA and Hill, TP
(2005).
One-dimensional dynamical systems and Benford's law.
Transactions of the American Mathematical Society 357(1), 197-219. ISSN: 0002-9947. |
|
|
|
|
Berger, A and Hill, TP
(2006).
A characterisation of Newton maps.
ANZIAM J. 48, 211-223. |
|
|
|
|
Berger, A and Hill, TP
(2007).
Newton’s method obeys Benford’s law.
American Mathematical Monthly 114 (7), 588-601. ISSN: 0002-9890. |
|
|
|
|
Berger, A, Hill, TP and Morrison, KE
(2008).
Scale-Distortion Inequalities for Mantissas of Finite Data Sets.
Journal of Theoretical Probability 21(1), 97-117. ISSN: 0894-9840. |
|
|
|
|
Berger, A and Siegmund, S
(2007).
On the distribution of mantissae in nonautonomous difference equations.
Journal of Difference Equations and Applications 13(8-9), 829-845. ISSN: 1023-6198. |
|
|
|
|
Berleant, D, Cheong, MP and Chu,C, Guan,Y, Kamal,A, Shedble, G, Ferson,S, Peters, JF
(2003).
Dependable Handling of Uncertainty.
Reliable Computing 9(6), 407-418. ISSN: 1385-3139. |
|
|
|
|
Berton, L
(1995).
He’s Got Their Number: Scholar Uses Math to Foil Financial Fraud.
The Wall Street Journal, pg B1, July 10. |
|
|
|
|
Bhattacharya, P, Chatterjee, A and Chakrabarti, BK
(2005).
A common mode of origin of the power law distributions in models of market and earthquake.
http://arxiv.org/abs/physics/0510038. |
|
|
|
|
Bhattacharya, S
(2002).
From Kautilya to Benford – Trends in Forensic and Investigative Accounting.
9th World Congress of Accounting Historians, Deakin University. |
|
|
|
|
Bialik, C
(2009).
Rise and Flaw of Internet's Election-Fraud Hunters.
The Wall Street Journal, 1 July. |
|
|
|
|
Blum, W
(2007).
Die Nummer eins im Alltag.
Süddeutsche Zeitung, May 23. |
|
|
|
|
Bogomolny, A
(2004).
Benford’s Law and Zipf's Law.
|
|
|
|
|
Bolton, RJ and Hand, DJ
(2002).
Statistical Fraud Detection: a review.
Statistical Science 17(3), 235-249. |
|
|
|
|
Boring, EG
(1920).
The logic of the normal law of error in mental measurement.
American Journal of Psychology 31, 1-33. ISSN: 0002-9556. |
|
|
|
|
Bourke, N and van Peursem, K
(2004).
Detecting fraudulent financial reporting: teaching the 'watchdog' new tricks.
Working paper 79, University of Waikato. ISSN: 1173-7182. |
|
|
|
|
Boyle, J
(1994).
An Application of Fourier Series to the Most Significant Digit Problem.
American Mathematical Monthly 101(9), 879-886. ISSN: 0002-9890. |
|
|
|
|
Bradley, JR and Farnsworth, DL
(2009).
What is Benford's Law?.
Teaching Statistics 31(1), 2-6. |
|
|
|
|
Brady, WG
(1978).
More on Benford’s law.
Fibonacci Quarterly 16, 51-52. |
|
|
|
|
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. |
|
|
|
|
Brown, JR and Duncan, RL
(1970).
Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences.
Fibonacci Quarterly 8, 482-486. ISSN: 0015-0517. |
|
|
|
|
Brown, P, Chua, A and Mitchell, J
(2002).
The influence of cultural factors on price clustering: Evidence from Asia–Pacific stock markets.
Pacific-Basin Finance Journal, 10(3), 307-332. |
|
|
|
|
Brown, P and Mitchell, J
(2008).
Culture and stock price clustering: evidence from the peoples’ republic of China.
Pacific-Basin Finance Journal 16(1), 95-120 . ISSN: 0927-538X. |
|
|
|
|
Brown, RJC
(2005).
Benford's Law and the screening of analytical data: the case of pollutant concentrations in ambient air.
Analyst 130(9), 1280-1285. ISSN: 0002-2654. |
|
|
|
|
Brown, RJC
(2007).
The use of Zipf's law in the screening of analytical data: a step beyond Benford.
Analyst 132(4), 344-349. ISSN: 0003-2654. |
|
|
|
|
Browne, MW
(1998).
Following Benford’s law, or looking out for no. 1.
The New York Times, August 4, 1998. |
|
|
|
|
Buck, B, Merchant, AC and Perez, SM
(1993).
An illustration of Benford’s first digit law using alpha decay half lives.
European Journal of Physics 14, 59-63. |
|
|
|
|
Bumby, R and Ellentuck, E
(1969).
Finitely additive measures and the first digit problem.
Fundamenta Mathematicae 65, 33-42. |
|
|
|
|
Burke, J and Kincanon, E
(1991).
Benford Law and Physical Constants - The Distribution of Initial Digits.
American Journal of Physics 59 (10), 952. ISSN: 0002-9505. |
|
|
|
|
Burns, B
(2009).
Sensitivity to statistical regularities: People (largely) follow Benford’s law.
pp 2872-2877 in: Proceedings of CogSci 2009, Amsterdam, The Netherlands. |
|
|
|
|
Busta, B and Sundheim, R
(1992).
Detecting manipulated tax returns with the use of Benford's Law.
Center for Business Research Working Paper W95-106-94, St. Cloud State University, Minnesota. |
|
|
|
|
Busta, B and Sundheim, R
(1992).
Tax return numbers tend to obey Benford's law.
Center for Business Research Working Paper No. W93-106-94, St. Cloud State University, Minnesota. |
|
|
|
|
Busta, B and Weinberg, R
(1998).
Using Benford’s law and neural networks as a review procedure.
Managerial Auditing Journal 13(6), 356-366. |
|
|
|
|
Buyse, M, George, SL and et al.
(1999).
The Role of Biostatistics in the Prevention, Detection and Treatment of Fraud in Clinical Trials.
Statistics in Medicine 18 (24), 3435-3451. ISSN: 0277-6715. |
|
|
|
|
Byalko, AV
(1991).
Statistics of Coefficients in Physical Formulas.
Theoretical and Mathematical Physics 88(1), 782-787. ISSN: 0040-5779. |
|
|
|
|
Cáceres, JLH, García, JLP and et al.
(2008).
First digit distribution in some biological data sets. Possible explanations for departures from Benford's Law.
Electronic J Biomed 1, 27-35. |
|
|
|
|
Caldwell, CC
(2008).
Does Benford's law apply to prime numbers?.
The Prime Pages. |
|
|
|
|
Candeloro, D
(1998).
Some remarks on the first digit problem.
Atti Sem. Mat. Fis. Univ. Modena 46 (1998), suppl., 511-532. |
|
|
|
|
Canessa, E
(2003).
Theory of analogous force on number sets.
Physica A 328, 44-52. |
|
|
|
|
Carslaw, CAPN
(1988).
Anomalies in Income Numbers: Evidence of Goal Oriented Behavior.
The Accounting Review 63, No. 2, 321-327. |
|
|
|
|
Casey, MC
(2004).
Integrated Learning in Multi-net Systems.
University of Surrey Ph.D. Thesis submitted Feb 2004. |
|
|
|
|
Caster, P, Mittag, B and Scherga, C
(2003).
Application of Digital Analysis To Assess the Quality and Usability of the ATA Database.
Journal of Forensic Accounting 4, 95-104. |
|
|
|
|
Chaitin-Chatelin, F
(1994).
Le calcul sur ordinateur a precision finie. Theorie et etat de l’art.
CERFACS REPORT TR/PA/94/05. |
|
|
|
|
Chaitin-Chatelin, F
(1995).
Le calcul qualitatif. Comment donner un sens a des resultats faux?.
CERFACS REPORT TR/PA/95/10. |
|
|
|
|
Chaitin-Chatelin, F
(1996).
Is finite precision arithmetic useful for physics?.
Journal of Universal Computer Science 2(5), 380-395. |
|
|
|
|
Chaitin-Chatelin, F and Frayssé, V
(1996).
Lectures on Finite Precision Computations.
SIAM. |
|
|
|
|
Chiverton, J and Wells, K
(2006).
Mixture effects in FIR low-pass filtered signals.
IEEE Signal Processing Letters 13(6), 369-372. ISSN: 1070-9908. |
|
|
|
|
Cho, WKT and Gaines, BJ
(2007).
Breaking the (Benford) law: Statistical fraud detection in campaign finance.
American Statistician 61(3), 218-223. ISSN: 0003-1305. |
|
|
|
|
Chou, MC, Kong, Q and Teo, CP, Wang, Z, Zheng, H
(2009).
Benford's Law and Number Selection in Fixed-Odds Numbers Game.
Journal of Gambling Studies. |
|
|
|
|
Christensen, JA and Byington, JR
(2003).
The computer: an essential fraud detection tool.
Journal of Corporate Accounting & Finance 14(5), 23-27. |
|
|
|
|
Christian, CW and Gupta, S
(1993).
New evidence on "Secondary Evasion".
The Journal of the American Taxation Association 15, 72-93. |
|
|
|
|
Cigler, J
(1964).
Methods of summability and uniform distribution mod 1.
Compositio Mathematica 16, 44-51. |
|
|
|
|
Cigler, J and Helmberg, G
(1961).
Neuere Entwicklungen der Theorie der Gleichverteilung.
Jahresbericht der Deutschen Mathematiker Vereinigung 64, 1-50. |
|
|
|
|
Ciofalo, M
(2009).
Entropy, Benford’s first digit law, and the distribution of everything.
Dipartimento di Ingegneria Nucleare, Universitŕ 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. |
|
|
|
|
Cockshott, WP, McGregor, D and Wilson, J
(1998).
High-Performance Operations Using a Compressed Database Architecture.
The Computer Journal 41(5), 283-296. ISSN: 0010-4620. |
|
|
|
|
Coderre, D.
(1999).
Fraud Detection: Using Data Analysis Techniques to Detect Fraud.
Global Audit Publications, ACL, Vancouver, Canada. |
|
|
|
|
Cohen, DIA
(1976).
An Explanation of First Digit Phenomenon.
Journal of Combinatorial Theory Series A 20(3), 367-370. ISSN: 0097-3165. |
|
|
|
|
Cohen, DIA and Katz, TM
(1984).
Prime Numbers and the First Digit Phenomenon.
Journal of Number Theory 18(3), 261-268. ISSN: 0022-314X. |
|
|
|
|
Corazza, M, Ellero, A and Zorzi, A
(2008).
What sequences obey Benford's law?.
Working Paper n. 185/2008, November 2008, Department of Applied Mathematics, University of Venice. ISSN: 1828-6887. |
|
|
|
|
Costas, E, López-Rodas, V and Toro, FJ, Flores-Moya, A
(2008).
The number of cells in colonies of the cyanobacterium Microcystis aeruginosa satisfies Benford's law.
Aquatic Botany 89(3), 341-343. |
|
|
|
|
Craig, TR
(1992).
Round-off bias in earnings-per-share calculations.
Journal of Applied Business Research 8 (4), 106-113. |
|
|
|
|
Das, S and Zhang, H
(2001).
The stock market’s under-reaction to rounding-up in EPS.
Preprint. |
|
|
|
|
Das, S and Zhang, H
(2003).
Rounding-up in reported EPS, behavioral thresholds, and earnings management.
Journal of Accounting & Economics 35(1), 31-50. ISSN: 0165-4101. |
|
|
|
|
Davis, B
(1976).
Some Remarks on Initial Digits.
Fibonacci Quarterly 14(1), 13-14. ISSN: 0015-0517. |
|
|
|
|
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. |
|
|
|
|
Deakin, MAB
(1993).
Another derivation of Benford’s law.
Australian Mathematical Society Gazette 20, 162-163. |
|
|
|
|
Dehaene, S and Mehler, J
(1992).
Cross-Linguistic Regularities in the Frequency of Number Words.
Cognition 43(1), 1-29. ISSN: 0010-0277. |
|
|
|
|
Del Acebo, E and Sbert, M
(2005).
Benford's Law for Natural and Synthetic Images.
Computational Aesthetics in Graphics, Visualization and Imaging 2005, pp. 169-176. ISSN: 1816-0859. |
|
|
|
|
Diaconis, P
(1977).
Distribution of Leading Digits and Uniform Distribution Mod 1.
Annals of Probability 5(1), 72-81. ISSN: 0091-1798. |
|
|
|
|
Diaconis, P
(2002).
G.H. Hardy and Probability ???.
Bulletin of the London Mathematical Society 34, 385-402. |
|
|
|
|
Diaconis, P and Freedman, D
(1979).
On Rounding Percentages.
Journal of the American Statistical Association 74(366), 359-364. ISSN: 0162-1459. |
|
|
|
|
Dickinson, JR
(2002).
A universal mathematical law criterion for algorithmic validity.
Developments in Business Simulation and Experiential Learning 29, 26-33. |
|
|
|
|
Diekmann, A
(2002).
Sources of bias and quality of data in social science research.
Institute of Technology Assessment (ITA) Working Paper No. ITA-02-04. |
|
|
|
|
Diekmann, A
(2007).
Not the First Digit! Using Benford's Law to Detect Fraudulent Scientific Data.
Journal of Applied Statistics 34(3), 321-329. ISSN: 0266-4763. |
|
|
|
|
Dlugosz, S
(2004).
Digitalanalyse als Ansatz zur Betrugserkennung in Finanzdaten.
Diploma thesis, Westfälische Wilhelms-Universität Münster, Germany. |
|
|
|
|
Dominguez, MP and Burguillo, JDA
(1999).
El primer digito significativo.
Revista Epsilon de la S.A.E.M. "Thales", 45 (15/3), 339-352. |
|
|
|
|
Dong-Dong, N, Lai, W and Zhong-Zhou, R
(2009).
Benford's Law and β-Decay Half-Lives.
Commun. Theor. Phys. 51, 713-716. |
|
|
|
|
Dorfleitner, G and Klein, C
(2009).
Psychological barriers in European stock markets: Where are they?.
Global Finance Journal 19(3), 268-285. |
|
|
|
|
Dorogovtsev, SN, Mendes, JFF and Oliveira, JG
(2006).
Frequency of occurrence of numbers in the World Wide Web.
Physica A: Statistical Mechanics and its Applications 360(2), 548-556. ISSN: 0378-4371. |
|
|
|
|
Dorrestijn, J
(2008).
Graphing conformity of distributions to Benford’s Law for various bases.
MSc thesis, Universiteit Utrecht, The Netherlands. |
|
|
|
|
Doucouliagos, C
(2004).
Number preference in Australian stocks.
Applied Financial Economics 14(1), 43-54. |
|
|
|
|
Doucouliagos, C
(2005).
Price exhaustion and number preference: time and price confluence in Australian stock prices.
The European Journal of Finance 11(3), 207-222. |
|
|
|
|
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. |
|
|
|
|
Duncan, RL
(1967).
An application of uniform distributions to the Fibonacci numbers.
Fibonacci Quarterly 5, 137-140. |
|
|
|
|
Duncan, RL
(1969).
Note on the initial digit problem.
Fibonacci Quarterly 7(5), 474-475. |
|
|
|
|
Duran, JP
(1974).
Almost convergence, summability and ergodicity.
Canadian Journal of Mathematics 26(2), 372-387. |
|
|
|
|
Durrett, R
(1996).
Probability: Theory and Examples (2nd ed).
p 301. |
|
|
|
|
Durtschi, C, Hillison, W and Pacini, C
(2004).
The effective use of Benford’s law to assist in detecting fraud in accounting data.
Journal of Forensic Accounting 1524-5586/Vol. V, 17-34. |
|
|
|
|
Dworschak, M
(1998).
Weiter Weg zur Zwei.
pp 228-229 in: Der Spiegel 47, 16 November. |
|
|
|
|
Engel, HA and Leuenberger, C
(2003).
Benford's law for exponential random variables.
Statistics & Probability Letters 63, 361-365. ISSN: 0167-7152. |
|
|
|
|
Ettredge, ML and Srivastava, RP
(1999).
Using digital analysis to enhance data integrity.
Issues in Accounting Education 14(4), 675-690. |
|
|
|
|
Favaretto, F
(2007).
Verificacao da qualidade de dados atraves da lei de Benford.
XXVII Brazilian National Conference on Engineering, October 2007. |
|
|
|
|
Feldstein, A and Goodman, R
(1976).
Convergence Estimates for Distribution of Trailing Digits.
Journal of the Association for Computing Machinery, 23(2), 287-297. ISSN: 0004-5411. |
|
|
|
|
Feldstein, A and Turner, P
(1986).
Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction.
IMA Journal of Numerical Analysis 6, 241-251. |
|
|
|
|
Feldstein, A and Turner, PR
(1996).
Overflow and underflow in multiplication and division.
Applied Numerical Mathematics 21(3), 221-239. ISSN: 0168-9274. |
|
|
|
|
Feller, W
(1971).
An Introduction to Probability Theory and Its Applications.
p 63, vol 2, 2nd ed. J. Wiley. |
|
|
|
|
Fewster, RM
(2009).
A simple Explanation of Benford's Law.
American Statistician 63(1), 20-25. |
|
|
|
|
Filipponi, P
(1994).
Fn and Ln cannot have the same initial digit.
Pi Mu Epsilon Journal 10.1, 5-6. |
|
|
|
|
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. |
|
|
|
|
Flam, F
(2000).
Math formula could help spot tax cheats.
The Pittsburg Post-Gazette, 19 April. |
|
|
|
|
Flehinger, BJ
(1966).
On Probability that a Random Integer has Initial Digit A.
American Mathematical Monthly 73(10), 1056-1061. ISSN: 0002-9890. |
|
|
|
|
Florack, LMJ
(1999).
Visual representations embodying spacetime structure.
Technical Report, University Utrecht, UU-CS-1999-07. |
|
|
|
|
Franel, J
(1917).
A propos des tables de logarithmes.
Festschrift der Naturforschenden Gesellschaft in Zürich, Vierteljahrsschrift 62, 286-295. |
|
|
|
|
Frank, A
(2006).
Benford's law.
http://reason-and-rhyme.blogspot.com/2006/10/benfords-law.html. |
|
|
|
|
Frey, B
(2006).
Spot Faked Data.
Hack #64 in: Statistic Hacks, pp 251-262 |
|
|
|
|
Friedberg, SH
(1984).
The Distribution of First Digits.
College Mathematics Journal 15(2), 120-125. ISSN: 0049-4925. |
|
|
|
|
Frieden, BR
(1999).
F-Information, a Unitless Variant of Fisher Information.
Foundations of Physics 29(10), 1521-1541. ISSN: 0015-9018. |
|
|
|
|
Fuchs, A and Letta, G
(1984).
Sur le problčme du premier chiffre décimal.
Boll. Unione Mat. Ital., VI. Ser., B 3, 451-461. |
|
|
|
|
Fuchs, A and Letta, G
(1996).
Le problčme du premier chiffre decimal pour les nombres premiers.
The Electronic Journal of Combinatorics 3(2), R25. |
|
|
|
|
Fuchs, A and Nanopoulos, P
(1985).
Mesures invariantes par translation, classes de Dynkin first-digit problem.
Advances in Mathematics 55, 24-74. |
|
|
|
|
Furlan, LV
(1946).
Das Harmoniegesetz der Statistik: Eine Untersuchung ueber die metrische Interdependenz der sozialen Erscheinungen.
Basel, Verlag fuer Recht und Gesellschaft AG, xiii:504p. |
|
|
|
|
Furry, WH and Hurwitz, H
(1945).
Distribution of numbers and distribution of significant figures.
Nature 155(3924), 52-53. |
|
|
|
|
Garcia-Berthou, E and Alcaraz, C
(2004).
Incongruence between test statistics and P values in medical papers.
BMC Medical Research Methodology 4(13). |
|
|
|
|
Gauvrit, N and Delahaye, JP
(2008).
A new general explanation of Bendford’s law.
Mathematiques et sciences humaines/ Mathematics and social sciences, 182, 7-16. |
|
|
|
|
Gauvrit, N and Delahaye, JP
(2009).
Loi de Benford générale (General Benford Law).
Mathématiques et sciences humaines/ Mathematics and Social Sciences 186, 5–15. |
|
|
|
|
Gauvrit, N and Delahaye, JP
(2009).
Scatter and regularity imply Benford's Law ... and more.
arXive preprint. |
|
|
|
|
Geiringer, H
(1948).
Review of L.V. Furlan’s book.
Journal of the American Statistical Association 43, 325-328. |
|
|
|
|
Gelman, A and Nolan, D
(2002).
Some Statistical Sampling and Data Collection Activities.
Mathematics Teacher 95(9), 688. |
|
|
|
|
Gelman, A and Nolan, D
(2002).
Teaching Statistics: a bag of tricks.
Oxford University Press. |
|
|
|
|
Gent, I and Walsh, T
(2001).
Benford’s law.
Preprint. APES Research Report, 2001. |
|
|
|
|
Geyer, CL and Williamson, PP
(2004).
Detecting Fraud in Data Sets Using Benford's Law.
Communications in Statistics: Simulation and Computation 33(1), 229-246. ISSN: 0361-0918. |
|
|
|
|
Giles, DE
(2007).
Benford's law and naturally occurring prices in certain eBay auctions.
Applied Economics Letters 14(3), 157-161. ISSN: 1350-4851. |
|
|
|
|
Gilio, A
(1986).
An application of the pseudodensity concept to the first digit problem significant for statistical data.
Rend. Mat. Appl., VII. Ser. 6 (1-2), 215-224. |
|
|
|
|
Gini, C
(1957).
Sulla frequenza delle cifre iniziali dei numeri osservati.
Bull. Inst. Internat. Stat., 29th session, 35(2), 57-76. |
|
|
|
|
Giuliano Antonioni, R
(1991).
On the notion of uniform distribution mod 1.
Fibonacci Quarterly 29(3), 230-234. |
|
|
|
|
Giuliano Antonioni, R and Grekos, G
(2005).
Regular sets and conditional density: an extension of Benford's law.
Colloq. Math. 103, 173-192. |
|
|
|
|
Glück, M
(2008).
Benfords Gesetz.
http://www.benfords-gesetz.de/index.html. |
|
|
|
|
Glück, MIS
(2007).
Die Benford-Verteilung - Anwendung auf reale Daten der Marktforschung.
Diploma thesis, TU Dresden, published as e-book by Grin Verlag. |
|
|
|
|
Göb, R
(2007).
Data Conformance Testing by Digital Analysis–A Critical Review and an Approach to More Appropriate Testing.
Quality Engineering 19 (4), 281-297. |
|
|
|
|
Gonzalez-Garcia, J and Pastor, G
(2009).
Benford’s Law and Macroeconomic Data Quality.
International Monetary Fund Working Paper WP/09/10, Statistics Department, January 2009. |
|
|
|
|
Good, IJ
(1965).
Letter to the Editor.
The American Statistician 19(3), 43. |
|
|
|
|
Good, IJ
(1986).
Some statistical applications of Poisson’s work.
Statistical Science 1(2), 157-170. |
|
|
|
|
Goodman, RH, Feldstein, A and Bustoz, J
(1985).
Relative Error in Floating-Point Multiplication.
Computing 35, 127-139. ISSN: 1436-5057. |
|
|
|
|
Goto, K
(1992).
Some examples of Benford sequences.
Mathematical Journal of the Okayama University 34, 225-232. |
|
|
|
|
Goto, K and Kano, T
(1985).
Uniform distribution of some special sequences.
Proc. Japan Acad. Ser. A Math. Sci. 61(3), 83-86. |
|
|
|
|
Gottwald, GA and Nicol, M
(2002).
On the nature of Benford’s law.
Physica A: Statistical Mechanics and its Applications 303(3-4), 387-396. |
|
|
|
|
Goudsmit, SA
(1977).
Pitfalls in Elementary Probability.
Proceedings of the American Philosophical Society 121(2), 188-189. ISSN: 0003-049X. |
|
|
|
|
Goudsmit, SA and Furry, WH
(1944).
Significant figures of numbers in statistical tables.
Nature 154(3921), 800-801. ISSN: 0028-0836. |
|
|
|
|
Grabowski, F and Trojanowski, P
(2006).
Benford's law in image analysis.
Tools of Information Technology, Rzeszow, 15 Sep 2006. |
|
|
|
|
Grandison, S and Morris, RJ
(2008).
Biological pathway kinetic rate constants are scale-invariant.
Bioinformatics 24(6), 741-743. ISSN: 1367-4803. |
|
|
|
|
Griffiths, TL and Kalish, ML
(2002).
A multidimensional scaling approach to mental multiplication.
Memory & Cognition 30(1), 97-106. ISSN: 0090-502X. |
|
|
|
|
Groce, D
(2005).
Benford's Law.
Presentation at the Lyncean Group, California, USA, 23 March. |
|
|
|
|
Guan, L, He, D and Yang, D
(2006).
Auditing, integral approach to quarterly reporting, and cosmetic earnings management.
Managerial Auditing Journal 21(6), 569-581. |
|
|
|
|
Guan, L, Skousen, CJ and Wetzel, TS
(2005).
Unusual Patterns in Reported Earnings: Additional Evidence.
Journal of Forensic Accounting 6(2), 317-332. |
|
|
|
|
Günnel, S and Tödter, KH
(2009).
Does Benford's law hold in economic research and forecasting?.
Empirica 36, 273-292. |
|
|
|
|
Haber, S
(1983).
Parameters for Integrating Periodic Functions of Several Variables.
Mathematics of Computation 41(163), 115-129. ISSN: 0025-5718. |
|
|
|
|
Hafner, EM
(1979).
Circular slide roulette.
IEEE Communications Magazine 17(2), 29-32. |
|
|
|
|
Haigh, J
(2003).
Benford's Law.
pp 283-286 in: Taking Chances: Winning with Probability, Oxford University Press. |
|
|
|
|
Hamming, R
(1970).
On the distribution of numbers.
Bell Syst. Tech. J. 49(8), 1609-1625. |
|
|
|
|
Harrington, JE
(2005).
Detecting Cartels.
Economics Working Paper 526, Johns Hopkins University, to appear in: Advances in the Economics of Competition Law. |
|
|
|
|
Hassan, B
(2002).
Assessing data authenticity with Benford’s law.
Information Systems Control Journal 6. |
|
|
|
|
Hassan, B
(2003).
Examining data accuracy and authenticity with leading digit frequency analysis.
Industrial Management & Data Systems 103(1-2), 121-125. ISSN: 0263-5577. |
|
|
|
|
Havil, J
(2003).
Benford's Law.
Sec 14.2, pp 145-155 in: Gamma: Exploring Euler's Constant, Princeton University Press, USA. |
|
|
|
|
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. |
|
|
|
|
Hayes, S
(2009).
Benford’s law in relation to terminal digit preference.
Journal of Clinical Pathology 62(6), 575-576. |
|
|
|
|
Herrmann, D and Thomas, WB
(2005).
Rounding of Analyst Forecasts.
Accounting Review 80(3), 805-823. ISSN: 0001-4826. |
|
|
|
|
Herzel, A
(1956).
Sulla distribuzione delle cifre iniziali die numeri statistici.
Atti XV e XVI Riunione sci., Roma 1956, 205-228. |
|
|
|
|
Hesman, T
(1999).
Randomness rules.
The Dallas Morning News, August 9. |
|
|