| 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. The American Statistician 64(3), 221–227. ISSN:0003-1305. |
 |
|
|
|
| Alexander, J (2009). Remarks on the use of Benford's law. Social Science Research Network(November, 13 2009). Available at SSRN: http://ssrn.com/abstract=1505147 or http://dx.doi.org/10.2139/ssrn.1505147. |
 |
|
|
|
| Anderson, TC, Rolen, L and Stoehr, R (2011). Benford's Law for Coefficients of Modular Forms and Partition Functions. Proceedings of the American Mathematical Society, Vol. 139, No. 5, May 2011, pp 1533-1541. ISSN:0002-9939. |
 |
|
|
|
| Bailly, N (2006). Prominence trend in maximum lengths recorded for fishes: a preliminary analysis. pp 12-17 in: Palomares, MLD, Stergiou, KI, and Pauly, D (eds.), Fishes in databases and ecosystems. Proceedings of the 2006 FishBase Symposium. Fisheries Centre Research Reports, 2006, Vol. 14, No. 4. ISSN:1198-6727. |
 |
|
|
|
| Baiocchi, G (2004). Using Perl for Statistics: Data Processing and Statistical Computing. Journal of Statistical Software, 2004 , Vol. 11, Issue 1. |
 |
|
|
|
| Balanzario, EP (2012). Benford’s law for mixtures. Preprint. |
 |
|
|
|
| Becker, T, Greaves-Tunnell, A, Miller, SJ, Ronan, R and Strauch, FW (2011). Benford's Law and Continuous Dependent Random Variables. Preprint, Math arXiv:1111.0568. |
 |
|
|
|
| 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 (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), 137-159. |
 |
|
|
|
| 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 (2007). Newton’s method obeys Benford’s law. American Mathematical Monthly 114 (7), 588-601. ISSN:0002-9890. |
 |
|
|
|
| Berger, A and Hill, TP (2010). Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law. University of Alberta preprint. |
 |
|
|
|
| Berger, A and Hill, TP (2011). Benford's Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem. The Mathematical Intelligencer 33(1), 85-91. |
 |
|
|
|
| Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, 1-126 (2011) . |
 |
|
|
|
| Berger, A, Hill, TP, Kaynar, B and Ridder, A (2011). Finite-state Markov Chains Obey Benford's Law. SIAM Journal of Matrix Analysis and Applications 32(3), 665-684. |
 |
|
|
|
| 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. |
 |
|
|
|
| Block, HW and Savits, TH (2010). A General Example for Benford Data. The American Statistician 64(4), 335-339. |
 |
|
|
|
| Bolton, RJ and Hand, DJ (2002). Statistical Fraud Detection: a review. Statistical Science 17(3), 235-249. |
 |
|
|
|
| Bonache, A, Moris, K and Maurice, J (2009). Risque associé à l'utilisation de la loi de Benford pour détecter les fraudes
dans le secteur de la mode. Munich Personal RePEc Archive (MPRA) Paper No. 15352, posted 26 May 2009. |
 |
|
|
|
| Bonache, AB, Moris, K and Maurice, J (2010). Détection de fraudes et loi de Benford: Quelques risques associés. Revue Française de Comptabilité n°431, 24-27. |
 |
|
|
|
| Bradley, JR and Farnsworth, DL (2009). What is Benford's Law?. Teaching Statistics 31(1), 2-6. |
 |
|
|
|
| Bradley, JR and Farnsworth, DL (2009). Beispiele und Schüleraktivitäten zum BENFORD-Gesetz. Stochastik in der Schule (SiS) 29, 28-32 . ISSN:1614-0443. |
 |
|
|
|
| Brähler, G, Bensmann, M and Emke, AL (2010). Der Einsatz mathematisch-statistischer Methoden in der
digitalen Betriebsprüfung. Illmenauer Schriften zur Betriebswirtschaftslehre 4/2010. |
 |
|
|
|
| Brähler, G, Bensmann, M and Jakobi, HR (2011). Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Prüfung von Fahrtenbüchern. Ilmenauer Schriften zur Betriebswirtschaftslehre 3/2011. |
 |
|
|
|
| Breunig, C and Goerres, A (2011). Searching for Electoral Irregularities in an Established Democracy: Applying Benford’s Law Tests to Bundestag Elections in Unified Germany. Electoral Studies 30(3) September 2011, pp. 534-545. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| Canessa, E (2003). Theory of analogous force on number sets. Physica A 328, 44-52. |
 |
|
|
|
| Cantu, F and Saiegh, SM (2011). Fraudulent Democracy? An Analysis of Argentina’s Infamous Decade Using Supervised Machine Learning. Political Analysis (Autumn 2011) 19 (4): 409-433; doi:10.1093/pan/mpr033. |
 |
|
|
|
| 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, MJ, Eltinge, JL and Swanson, D (2003). Inferential methods to identify possible interviewer fraud using leading digit preference patterns and design effect matrices. Proceedings of the American Statistical Association. |
 |
|
|
|
| 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, Teo, CP, Wang, Z and Zheng, H (2009). Benford's Law and Number Selection in Fixed-Odds Numbers Game. Journal of Gambling Studies 25(4), pp. 503-521. |
 |
|
|
|
| Ciofalo, M (2009). Entropy, Benford’s first digit law, and the distribution of everything. Dipartimento di Ingegneria Nucleare, Università degli Studi di Palermo, Italy. |
 |
|
|
|
| Clippe, P and Ausloos, M (2012). Benford's law and Theil transform of financial data. Physica A: Statistical Mechanics and its Applications, 2012, Vol. 391, No. 24, 6556–6567. |
 |
|
|
|
| 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. |
 |
|
|
|
| Corazza, M, Ellero, A and Zorzi, A (2010). Checking financial markets via Benford's law: the S&P 500 case. pp 93-102 in: Corazza, M and Pizzi, C (Eds.): Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer. |
 |
|
|
|
| Cuff, V , Lewis, A and Miller, SJ (2009). The Weibull distribution and Benford’s law. Preprint. |
 |
|
|
|
| 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. |
 |
|
|
|
| Diaconis, P (2002). G.H. Hardy and Probability ???. Bulletin of the London Mathematical Society 34, 385-402. |
 |
|
|
|
| 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. |
 |
|
|
|
| Diekmann, A (2012). Making Use of ‘‘Benford’s Law’’ for the
Randomized Response Technique. Sociological Methods and Research 41(2):325-334. |
 |
|
|
|
| Diniz, JA, dos Santos, J, Dieng, M and Diniz, MAA (2006). Comprovação de Eficácia da Aplicação de Modelos Contabilométricos no Campo daAuditoria Digital das Contas Públicas Municipais: caso de um Tribunal de Contas de um estado brasileiro. |
 |
|
|
|
| Docampo, S, del Mar Trigo, M, Aira, M, Cabezudo, B and Flores-Moya, A (2009). Benford’s law applied to aerobiological data and its potential as a quality control tool . Aerobiologia 25, 275-283 . ISSN:0393-5965. |
 |
|
|
|
| Dorfleitner, G and Klein, C (2009). Psychological barriers in European stock markets: Where are they?. Global Finance Journal 19(3), 268-285. |
 |
|
|
|
| Dorrestijn, J (2008). Graphing conformity of distributions to Benford’s Law for various bases. MSc thesis, Universiteit Utrecht, The Netherlands. |
 |
|
|
|
| Dos Santos, J, Diniz, JA and Corrar, LJ (2005). O Foco é a Teoria Amostral nos Campos da Auditoria Contábil Tradicional e da Auditoria Digital: testando a Lei de Newcomb-Benford para o primeiro digito nas contas publicas. Brazilian Business Review 2 (1), 71-89. |
 |
|
|
|
| Dumas, CF and Devine, JH (2000). Detecting Evidence of Non-Compliance in Self-
Reported Pollution Emissions Data: An Application of Benford’s Law. Selected Paper, American Agricultural Economics Association, Annual meeting. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| Fewster, RM (2009). A simple Explanation of Benford's Law. American Statistician 63(1), 20-25. |
 |
|
|
|
| Formann, AK (2010). The Newcomb-Benford Law in Its Relation to Some Common Distributions. PLoS ONE 5(5): e10541. doi:10.1371/journal.pone.0010541. |
 |
|
|
|
| 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
O'Reilley Media, Sebastopol, CA. ISSN:ISBN-13: 978-0-596-1. |
 |
|
|
|
| Friar, JL, Goldman, T and Pérez–Mercader, J (2012). Genome Sizes and the Benford Distribution. PLoS ONE 7(5): e36624. doi:10.1371/journal.pone.0036624
Public Library of Science. |
 |
|
|
|
| Fu, D, Shi, YQ and Su, W (2007). A generalized Benford’s law for JPEG coefficients
and its applications in image forensics. Proceedings of SPIE, Volume 6505, Security, Steganography and Watermarking of Multimedia Contents IX, San Jose, California, January 28 - February 1, 2007. |
 |
|
|
|
| Gauvrit, N and Delahaye, J-P (2008). Pourquoi la loi de Benford n’est pas mystérieuse - A new general explanation of Benford’s law. Mathematiques et sciences humaines/ Mathematics and social sciences, 182(2), 7-15. ISSN:0987-6936. |
 |
|
|
|
| Gauvrit, N and Delahaye, J-P (2009). Scatter and regularity imply Benford's Law ... and more. arXiv preprint -http://arxiv.org/pdf/0910.1359.pdf. |
 |
|
|
|
| Gauvrit, N and Delahaye, J-P (2009). Loi de Benford générale (General Benford Law). Mathématiques et sciences humaines/ Mathematics and Social Sciences 186, 5–15. |
 |
|
|
|
| Gauvrit, N and Delahaye, J-P (2011). Scatter and Regularity Implies Benford's Law... and More. in H. Zenil (Ed.) Randomness Through Complexity, Singapore, World Scientific, 53-69. ISSN:13978-981-4327-74-9. |
 |
|
|
|
| Genolini, C and Driss, T (2010). Eveiller l'intérêt pour la statistique par l'exemple. Statistique et Enseignement 1(2), 49-57. |
 |
|
|
|
| Geyer, A and Martì, J (2012). Applying Benford’s law to volcanology. Geology 40(4), pp. 327-330. |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| Göb, R (2007). Data Conformance Testing by Digital Analysis - A Critical Review and an Approach to More Appropriate Testing. Quality Engineering Volume 19(4), 281-297 (2007), doi:10.1080/08982110701633721. |
 |
|
|
|
| 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. |
 |
|
|
|
| Grandison, S and Morris, RJ (2008). Biological pathway kinetic rate constants are scale-invariant. Bioinformatics 24(6), 741-743. ISSN:1367-4803. |
 |
|
|
|
| Guettler, S, Thiemann, F and Mueller, R.A.E. (2012). Benfords Gesetz: Ein Qualitätstest für statistische Reihen angewendet auf Handelsdaten für Agrarprodukte. Clasen, M., Fröhlich, G., Bernhardt, H., Hildebrand, K. und Theuvsen, B. (eds.) (2012): Informationstechnologie für eine nachhaltige Landbewirtschaftung. Referate der 32. GIL-Jahrestagung, 29. Februar – 1. März 2012, Freising. Lecture Notes in Informatics. ISSN:1617-5468 / 978-8857. |
 |
|
|
|
| Guillou, A and Hall, P (2001). A diagnostic for selecting the threshold in extreme value analysis. Journal of the Royal Statistical Society Series B - Statistical Methodology 63(2), 293-305. ISSN:1369-7412. |
 |
|
|
|
| Günnel, S and Tödter, KH (2009). Does Benford's law hold in economic research and forecasting?. Empirica 36, 273-292. |
 |
|
|
|
| Hales, DN, Chakravorty, SS and Sridharan, V (2009). Testing Benford’s Law for improving supply chain decision-making: A field experiment. Int. J. Production Economics 122 (2009) pp. 606–618. |
 |
|
|
|
| Hales, DN, Sridharan, V, Radhakrishnan, A, Chakravorty, SS and Sihad, SM (2008). Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods. European Journal of Operational Research 189(3), 583-593. |
 |
|
|
|
| Hamadeh, N (2004). Wireless Security and Traffic Modeling Using Benford's Law. Master’s Thesis, University of New Mexico, Albuquerque, NM, 2004 (99 pgs). |
 |
|
|
|
| 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. |
 |
|
|
|
| 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. |
 |
|
|
|
| Hickman, MJ and Rice, SK (2010). Digital Analysis of Crime Statistics: Does Crime Conform to Benford’s Law?. Journal of Quantitative Criminology 26(3), 333-349. |
 |
|
|
|
| Hill, TP (1996). A note on distributions of true versus fabricated data. Perceptual and Motor Skills 83, 776-778 Part 1. ISSN:0031-5215. |
 |
|
|
|
| Hill, TP (1997). Benford law. Encyclopedia of Mathematics Supplement, vol. 1, 102-103. |
 |
|
|
|
| Hill, TP (1998). The First-Digit Phenomenon. American Scientist 86 (4), 358-363. ISSN:0003-0996. |
 |
|
|
|
| Hill, TP (1999). Le premier chiffre significatif fait sa loi. La Recherche Hors Serie 316, 72-74. |
 |
|
|
|
| Hill, TP (1999). The difficulty of faking data. Chance 12(3), 27-31. |
 |
|
|
|
| Hill, TP (2001). Response to "Benfords Gesetz", Brief an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 3/2001, p 4. |
 |
|
|
|
| Hill, TP and Schürger, K (2005). Regularity of digits and significant digits of random variables. Journal of Stochastic Processes and their Applications 115(10), 1723-1743. |
 |
|
|
|
| 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. |
 |
|
|
|
| Hoyle, DC, Rattray, M, Jupp, R and Brass, A (2002). Making sense of microarray data distributions. Bioinformatics 18(4), 576-584. ISSN:1367-4803. |
 |
|
|
|
| Huang, SM, Yen, DC, Yang, LW and Hua, JS (2008). An investigation of Zipf's Law for fraud detection. Decision Support Systems 46(1), 70-83. |
 |
|
|
|
| Hungerbühler, N (2007). Benfords Gesetz über führende Ziffern: Wie die Mathematik Steuersündern das Fürchten lehrt. EducETH. |
 |
|
|
|
| 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. |
 |
|
|
|
| Iudica, F (2012). Benford’s Law: Mathematical Properties and Forensic Accounting Applications. Master’s Thesis, Luiss Guido Carli University, Rome, Italy, 2012. |
 |
|
|
|
| Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG. |
 |
|
|
|
| Jang, D, Kang, JU, Kruckman, A, Kudo, J and Miller, SJ (2008). Chains of distributions, hierarchical Bayesian models and Benford's Law. Journal of Algebra, Number Theory: Advances and Applications 1(1), 37-60. |
 |
|
|
|
| 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. |
 |
|
|
|
| Janvresse, É and de la Rue, T (2009). Benford’s law. (Catalan. Catalan summary). Butl. Soc. Catalana Mat.,
24(1):5{12, 2009. Translated by Frederic Utzet. |
 |
|
|
|
| Jasak, Z (2010). Benfordov zakon i reinforcement učenje (Benford's Law and reinforcment learning)
. MSc Thesis, University of Tuzla, Bosnia. |
 |
|
|
|
| Jasak, Z and Banjanovic-Mehmedovic, L (2008). Detecting Anomalies by Benford's Law. pp 453-458 in: IEEE International Symposium on Signal Processing and Information Technology, 2008. ISSPIT 2008. ISSN:978-1-4244-3554-8. |
 |
|
|
|
| Jolion, JM (2001). Images and Benford's Law. Journal of Mathematical Imaging and Vision 14(1), 73-81. ISSN:0924-9907. |
 |
|
|
|
| Judge, G and Schechter, L (2009). Detecting problems in survey data using Benford’s law. J. Human Resources 44, 1-24. |
 |
|
|
|
| Kafri, O (2007). The Second Law as a Cause of the Evolution. Preprint arXiv: 0711.4507, 2007 - arxiv.org. |
 |
|
|
|
| Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. arXiv:0901.3047v2. |
 |
|
|
|
| Kendal, WS (2004). Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models. Ecological Complexity 1(3), 193-209. |
 |
|
|
|
| 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. |
 |
|
|
|
| Kossovsky, AE (2006). Towards A Better Understanding Of The Leading Digits Phenomena. arXiv:math/0612627. Last updated Oct 31, 2012. |
 |
|
|
|
| Kottke, J (2006). Catching cheaters with Benford's Law . http://www.kottke.org/06/02/catching-cheaters-with-benfords-law. |
 |
|
|
|
| Krengel, U (2005). Die Anfangszifferverteilung. pp 136-137 in: Einführung in die Wahrscheinlichkeitstheorie und Statistik, 8th ed,
Vieweg und Sohn, Wiesbaden. ISSN:ISBN 3-8348-0063-5. |
 |
|
|
|
| Kulikova, AA and Prokhorov, YV (2005). Completely asymmetric stable laws and Benford’s law. Theory of Probability and its Application 49(1), 163-169. |
 |
|
|
|
| Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, 289-303. ISSN:0024-6107. |
 |
|
|
|
| Leemis, LM, Schmeiser, BW and Evans, DL (2000). Survival Distributions Satisfying Benford's Law. American Statistician 54(4), 236-241. ISSN:0003-1305. |
 |
|
|
|
| Li, Z, Cong, L and Wang, H (2004). Discussion on Benford’s law and its application. http://arxiv.org/abs/math.ST/0408057. |
 |
|
|
|
| Li, Z, Cong, L and Wang, H (2004). Discussion on Benford's Law and its Application. arXiv preprint math/0408057, 2004 - arxiv.org. |
 |
|
|
|
| Lim Kai Jie, S and Kalaichelvan, M (2012). A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford's Law. International Research Journal of Finance and Economics No. 95 (2012) pp. 196-210. ISSN:1450-2887. |
 |
|
|
|
| Lin, F, Chang, C and Wu, S (2009). A study on the relationship between related party transactions and monthly sales in Taiwan's publicly issued companies. to appear in: Journal of the Chinese Institute of Industrial Engineers. |
 |
|
|
|
| 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. |
 |
|
|
|
| Lolbert, T (2008). On the non-existence of a general Benford's law. Mathematical Social Sciences 55(2), 103-106. ISSN:0165-4896. |
 |
|
|
|
| Lowe, T, Murphy, S and Hayward, J (1999). The first digit law. Preprint. |
 |
|
|
|
| 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 and Boritz, JE (2005). Detecting Fraud in Health Insurance Data: Learning to Model Incomplete Benford’s Law Distributions. Machine Learning: ECML 2005 (Proceedings). Lecture Notes in Artificial Intelligence 3270, 633-640. ISSN:0302-9743. |
 |
|
|
|
| Lu, F, Boritz, JE and Covvey, D (2006). Adaptive fraud detection using Benford’s Law. Lecture Notes in Computer Science 4013, 347-358. |
 |
|
|
|
| Luque, B and Lacasa, L (2009). The first-digit frequencies of prime numbers and Riemann zeta zeros. Proc. Royal Soc. A, published online 22Apr09. |
 |
|
|
|
| Manoochehrnia, P, Rachidi, F, Rubinstein, M, Schulz, W and Diefendorfer, G (2010). Benford’s Law and Its Application to Lightning Data. IEEE Transactions on Electromagnetic Compatibility 52(4), 956-961. |
 |
|
|
|
| Martín, AB (2003). Sistematización del proceso de depuración de los datos en estudios con seguimientos. PhD Thesis, Universitat Autònoma de Barcelona, Spain. |
 |
|
|
|
| Mebane, WR Jr (2006). Detecting Attempted Election Theft: Vote Counts, Voting Machines and Benford’s Law. Paper prepared for the 2006 Annual Meeting of the Midwest Political Science Association, Chicago, IL. |
 |
|
|
|
| Mebane, WR Jr (2006). Election Forensics: Vote Counts and Benford’s Law. Summer Meeting of the Political Methodology Society. |
 |
|
|
|
| Mebane, WR Jr (2008). Election Forensics: The Second-digit Benford’s Law Test and Recent American Presidential Elections. pp 161-181 in: Alvarez, RM, Hall, TE and Hyde, SD (eds.), Election Fraud: Detecting and Deterring Electoral Manipulation. Brookings Press, Washington DC. |
 |
|
|
|
| Mebane, WR Jr (2010). Fraud in the 2009 presidential election in Iran?. Chance 23(1), 6-15. |
 |
|
|
|
| Merberg, A and Miller, SJ (2008). The Cramér-Rao Inequality. Course Notes for Math 162: Mathematical Statistics. |
 |
|
|
|
| Miller, SJ (2007). When the Cramér-Rao Inequality provides no information. Communications in Information and Systems 7(3), 265-272. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2006). Order Statistics and Shifted Almost Benford Behavior. Preprint. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2008). The Modulo 1 Central Limit Theorem and Benford's Law for Products. International Journal of Algebra 2(3), 119 - 130. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2008). Order Statistics and Benford's Law. International Journal of Mathematics and Mathematical Sciences, Art. ID 382948, 19 pp.. ISSN:0161-1712. |
 |
|
|
|
| Miller, SJ and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. |
 |
|
|
|
| Miller, SJ and Takloo-Bighash, R (2007). Introduction to Random Matrix Theory. From: An Invitation to Modern Number Theory, Princeton University Press. |
 |
|
|
|
| Mir, TA (2011). Law of the leading digits and the ideological struggle for numbers. physics arXiv:1104.3948. |
 |
|
|
|
| Mir, TA (2011). The law of the leading digits and the world religions. Physica A: Statistical Mechanics and its Applications, 391 (2012), 792-798. |
 |
|
|
|
| Mir, TA (2012). The leading digit distribution of the worldwide illicit financial flows. arXiv:1201.3432. |
 |
|
|
|
| Misiolek, E (2003). Swarm simulations of the power law distribution models. Poster session submission. |
 |
|
|
|
| Mochty, L (2002). Die Aufdeckung von Manipulationen im Rechnungswesen - Was leistet das Benford's Law?. Die Wirtschaftsprüfung 14, 725-736. |
 |
|
|
|
| Montenegro, MALO (2006). Policing Pollution Control in the Philippines: Issues and Prospects. |
 |
|
|
|
| Moret, MA, de Senna, V, Pereira, MG and Zebende, GF (2006). Newcomb-Benford law in astrophysical sources. International Journal of Modern Physics C 17(11), 1597-1604. ISSN:0129-1831. |
 |
|
|
|
| Morrow, J (2009). Benford's Law, Families of Distributions and a Test Basis. unpublished manuscript. |
 |
|
|
|
| Nguyen, HT, Kreinovich, V and Longpré, L (2003). Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals. The 12th IEEE International Conference on Fuzzy Systems. FUZZ’03. Fuzzy Systems 1, 67-73. |
 |
|
|
|
| Nguyen, HT, Kreinovich, V and Longpré, L (2004). Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Innite Intervals. Reliable Computing 10(2), 83-106. |
 |
|
|
|
| Ni, D and Ren, Z (2008). Benford’s law and half-lives of unstable nuclei. Eur. Phys. J. A 38, 251–255. |
 |
|
|
|
| Ni, D, Wei, L and Ren, Z (2009). Benford's Law and β-Decay Half-Lives. Commun. Theor. Phys. 51, 713-716. |
 |
|
|
|
| Nigrini, MJ (1999). Peculiar patterns of first digits. IEEE Potentials 18(2), 24-27. |
 |
|
|
|
| Nigrini, MJ (2005). An Assessment of the Change in the Incidence of Earnings Management Around the Enron-Andersen Episode. Review of Accounting and Finance 4, 92-110. |
 |
|
|
|
| Nigrini, MJ (2011). Forensic Analytics: Methods and Techniques for Forensic Accounting Investigations. John Wiley & Sons, Hoboken, New Jersey. ISSN:978-0-470-89046-2. |
 |
|
|
|
| Nigrini, MJ (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection . John Wiley & Sons, Hoboken, New Jersey. ISSN:978-1-118-15285-0. |
 |
|
|
|
| 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. |
 |
|
|
|
| Nye, J and Moul, C (2007). The Political Economy of Numbers: On the Application of Benford's Law to International Macroeconomic Statistics. The BE Journal of Macroeconomics 7(1). |
 |
|
|
|
| O'Brien, C (2003). Working Group on Methods on Fish Stock Assessments. ICES CM 2003/D:03 Ref. ACFM, G. |
 |
|
|
|
| Odueke, A and Weir, GRS (2012). Triage in Forensic Accounting using Zipf's Law. Issues in Cybercrime, Security and Digtal Forensics. Edited by G. R. S. Weir and A. Al-Nemrat. Glasgow. University of Strathclyde Publishing. 2012. pp. 33-43. |
 |
|
|
|
| Oleksy, M (2010). Data Mining und Benford's Law als Controllinginstrumente. Band 45, Wismarer Schriften zu Management und Recht, Europäischer Hochschulverlag, Bremen. ISSN:978-3867414-40. |
 |
|
|
|
| Oriol, JC (2007). Formation à la statistique par la pratique d'enquêtes par questionnaires et la simulation: étude didactique d'une experience d'enseignment dans u department d'IUT. Ph.D. Thesis, Université Lumière, Lyon, France. |
 |
|
|
|
| Orita, M, Moritomo, A, Niimi, T and Ohno, K (2010). Use of Benford’s law in drug discovery data. Drug Discovery Today 15(9/10), 328-331. |
 |
|
|
|
| Otey, ME (2006). Approaches to Abnormality Detection with Constraints. PhD thesis, The Ohio State University, USA. |
 |
|
|
|
| Pain, JC (2008). Benford’s law and complex atomic spectra. Physical Review E 77(1): Art. No. 012102. ISSN:1539-3755. |
 |
|
|
|
| Pericchi, LR and Torres, D (2004). La Ley de Newcomb-Benford y sus aplicaciones al Referendum
Revocatorio en Venezuela. Reporte Técnico-definitivo 2a. versión: Octubre 01,2004. |
 |
|
|
|
| Pocheau, A (2006). The significant digit law: a paradigm of statistical scale symmetries . European Physical Journal B 49(4), 491-511. ISSN:1434-6028. |
 |
|
|
|
| Popescu, II (2002). On the Lavelette’s nonlinear Zipf’s law. Website. |
 |
|
|
|
| Posch, PN (2004). Ziffernanalyse in der Fälschungsaufspürung. Benford’s Gesetz und Steuererklärungen in Theorie und Praxis. unpublished manuscript. |
 |
|
|
|
| Posch, PN (2008). A Survey on Sequences and Distribution Functions
satisfying the First-Digit-Law. Journal of Statistics & Management Systems 11(1), 1-19. |
 |
|
|
|
| Posch, PN (2010). Ziffernanalyse. VEW Verlag Europäische Wirtschaft: Munich
2nd edition. |
 |
|
|
|
| Posch, PN and Kreiner, WA (2005). A general approach to digital analysis exemplified by stock market indices. unpublished manuscript. |
 |
|
|
|
| Posch, PN and Kreiner, WA (2006). Analysing digits for portfolio formation and index tracking. Journal of Asset Management 7(1), 69-80. |
 |
|
|
|
| Rauch, B, Brähler, G, Engel, S and Göttsche, M (2011). Fact and Fiction in EU-Governmental Economic Data. German Economic Review 12(3), 243-255. |
 |
|
|
|
| Rodriguez, RJ (2004). First Significant Digit Patterns from Mixtures of Uniform Distributions. American Statistician 58(1), 64-71. ISSN:0003-1305. |
 |
|
|
|
| Rodriguez, RJ (2004). Reducing False Alarms in the Detection of Human Influence on Data. Journal of Accounting, Auditing & Finance 19(2), 141-158. |
 |
|
|
|
| Ross, KA (2011). Benford's Law, a growth industry. American Mathematical Monthly 118, 571-583. |
 |
|
|
|
| Rücker, G (2003). Benford's Law in Medical Data Sets. presentation given at: 49th Biometric Conference of the German Region of theInternational Biometric Society at Wuppertal, March 2003. |
 |
|
|
|
| Ryder, P (2009). The Relationship Between the Newcomb-Benford Law and the Distribution of Rational Numbers. Zeitschrift für Naturforschung 64a, 615-617. |
 |
|
|
|
| Ryder, P (2009). Multiple origins of the Newcomb-Benford law: rational numbers, exponential growth and random fragmentation. Staats- und Universitätsbibliothek Bremen, Germany. |
 |
|
|
|
| Sambridge, M, Tkalčić, H and Arroucau, P (2011). Benford's Law of First Digits: From Mathematical Curiosity to Change Detector. Asia Pacific Mathematics Newsletter 1(4), October 2011, 1-6. ISSN:2010-3484. |
 |
|
|
|
| Sambridge, M, Tkalčić, H and Jackson, A (2010). Benford's law in the Natural Sciences. Geophysical Research Letters 37 (2010) L22301, doi:10.1029/2010GL044830. |
 |
|
|
|
| Sandron, F (2002). Do populations conform to the law of anomalous numbers?. Population 57(4/5), 753-761 (translated from French by SR Hayford). ISSN:1634-2941. |
 |
|
|
|
| Saville, A (2003). Using Benford's Law to predict data error and fraud. An examination of companies listed on the JSE securities exchange. |
 |
|
|
|
| Saville, A (2006). Using Benford's law to detect data error and fraud: an examination of companies listed on the Johannesburg Stock Exchange. South African Journal of Economic and Management Sciences 9(3), 341-354. ISSN:1015-8812. |
 |
|
|
|
| Schäfer, C, Bömermann, H, Nauenburg, R, Wenzel, K, Müller, KR and Wagner, GG (2006). Qualitätssicherung des Faktors Interviewer für den Mikrozensus. pp 209-216 in: Kehlenbach, J, Rockmann, U (eds.): Amtliche Mikrodaten für die Sozial- und Wirtschaftswissenschaften, Forschungsdatenzentrum der Statistischen Landesämter: Beiträge zu den Nutzerkonferenzen des FDZ der Statistischen Landesämter 2005. |
 |
|
|
|
| Schäfer, C, Schräpler, JP and Müller, KR (2004). Identification, Characteristics and Impact of Faked and Fraudulent Interviews in Surveys. |
 |
|
|
|
| Schäfer, C, Schräpler, JP, Müller, KR and Wagner GG (2004). Automatic Identification of Faked and Fraudulent Interviews in Surveys by Two Different Methods. Discussion paper 441, DIW Berlin (German Institute for Economic Research). |
 |
|
|
|
| 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. |
 |
|
|
|
| Schraepler, J-P (2010). Benford's Law as an instrument for fraud detection in surveys using the data of the Socio-Economic Panel (SOEP). Socio-Economic Panel (SOEP) paper No. 273, March 2, 2010.. |
 |
|
|
|
| Schräpler, JP and Wagner, GG (2003). Identification, characteristics and impact of faked interviews in surveys. An analysis by means of genuine fakes in the raw data of SOEP. IZA Discussion paper no. 969. Also published as DIW Berlin (German Institute for Economic Research) discussion paper 392, December 2003 - online at www.diw-berlin.de/documents/publikationen/73/41110/dp392.pdf. |
 |
|
|
|
| Schürger, K (2008). Extensions of Black-Scholes processes and Benford's law. Stochastic Processes and their Applications 118(7), 1219-1243. ISSN:0304-4149. |
 |
|
|
|
| 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. |
 |
|
|
|
| Sen, A and Sen, U (2011). Benford's law detects quantum phase transitions similarly as earthquakes. EPL (Europhysics Letters) 95(5), 50008, 1-6. |
 |
|
|
|
| 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. Astroparticle Physics 33, 255-262. |
 |
|
|
|
| Shao, L and Ma, BQ (2010). The significant digit law in statistical physics. Physica A 389, 3109-3116. |
 |
|
|
|
| Shao, L and Ma, BQ (2010). First-digit law in nonextensive statistics. Physical Review E 82, 041110. |
 |
|
|
|
| Shi, YQ (2009). First digit law and its application to digital forensics. In H. J. Kim, S. Katzenbeisser, & A.T.S. Ho (Eds.), Digital watermarking: Seventh International Workshop (IWDW ’08) (pp. 444–456). Berlin: Springer-Verlag. ISSN:978-3-642-04437-3. |
 |
|
|
|
| Shikano, S and Mack, V (2011). When does 2nd Digit Benford´s Law-Test signal an election fraud? Facts or misleading test results. Jahrbücher für Nationalökonomie und Statistik 231 (5+6), 719-732. |
 |
|
|
|
| Snyder, MA, Curry, JH and Dougherty, AM (2001). Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law. Physical Review E 64(2), Art. No. 026222. ISSN:1063-651X. |
 |
|
|
|
| Stoschek, EP and Schönfeld, D (2002). Benford's Law - Places of interest near Benford`s Law. Module 45 of: Workshop on Design of Algorithms. |
 |
|
|
|
| Swanson, D, Cho, MJ and Eltinge, J (2003). Detecting possibly fraudulent or error-prone survey data using Benford’s law. pp 4172-4177 in: 2003 Joint Statistical Meetings - Section on Survey Research Methods, Proceedings of the American Statistical Association. |
 |
|
|
|
| Taylor, J (2005). Too many ties? An empirical analysis of the Venezuelan recall referendum counts. unpublished manuscript, Stanford University, USA. |
 |
|
|
|
| Tödter, KH (2009). Benford's Law as an Indicator of Fraud in Economics. German Economic Review 10(3), 339-351. |
 |
|
|
|
| Tolle, CR, Budzien, JL and LaViolette, RA (2000). Do dynamical systems follow Benford's law?. Chaos, 10(2), 331-336. ISSN:1054-1500. |
 |
|
|
|
| Torres, J, Fernandez, S, Gamero, A and Sola, A (2007). How do numbers begin? (The first digit law). European Journal of Physics 28(3), L17-L25. ISSN:0143-0807. |
 |
|
|
|
| Tsung, F, Zhou, Z and Jiang, W (2007). Applying manufacturing batch techniques to fraud detection with incomplete customer information. IIE Transactions 39(6), 671-680. |
 |
|
|
|
| Turner, P (2007). A classroom exploration of Benford's Law and some error finding tricks in accounting . Proceedings of the 21st biennial conference of the Australian Association of Mathematics Teachers Inc. Mathematics: Essential for Learning, Essential for Life, edited by K. Milton, H. Reeves & T. Spencer, 2007, pp. 250-259
. ISSN:978-1-875900-63-3. |
 |
|
|
|
| Valadier, M (2012). The Benford phenomenon for random variables. Discussion of Feller's way. arXiv:1203.2518. |
 |
|
|
|
| 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. |
 |
|
|
|
| Waaldijk, F (2005). On the foundations of constructive mathematics - Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10(3), 249-324. |
 |
|
|
|
| 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. |
 |
|
|
|
| Weisstein, EW (2003). Benford's Law. pp 181-182 in: CRC concise encyclopedia of mathematics, Chapman & Hall. |
 |
|
|
|
| Weisstein, EW (2009). Benford's Law. MathWorld (A Wolfram Web Resource). |
 |
|
|
|
| Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2007). Quantifying the Partial Volume Effect in PET Using Benford's Law. IEEE Transactions on Nuclear Science 54(5), 1616-1625 Part 1. ISSN:0018-9499. |
 |
|
|
|
| Williamson, J (2000). Random probability functions. Preprint. |
 |
|
|
|