Benford Online Bibliography

Newcomb, S (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics 4(1), pp. 39-40.

This work 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 again at a later date.

Abrantes-Metz, RM, Kraten, M, Metz, AD and Seow, G (2012). Libor Manipulation?. Journal of Banking & Finance 36(1), pp. 136-150. ISSN/ISBN:0378-4266. DOI:10.1016/j.jbankfin.2011.06.014.
Akkas, ME (2007). Denetimde Benford Kanununun Uygulanmasi (Application of Benford's Law in Audit). Gazi Universitesi Iktisadi ve Idari Bilimler Fakultesi Dergisi, vol.9, no.1, pp. 191-206. TUR
Alagoz, A and Ay, M (2001). Muhasebe denetiminde Benford kanunu temelli dijital analiz. Selçuk Üniversitesi Sosyal ve Ekonomik Araştırmalar Dergisi 4: 59-76. TUR
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 . DOI:10.2139/ssrn.1505147.
Alexopoulos, T and Leontsinis, S (2014). Benford's Law in Astronomy. Journal of Astrophysics and Astronomy, 35(4), pp. 639-648. ISSN/ISBN:0250-6335. DOI:10.1007/s12036-014-9303-z.
Alves, AD, Yanasee, HH and Soma, NY (2016). An analysis of bibliometric indicators to JCR according to Benford’s law. Scientometrics 107(3), pp. 1489–1499. DOI:10.1007/s11192-016-1908-3.
Alves, AD, Yanasse, HH and Soma, NY (2014). Benford's Law and articles of scientific journals: comparison of JCR® and Scopus data. Scientometrics 98, pp. 173-184. ISSN/ISBN:0138-9130. DOI:10.1007/s11192-013-1030-8.
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/ISBN:0002-9939.
Andriotis, P, Oikonomou, G and Tryfonas, T (2013). JPEG steganography detection with Benford's law. Digital Investigation 9(3-4), pp. 246-57. DOI:10.1016/j.diin.2013.01.005.
Arita, M (2005). Scale-freeness and biological networks. Journal of Biochemistry, 138 (1): 1-4. ISSN/ISBN:0021-924X. DOI:10.1093/jb/mvi094.
Ausloos, M, Castellano, R and Cerqueti, R (2016). Regularities and discrepancies of credit default swaps: a data science approach through Benford's law. Chaos, Solitons & Fractals 90, pp. 8-17. DOI:10.1016/j.chaos.2016.03.002.
Ausloos, M, Cerqueti, R and Lupi, C (2017). Long-range properties and data validity for hydrogeological time series: The case of the Paglia river. Physica A: Statistical Mechanics and its Applications 470, pp. 39-50. DOI:10.1016/j.physa.2016.11.137.
Ausloos, M, Cerqueti, R and Mir, TA (2017). Data science for assessing possible tax income manipulation: The case of Italy. Chaos, Solitons and Fractals 104, pp. 238–256. DOI:10.1016/j.chaos.2017.08.012.
Ausloos, M, Herteliu, C and Ileanu, B (2015). Breakdown of Benford’s law for birth data. Physica A: Statistical Mechanics and its Applications Volume 419, pp. 736–745. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2014.10.041.
Badal-Valero, E, Alvarez-Jareño, JA and Pavía, JM (2018). Combining Benford's Law and machine learning to detect money laundering. An actual Spanish court case. Forensic Science International 282, pp. 24-34. DOI:10.1016/j.forsciint.2017.11.008.
Baer, MB (2006). Rényi to Rényi - Source Coding under Siege. Proceedings of 2006 IEEE International Symposium on Information Theory, Seattle, WA, pp. 1258--1262. DOI:10.1109/ISIT.2006.262027.
Baer, MB (2006). Prefix coding under Siege. Preprint on CoRR archive: arXiv cs/0605099; last updated 28 March 2009.
Baer, MB (2007). Reserved-Length Prefix Coding. Proceedings of 2008 IEEE International Symposium on Information Theory, {ISIT}, Toronto, ON, Canada, July 6-11, 2008, pp. 2469--2473. DOI:10.1109/ISIT.2008.4595435.
Baer, MB (2007). Bounds on Generalized Huffman Codes. Preprint on CoRR archive: arXiv cs/0702059; last updated 7 Oct 2010.
Baláž, V, Nagasaka, K and Strauch, O (2010). Benford's law and distribution functions of sequences in (0, 1). Mathematical Notes, 2010, Vol. 88, No. 4, pp 449–463. Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 4, pp. 485–501. ISSN/ISBN:0001-4346. DOI:10.1134/S0001434610090178.
Barabesi, L, Cerasa, A, Cerioli, A and Perrotta, D (2018). Goodness-of-fit testing for the Newcomb-Benford law with application to the detection of customs fraud. Journal of Business & Economic Statistics 36(2), pp. 346-358. DOI:10.1080/07350015.2016.1172014.
Barbancho, I, Tardón, LJ, Barbancho, AM and Sbert, M (2016). Benford's Law for Music Analysis. Proceedings of the 16th ISMIR Conference, Malaga, Spain, pp. 735-741.
Baryła, M (2012). Some Remarks about Benford's Distribution. Mathematical Economics 8(15), pp. 5-15.
Baryła, M and Pociecha, J (2019). Euclidean distance as a measure of conformity to Benford's law in digital analysis for fraud detection. Book of Short Papers, Proceedings of the 12th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS), pp. 75-78.
Bauer, J and Gross, J (2011). Difficulties Detecting Fraud? The Use of Benford’s Law on Regression Tables. Journal of Economics and Statistics (Jahrbücher für Nationalökonomie und Statistik) 231(5-6), pp. 733-748.
Baumeister, J and Macedo, TG (2011). Von den Zufallszahlen und ihrem Gebrauch. Stand: 21, November 2011. GER
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/ISBN:0018-9529.
Becker, T, Burt, D, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J, Strauch, FW and Talbut, B (2018). Benford's Law and Continuous Dependent Random Variables. Annals of Physics 388, pp. 350–381. DOI:10.1016/j.aop.2017.11.013.
Becker, T, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J and Strauch, FW (2013). Benford's Law and Continuous Dependent Random Variables. Preprint arXiv:1309.5603 [math.PR]; last accessed October 23, 2018. DOI:10.1016/j.aop.2017.11.013.
Beer, TW (2009). Terminal digit preference: beware of Benford's law. Journal of Clinical Pathology 62(2), p. 192. DOI:10.1136/jcp.2008.061721.
Berger, A (2005). Multi-dimensional dynamical systems and Benford's law. Discrete and Continuous Dynamical Systems 13(1), pp. 219-237. ISSN/ISBN:1078-0947. DOI:10.3934/dcds.2005.13.219.
Berger, A (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), pp. 137-159. DOI:10.1080/10236198.2010.549012.
Berger, A (2015). Most linear flows on ℝ^d are Benford . Journal of Differential Equations 259(5), pp. 1933–1957. DOI:10.1016/j.jde.2015.03.016.
Berger, A, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), pp. 197-219. ISSN/ISBN:0002-9947. DOI:10.1090/S0002-9947-04-03455-5.
Berger, A and Eshun, G (2014). Benford solutions of linear difference equations. Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics Volume 102, pp. 23-60. ISSN/ISBN:978-3-662-44139-8. DOI:10.1007/978-3-662-44140-4_2.
Berger, A and Eshun, G (2016). A characterization of Benford's law in discrete-time linear systems. Journal of Dynamics and Differential Equations 28(2), pp. 432-469. ISSN/ISBN:1040-7294. DOI:10.1007/s10884-014-9393-y.
Berger, A and Hill, TP (2007). Newton’s method obeys Benford’s law. American Mathematical Monthly 114 (7), pp. 588-601. ISSN/ISBN:0002-9890.
Berger, A and Hill, TP (2010). Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law. University of Alberta preprint; posted on math arXiv 14May 2010.
Berger, A and Hill, TP (2011). Benford's Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem. The Mathematical Intelligencer 33(1), pp. 85-91. DOI:10.1007/ s00283-010-9182-3.
Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, pp. 1-126. DOI:10.1214/11-PS175.
Berger, A and Hill, TP (2015). An Introduction to Benford's Law. Princeton University Press: Princeton, NJ. ISSN/ISBN:9780691163062.
Berger, A, Hill, TP and Morrison, KE (2008). Scale-Distortion Inequalities for Mantissas of Finite Data Sets. Journal of Theoretical Probability 21(1), pp. 97-117. ISSN/ISBN:0894-9840.
Berger, A and Xu, C (2018). Best Finite Approximations of Benford’s Law. Journal of Theoretical Probability. DOI:10.1007/s10959-018-0827-z.
Berleant, D, Cheong, MP, Chu,C, Guan,Y, Kamal,A, Shedble, G, Ferson,S and Peters, JF (2003). Dependable Handling of Uncertainty. Reliable Computing 9(6), pp. 407-418. ISSN/ISBN:1385-3139. DOI:10.1023/A:1025888503247.
Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Turnage-Butterbaugh, C and Weinstein, M (2017). Benford Behavior of Generalized Zeckendorf Decompositions. In: Nathanson M. (eds) Combinatorial and Additive Number Theory II. CANT 2015, CANT 2016. Springer Proceedings in Mathematics & Statistics, vol 220. Springer, Cham. DOI:10.1007/978-3-319-68032-3_3.
Bharath, HM (2012). Benford’s Law: A theoretical explanation for base 2. Preprint arXiv:1211.7008 [stat.OT]; last accessed February 15, 2019.
Bhattacharya, S (2002). From Kautilya to Benford – Trends in Forensic and Investigative Accounting. Bond Business School Publications. Paper 60.
Bhole, G, Shukla, A and Mahesh, TS (2014). Benford distributions in NMR. Preprint arXiv:1406.7077 [physics.data-an]; last accessed June 7, 2018.
Bhole, G, Shukla, A and Mahesh, TS (2015). Benford analysis: A useful paradigm for spectroscopic analysis. Chemical Physics Letters 639, pp. 36–40. DOI:10.1016/j.cplett.2015.08.061.
Biau, D. (2015). The first-digit frequencies in data of turbulent flows. Physica A: Statistical Mechanics and its Applications Volume 440, pp. 147-154. DOI:10.1016/j.physa.2015.08.016.
Block, HW and Savits, TH (2010). A General Example for Benford Data. The American Statistician 64(4), pp. 335-339.
Blondeau Da Silva, S (2018). Benford or not Benford: new results on digits beyond the first. Preprint arXiv:1805.01291v1 [stat.OT]; last accessed July 29, 2018.
Blondeau Da Silva, S (2019). Benford or Not Benford: A Systematic But Not Always Well-Founded Use of an Elegant Law in Experimental Fields. Communications in Mathematics and Statistics, pp. 1-35. ISSN/ISBN:2194-6701. DOI:10.1007/s40304-018-00172-1.
Blondeau da Silva, S (2019). BeyondBenford: An R Package to Determine Which of Benford’s or BDS’s Distributions is the Most Relevant. Preprint hal-02310013; also posted on arXiv:1910.06104 [physics.soc-ph]; last accessed October 21, 2019.
Bohachevsky, IO, Johnson, ME and Stein, ML (2006). A derivation of Benford’s law. American Journal of Mathematical and Management Sciences, 26(3–4), pp. 355–370. ISSN/ISBN:0196-6324. DOI:10.1080/01966324.2006.10737678.
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 [Risk of Reviews based on Benford Law in the Fashion Sector]. Munich Personal RePEc Archive (MPRA) Paper No. 15352, posted 26 May 2009. FRE
Boring, EG (1920). The logic of the normal law of error in mental measurement. American Journal of Psychology 31, pp. 1-33. ISSN/ISBN:0002-9556. DOI:10.2307/1413989.
Bormashenko, E, Shulzinger, E, Whyman, G and Bormashenko, Y (2016). Benford’s law, its applicability and breakdown in the IR spectra of polymers. Physica A 444, pp. 524–529. DOI:10.1016/j.physa.2015.10.090.
Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), pp. 879-886. ISSN/ISBN:0002-9890. DOI:10.2307/2975136.
Boztepe, E (2013). Benford Kanunu ve Muhasebe Denetiminde Kullanılabilirliği. EUL Journal of Social Sciences IV:I, pp. 73-83. TUR
Bradley, JR and Farnsworth, DL (2009). What is Benford's Law?. Teaching Statistics 31(1), pp. 2-6. DOI:10.1111/j.1467-9639.2009.00347.x.
Bradley, JR and Farnsworth, DL (2009). Beispiele und Schüleraktivitäten zum BENFORD-Gesetz. Stochastik in der Schule (SiS) 29(3), pp. 28-32 . ISSN/ISBN:1614-0443. GER
Brähler, G, Bensmann, M and Emke, AL (2010). Der Einsatz mathematisch-statistischer Methoden in der digitalen Betriebsprüfung. Illmenauer Schriften zur Betriebswirtschaftslehre 4/2010. GER
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. ISSN/ISBN:978-3-940882-28-8. GER
Brandolini, L and Travaglini, G (2012). La legge di Benford. Posted on: http://pmf.cilea.it/file.php/1/articoli/PMF2012_Benford.pdf; last retrieved June 8, 2018 . ITA
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.
Brooks, D (2001). War, Politics & Customer Loyalty: Forecasting Using Benford’s Law. Frequencies, The Journal of Size Law Applications, 1(1), Aug. 2001, pp. 1-15.
Brown, K (2000). Benford's Law. Posted on mathpages.com blog; last accessed August 19, 2019.
Brown, RJC (2005). Benford's Law and the screening of analytical data: the case of pollutant concentrations in ambient air. Analyst 130(9), pp. 1280-1285. ISSN/ISBN:0002-2654. DOI:10.1039/B504462F.
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, pp. 59-63.
Bugarin, MS and da Cunha, FCR (2015). A didactic note on the use of Benford’s Law in public works auditing with an application to the construction of the Brazilian ‘Amazon Arena’ 2014 World Cup soccer stadium. Economia 66(1),pp. 23-55.
Burke, J and Kincanon, E (1991). Benford's Law and Physical Constants - The Distribution of Initial Digits. American Journal of Physics 59 (10), p. 952. ISSN/ISBN:0002-9505. DOI:10.1119/1.16838.
Burns, BD (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 Weinberg, R (1998). Using Benford’s law and neural networks as a review procedure. Managerial Auditing Journal 13(6), pp. 356-366. DOI:10.1108/02686909810222375.
Byalko, AV (1991). Statistics of Coefficients in Physical Formulas. Theoretical and Mathematical Physics 88(1), pp. 782-787. ISSN/ISBN:0040-5779. DOI:10.1007/BF01016350.
Cabarle, C (2019). Predicting the Risk of Fraud in Equity Crowdfunding Offers and Assessing the Wisdom of the Crowd. PhD Thesis, Temple University, ProQuest Dissertations Publishing, 2019. 13863507.
Cáceres, JLH, García, JLP, Ortiz, CMM and Dominguez, LG (2008). First digit distribution in some biological data sets. Possible explanations for departures from Benford's Law. Electronic J Biomed 1, pp. 27-35.
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2017). Leading Digits of Mersenne Numbers. Preprint in arXiv:1712.04425 [math.NT]; last accessed October 23, 2018.
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2019). Leading digits of Mersenne numbers. Experimental Mathematics, to appear. DOI:10.1080/10586458.2018.1551162.
Cai, Z, Hildebrand, AJ and Li, J (2018). A local Benford Law for a class of arithmetic sequences. Preprint arXiv:1808.01496 [math.NT]; last accessed October 22, 2018.
Cakebread, K (2011). Detecting Manipulations in Data with Benford's Law – A C# Class. Posted on codeproject.com; last accessed Jun 8, 2019.
Campanario, JM and Coslado, MA (2011). Benford's law and citations, articles and impact factors of scientific journals. Scientometrics 88(2), pp. 421-432. DOI:10.1007/s11192-011-0387-9.
Campos, L, Salvo, AE and Flores-Moya, A (2016). Natural taxonomic categories of angiosperms obey Benford's law, but artificial ones do not. Systematics and Biodiversity 14(5), pp. 431-440. ISSN/ISBN:1477-2000 (Print)/ 1. DOI:10.1080/14772000.2016.1181683.
Cella, RS and Rech, IJ (2017). Petrobas Case: Could Benford's Law Detect a Fraud?. Revista de Gestão, Finanças e Contabilidade, UNEB, Salvador, v. 7, n. 3, pp. 86-104. ISSN/ISBN:2238-5320. POR
Cella, RS and Zanolla, E (2018). Benford’s Law and transparency: an analysis of municipal expenditure. Brazilian Business Review, 15(4), pp. 331-347. DOI:10.15728/bbr.2018.15.4.2.
Chaitin-Chatelin, F (1994). Le calcul sur ordinateur a precision finie. Theorie et etat de l’art. CERFACS REPORT TR/PA/94/05. FRE
Chaitin-Chatelin, F (1995). Le calcul qualitatif. Comment donner un sens a des resultats faux?. CERFACS REPORT TR/PA/95/10. FRE
Chaitin-Chatelin, F (1996). Is finite precision arithmetic useful for physics?. Journal of Universal Computer Science 2(5), pp. 380-395.
Chaitin-Chatelin, F and Frayssé, V (1996). Lectures on Finite Precision Computations. SIAM.
Chakrabarthy, B, Moulton, PC, Pugachev, L and Wang, X (2019). Catch Me If You Can: Improving the Scope and Accuracy of Fraud Prediction. E-print available at SSRN: https://ssrn.com/abstract=3352667, March 13, 2019. DOI:10.2139/ssrn.3352667.
Chang, JC (2017). A Study of Benford's Law, With Applications to the Analysis of Corporate Financial Statements. Masters Thesis, The Graduate School Eberly College of Science, The Pennsylvania State University.
Chenavier, N and Schneider, D (2018). On the discrepancy of powers of random variables. Statistics & Probability Letters 134, pp. 5-14. DOI:10.1016/j.spl.2017.10.006.
Cho, WKT and Gaines, BJ (2007). Breaking the (Benford) law: Statistical fraud detection in campaign finance. American Statistician 61(3), pp. 218-223. ISSN/ISBN:0003-1305. DOI:10.1198/000313007X223496.
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. DOI:10.1007/s10899-009-9145-9.
Cinko, M (2014). Testing distribution of BIST-100 returns by Benford law. Journal of Economics, Finance and Accounting – (JEFA) 1(3), pp.184–191. TUR
Ciofalo, M (2009). Entropy, Benford’s first digit law, and the distribution of everything. Unpublished manuscript.
Clippe, P and Ausloos, M (2012). Benford's law and Theil transform of financial data. Physica A: Statistical Mechanics and its Applications 391(24), pp. 6556–6567.
Cohen, DIA (1976). An Explanation of the First Digit Phenomenon. Journal of Combinatorial Theory Series A 20(3), pp. 367-370. ISSN/ISBN:0097-3165.
Cohen, DIA and Katz, TM (1984). Prime Numbers and the First Digit Phenomenon. Journal of Number Theory 18(3), pp. 261-268. ISSN/ISBN:0022-314X. DOI:10.1016/0022-314X(84)90061-1.
Cong, M, Li, C and Ma, BQ (2019). First digit law from Laplace transform. Phys. Lett. A, 383(16), pp. 1836-1844. DOI:10.1016/j.physleta.2019.03.017 .
Corazza, M, Ellero, A and Zorzi, A (2010). Checking financial markets via Benford's law: the S&P 500 case. In: Corazza, M and Pizzi, C (Eds.): Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer, pp. 93-102. DOI:10.1007/978-88-470-1481-7_10.
Corazza, M, Ellero, A and Zorzi, A (2018). The importance of being “one” (or Benford’s law). Lettera Matematica 6(1), pp. 33–39. DOI:10.1007/s40329-018-0218-4.
Costa, JI, dos Santos, J and Travassos, S (2012). An Analysis of Federal Entities’ Compliance with Public Spending: Applying the Newcomb-Benford Law to the 1st and 2nd Digits of Spending in Two Brazilian States*. R. Cont. Fin. – USP, São Paulo, v. 23, n. 60, pp. 187-198.
Costa, JI, Travassos, SK, Soeiro, T and dos Santos, J (2013). Statistical analysis in detection of deviation occurrence in the distribution of first significant digit of state public spending in relation to the standard distribution defined in Newcomb-Benford’s law. In Proceedings of 10th CONTECSI International Conference on Information Systems and Technology Management, São Paulo, SP, Brasil. DOI:10.5748/9788599693094-10CONTECSI/RF-92 . POR
Cournane, S, Sheehy, N and Cooke, J (2014). The novel application of Benford's second order analysis for monitoring radiation output in interventional radiology. Physica Medica 30(4), pp. 413–418. DOI:10.1016/j.ejmp.2013.11.004.
Crato, N (2010). Mr. Benford. In: Figuring It Out: Entertaining Encounters with Everyday Math, Springer-Verlag: Berlin, pp. 173-177. ISSN/ISBN:978-3-642-04833-3. DOI:10.1007/978-3-642-04833-3_41.
Crocetti, E and Randi, G (2016). Using the Benford's Law as a first step to assess the quality of the cancer registry data. Frontiers in Public Health 4:225. DOI:10.3389/fpubh.2016.00225.
Cuff, V , Lewis, A and Miller, SJ (2015). The Weibull distribution and Benford’s law. Involve Vol. 8 No. 5, pp. 859–874. DOI:10.2140/involve.2015.8.859.
Cymrot, R, da Rocha, FR and Ferreira, DS (2012). Análise dos Dígitos Industriais Baseada na Lei de Benford e sua Aplicação Utilizando Rotinas Computacionais. Revista Mackenzie de Engenharia e Computaco, vol.12, number 1. POR
da Cunha, FCR and Bugarin, MS (2015). Benford's law for audit of public works: an analysis of overpricing in Maracanã soccer arena's renovation. Economics Bulletin 35(2), pp. 1168-1176.
da Silva, ASCD (2013). The application of Benford’s Law in detecting accounting fraud in the Financial Sector. Masters Thesis, Lisboa School of Economics & Management.
da Silva, CG and Carreira, PMR (2011). Selecting Audit Targets Using Benford’s Law. Technical Report No. 8, Institute for Systems Engineering and Computers at Coimbra . ISSN/ISBN:645-2631.
da Silva, CG and Carreira, PMR (2013). Selecting Audit Samples Using Benford's Law. AUDITING: A Journal of Practice & Theory Vol. 32, No. 2, pp. 53-65. DOI:10.2308/ajpt-50340.
da Silva, CG and Carreira, PMR (2019). Estimating the Proportion of Misstated Records in an Audit Data set using Benford’s Law. Journal of Accounting, Finance and Auditing Studies 5(2), pp. 146-162. DOI:10.32602/jafas.2019.25.
da Silva, WB, Travassos, SKM and Costa, JIF (2017). Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time. Revista Contabilidade & Finanças 28(73), pp. 11–26. DOI:10.1590/1808-057x201702690 .
Daniels, J, Caetano, SJ, Huyer, D, Stephen, A, Fernandes, J, Lytwyn, A and Hoppe, FM (2017). Benford's Law for Quality Assurance of Manner of Death Counts in Small and Large Databases. Journal of Forensic Sciences 62(5), pp. 1326-1331. DOI:10.1111/1556-4029.13437.
Dantuluri, A and Desai, S (2018). Do tau lepton branching fractions obey Benford's law?. Physica A: Statistical Mechanics and its Applications 506, pp. 919-928. DOI:10.1016/j.physa.2018.05.013.
Das, RC, Mishra, CS and Rajib, P (2017). Detection of Anomalies in Accounting Data Using Benford’s Law: Evidence from India. Journal of Social Science Studies 4(1), pp. 123-139. DOI:10.5296/jsss.v4i1.9873.
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), pp. 263-279. DOI:10.1016/S0927-5398(97)00024-8.
de Macedo, IAS and de Figueiredo, JJS (2018). Using Benford’s law on the seismic reflectivity analysis. Interpretation 6(3), pp. T689-T697. DOI:10.1190/int-2017-0201.1.
De Vries, P and Murk, AJ (2013). Compliance of LC50 and NOEC data with Benford's Law: An indication of reliability?. Ecotoxicology and Environmental Safety 98, pp. 171–178. DOI:10.1016/j.ecoenv.2013.09.002.
Delahaye, J-P (1999). L'étonnante loi de Benford. Pour la Science No. 351, pp. 90-95. FRE
Deleanu, IS (2017). Do Countries Consistently Engage in Misinforming the International Community about Their Efforts to Combat Money Laundering? Evidence Using Benford's Law. PLoS One 12(1), p. e0169632. DOI:10.1371/journal.pone.0169632.
Depken, CA (2008). Benford, Zipf and the blogosphere. Applied Economics Letters, 15(9), pp. 689–692. ISSN/ISBN:1350-4851. DOI:10.1080/13504850600735270.
Diaz, J, Gallart, J and Ruiz, M (2014). On the Ability of the Benford’s Law to Detect Earthquakes and Discriminate Seismic Signals. Seismological Research Letters 86(1), pp. 192-201. DOI:10.1785/0220140131.
Dickinson, JR (2002). A universal mathematical law criterion for algorithmic validity. Developments in Business Simulation and Experiential Learning 29, pp. 26-33.
Diekmann, A (2007). Not the First Digit! Using Benford's Law to Detect Fraudulent Scientific Data. Journal of Applied Statistics 34(3), pp. 321-329. ISSN/ISBN:0266-4763. DOI:10.1080/02664760601004940.
Diekmann, A (2012). Making Use of ‘‘Benford’s Law’’ for the Randomized Response Technique. Sociological Methods and Research 41(2), pp. 325-334. DOI:10.1177/0049124112452525.
Diekmann, A and Jann, B (2010). Benford’s Law and Fraud Detection: Facts and Legends. German Economic Review 11(3), pp. 397–401. DOI:10.1111/j.1468-0475.2010.00510.x.
Dimm, WC (2015). Detecting Fraud Using Benford's Law. Criminal Justice, Summer2015, Vol. 30 Issue 2, pp. 67-68.
Diniz, JA, Corrar, LJ and Slomski, V (2010). Análise digital: uma abordagem cognitiva na detecção de não conformidade em prestações de contas municipais. Anais do Congresso Controladoria e Contabilidade USP, São Paulo, SP, Brasil. POR
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. Proceedings of 6th Congresso USP de Controladoria e Contabilidade. POR
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, pp. 275-283 . ISSN/ISBN:0393-5965. DOI:10.1007/s10453-009-9132-8.
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), pp. 548-556. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2005.06.064.
Dorrestijn, J (2008). Graphing conformity of distributions to Benford’s Law for various bases. MSc thesis, Universiteit Utrecht, The Netherlands.
dos Santos, J, Tenório, JNB and Silva, LGC (2003). Uma aplicação da Teoria das probabilidades na contabilometria: A Lei de Newcomb-Benford como medida para análise de dados no campo da auditoria contábil. Contabilidade, Gestão e Governança, 6(1), pp. 35-54. POR
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 congas publicas. [The Focus is the Sampling Theory in the Fields of Traditional Accounting Auditin. Brazilian Business Review 2 (1), pp. 71-89. POR
dos Santos, J, Diniz, JA and Corrar, LJ (2005). The focus is the sampling theory in the fields of traditional accounting audit and digital audit: testing the Newcomb-Benford Law for the first digit of in public accounts. Brazilian Business Review 2(1), pp. 69-86.
dos Santos, J, Diniz, JA and Ribeiro Filho, JF (2003). A Lei de Newcomb- Benford: uma aplicação para determinar o DNA-equivalente das despesas no setor público. Proceedings of 3rd Congresso usp de controladoria e contrabilidade congresso, Brazil. POR
dos Santos, J, Filho, JFR, Lagioia, U, Filho, BFA and Araújo, IJCD (2009). Applications of the Newcomb-Benford law in the tax audit of the service tax (ISS). Revista Contabilidade & Finanças 20(49), pp. 63-78. DOI:10.1590/S1519-70772009000100006. POR
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651.
Druica, E, Oancea, B and Valsan, C (2018). Benford's law and the limits of digit analysis. International Journal of Accounting Information Systems 31, pp. 75–82. DOI:10.1016/j.accinf.2018.09.004.
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, pp. 99-112. ISSN/ISBN:1083-589X. DOI:10.1214/ECP.v13-1358.
Durrett, R (1996). Probability: Theory and Examples (2nd ed). Duxbury Press (p 301); [Benford refs on different pages in newer editions.].
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, pp. 17-34.
Egghe, L (2011). Benford’s law is a simple consequence of Zipf’s law. ISSI Newsletter 7(3), pp. 55–56.
Egghe, L and Guns, R (2012). Applications of the generalized law of Benford to informetric data. Journal of the American Society for Information Science and Technology 63(8), pp. 1662-1665. ISSN/ISBN:1532-2882. DOI:10.1002/asi.22690.
El Mouaaouy, F and Riepe, J (2018). Benford and the Internal Capital Market: A Useful Indicator of Managerial Engagement. German Economic Review 19, pp. 309-329. DOI:10.1111/geer.12129.
El Sehity, T, Hoelzl, E and Kirchler, E (2005). Price developments after a nominal shock: Benford's Law and psychological pricing after the euro introduction. International Journal of Research in Marketing 22(4), pp. 471-480. ISSN/ISBN:0167-8116. DOI:10.1016/j.ijresmar.2005.09.002.
Eliazar, II (2013). Benford's Law: A Poisson Perspective. Physica A 392(16) pp. 3360–3373. DOI:10.1016/j.physa.2013.03.057.
Eliazar, II (2017). Harmonic statistics. Annals of Physics, Volume 380, pp. 168-187. DOI:10.1016/j.aop.2017.03.016.
Engel, HA and Leuenberger, C (2003). Benford's law for exponential random variables. Statistics & Probability Letters 63, pp. 361-365. ISSN/ISBN:0167-7152.
Falcão, CSS (2014). A lei Benford para a distribuição dos primeiros dígitos. TCC (graduação) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Curso de Matemática. POR
Farbaniec, M, Grabiński, T, Zabłocki, B and Zając, W (2011). Application of the first digit law in credibility evaluation of the financial accounting data based on particular cases. Presentation for 10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Kraków, September 14-16, 2011.
Farkas, J and Gyürky, G (2010). The significance of using the Newcomb-Benford law as a test of nuclear half-life calculations. Acta Physica Polonica B 41(6), pp. 1213-1221. ISSN/ISBN:PL 0587-4254.
Farnsworth, DF, Horan, KK and Galgon, RM (2007). A guide to Benford's law. Mathematics and Computer Education 41(3), pp. 230-243. ISSN/ISBN:0730-8639.
Fellman, J (2014). The Benford paradox. Journal of statistical and econometric methods 3(4), pp. 1-20. ISSN/ISBN:2241-0384 .
Fellman, J (2016). En statistisk paradox. Quintensen No.2, pp. 15-17. SWE
Fellman, J (2017). Benfordparadoxen. Arkhimedes 2017(4), pp. 26-33. SWE
Ferreira, MJM (2013). Lei de Benford e detecção de fraude contabilística – Aplicação à indústria transformadora em Portugal. TRABALHO FINAL DE MESTRADO, Instituto Superior de Economia e Gestão, Universidade Técnica de Lisboa, Portugal. POR
Fewster, RM (2009). A Simple Explanation of Benford's Law. American Statistician 63(1), pp. 26-32. DOI:10.1198/tast.2009.0005.
Filho, MAFM, Poker, JH, Belli, MM and Segura, LC (2016). Bolsas de Valores dos BRICS: Uma Análise das Informações Financeiras Baseada na Lei de Benford [BRICS Stock Exchanges: An Analysis of Financial Information Based on Benford's Law]. Revista Contabilidade Vista e Revista, Universidade Federal de Minas Gerais, 64 Belo Horizonte 27(2), mai/ago. ISSN/ISBN: 0103-734X. POR
Finch, S (2011). Newcomb-Benford Law. Online publication - last accessed July 16, 2018.
Fisher, L (2009). The Perfect Swarm: The Science of Complexity in Everyday Life. Basic Books, pp. 159-162, 168, 242-243. ISSN/ISBN:978-0-465-01884-0.
Fonseca, PMT da (2016). Digit analysis using Benford's Law: A Bayesian approach. Masters Thesis, ISEG - Instituto Superior de Economia e Gestão, Lisbon School of Economics & Management, Portugal.
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.
Forster, RP (2006). Auditoria contábil em entidades do terceiro setor : uma aplicação da Lei Newcomb-Benford. Universidade de Brasília, Brasília. POR
Fox, RF and Hill, TP (2014). Hubble’s Law Implies Benford’s Law for Distances to Stars. Prerprint Physics arXiv; posted on December 4, 2014.
Frank, A (2006). Benford's law. Reason-and-Rhyme Blog.
Freeman, RB (2018). Benford's Law. Lecture 17 notes for Economics 1818 course, Harvard University.
Freidank, C-C and Kusch, A (2008). Das Benfordsche Gesetz als Instrument zur Aufdeckung von Unregelmäßigkeiten im Rahmen der Jahresabschlussprüfung. Wirtschaftswissenschaftliches Studium, Vol. 37, No. 2, pp. 100-102. ISSN/ISBN:0340-1650. GER
Frey, B (2006). Spot Faked Data. Hack #64 in: Statistic Hacks, pp 251-262 O'Reilley Media, Sebastopol, CA. ISSN/ISBN:978-0-596-10164-0.
Friar, JL, Goldman, T and Pérez-Mercader, J (2016). Ubiquity of Benford’s law and emergence of the reciprocal distribution. Physics Letters A 380(22), pp. 1895–1899. ISSN/ISBN:0375-9601. DOI:10.1016/j.physleta.2016.03.045.
Friedberg, SH (1984). The Distribution of First Digits. College Mathematics Journal 15(2), pp. 120-125. ISSN/ISBN:0049-4925. DOI:10.2307/2686516.
Frunza, M-C (2016). Benford's Law. Chapter 2K in: Solving Modern Crime in Financial Markets: Analytics and Case Studies, Academic Press, New York, pp. 233-245. DOI:10.1016/B978-0-12-804494-0.00017-6.
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, pp. 65051L-65051L-11. DOI:10.1117/12.704723.
Fu, Q, Villas-Boas, SB and Judge, G (2019). Does china income FSDs follow Benford? A comparison between Chinese income first significant digit distribution with Benford distribution. China Economic Journal 12(1), pp. 68-76. DOI:10.1080/17538963.2018.1477418.
Gambini, A, Scarpello, GM and Ritelli, D (2012). Probability of digits by dividing random numbers: A ψ and ζ functions approach. Expositiones Mathematicae, Vol. 30, No. 3, pp. 223–238. DOI:10.1016/j.exmath.2012.03.001.
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), pp. 7-15. ISSN/ISBN:0987-6936. DOI:10.4000/msh.10363. FRE
Gauvrit, N and Delahaye, J-P (2009). Scatter and regularity imply Benford's Law ... and more. Preprint arXiv: 0910.1359 [math.PR]; last accessed July 18, 2018 .
Gauvrit, N and Delahaye, J-P (2009). Loi de Benford générale (General Benford Law). Mathématiques et sciences humaines/ Mathematics and Social Sciences 186, pp. 5–15. FRE
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/ISBN:13978-981-4327-74-9.
Gauvrit, N, Houillon, J-C and Delahaye, J-P (2017). Generalized Benford’s Law as a Lie Detector. Advances in Cognitive Psychology 13(2), pp. 121-127. DOI:10.5709/acp-0212-x.
Gava, AM and Vitiello, L (2014). Inflation, Quarterly Balance Sheets and the Possibility of Fraud: Benford's Law and the Brazilian case. Journal of Accounting, Business & Management Vol. 21 Issue 1, pp. 43-52. ISSN/ISBN:0216-423X.
Gava, AM and Vitiello, LRdS (2007). Inflation, Quarterly Financial Statements and Fraud: Benford’s Law and the Brazilian Case. XXXI Encontro da ANPAD, Rio de Janeiro, Sep 22-26, 2007.
Genest, V and Genest, C (2011). La loi de Newcomb-Benford ou la loi du premier chiffre significatif. Bulletin Association Mathématique du Québec, Vol. LI, no 2, pp. 22-39. FRE
Genolini, C and Driss, T (2010). Eveiller l'intérêt pour la statistique par l'exemple. Statistique et Enseignement 1(2), pp. 49-57. FRE
Gent, I and Walsh, T (2001). Benford’s Law. Preprint. APES Research Report, 2001.
Geyer, A and Martì, J (2012). Applying Benford’s law to volcanology. Geology 40(4), pp. 327-330. DOI:10.1130/G32787.1 .
Geyer, CL and Williamson, PP (2004). Detecting Fraud in Data Sets Using Benford's Law. Communications in Statistics: Simulation and Computation 33(1), pp. 229-246. ISSN/ISBN:0361-0918. DOI:10.1081/SAC-120028442.
Geyer, D (2010). Detecting fraud in financial data sets. Journal of Business and Economics Research 8 (7), pp.75-83.
Giles, DE (2006). The Exact Asymptotic Distribution Function of Watson's U_N² for Testing Goodness-of-Fit with Circular Discrete Data. University of Victoria, Econometrics Working Paper EWP0607. ISSN/ISBN:1485-6441.
Giles, DE (2007). Benford's law and naturally occurring prices in certain eBay auctions. Applied Economics Letters 14(3), pp. 157-161. ISSN/ISBN:1350-4851. DOI:10.1080/13504850500425667.
Giuliano, R and Janvresse, E (2010). A unifying probabilistic interpretation of Benford's Law. Uniform Distribution Theory 5(2), pp. 169-182. ISSN/ISBN:1336-913X.
Göb, R (2007). Data Conformance Testing by Digital Analysis - A Critical Review and an Approach to More Appropriate Testing. Quality Engineering Volume 19(4), pp. 281-297. DOI:10.1080/08982110701633721.
Goodman, WM (2013). Reality Checks for a Distributional Assumption: The Case of “Benford’s Law”. JSM Proceedings. Alexandria, VA: American Statistical Association (2013), pp. 2789-2803. (Also published on the Statistical Literacy website, at URL: http://www.statlit.org/pdf/2013-Goodman-ASA.pdf) .
Goodman, WM (2016). The promises and pitfalls of Benford's law. Significance 13(3) pp. 38-41. DOI:10.1111/j.1740-9713.2016.00919.x.
Gorroochurn, P (2012). Benford and the Peculiar Behavior of the First Significant Digit (1938). Chapter 27 in: Classic problems of probability. John Wiley & Sons: Hoboken, NJ, 2012. ISSN/ISBN:978-1-118-06325-5 . DOI:10.1002/9781118314340.
Gottwalt, F, Waller, A and Liu, W (2016). Natural Laws as a Baseline for Network Anomaly Detection. In: Proceedings of 2016 IEEE Trustcom/BigDataSE/ISPA, pp. 370-377. DOI:10.1109/TrustCom.2016.0086.
Grabiński, K and Paszek, Z (2013). Examining Reliability of Large Financial Datasets Using Benford's Law. Economic Themes Vol. 51 Issue 3, pp. 515-524.
Grabowski, F and Trojanowski, P (2006). Benford's law in image analysis. Proceedings of the 1st Conference on Tools of Information Technology, Rzeszów, Poland, 15 September 2006, pp. 72-78.
Graham, SDJ, Hasseldine, J and Paton, D (2009). Statistical fraud detection in a commercial lobster fishery. New Zealand Journal of Marine and Freshwater Research Volume 43, Issue 1, pp. 457-463. DOI:10.1080/00288330909510014.
Gramm, R, Yost, J, Su, Q and Grobe, R (2017). Applications of the first digit law to measure correlations. Phys. Rev. E 95, 042136. DOI:10.1103/PhysRevE.95.042136.
Grammatikos, T and Papanikolaou, NI (2016). Applying Benford’s Law to Detect Accounting Data Manipulation in the Banking Industry. Luxembourg School of Finance Working Paper Series 11. DOI:10.2139/ssrn.2352775.
Grandison, S and Morris, RJ (2008). Biological pathway kinetic rate constants are scale-invariant. Bioinformatics 24(6), pp. 741-743. ISSN/ISBN:1367-4803. DOI:10.1093/bioinformatics/btn041.
Grendar, M, Judge, G and Schechter, L (2007). An empirical non-parametric likelihood family of data-based Benford-like distributions. Physica A: Statistical Mechanics and its Applications 380, pp. 429-438. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2007.02.062.
Grime, J (2011). Benford's Law - How mathematics can detect fraud!. singingbanana.com youtube channel; last accessed July 28, 2018.
Groce, D (2005). Benford's Law. Presentation at the Lyncean Group, California, USA, 23 March.
Guettler, S, Thiemann, F and Mueller, RAE (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/ISBN:1617-5468 / 978-8857. GER
Guilherme, HF, Montenegro, JM and dos Santos, J (2003). Uma aplicação da teoria das probabilidades na contabilometria: A Lei de Newcomb-Benford como uma Medida para Análise de Dados no Campo da Auditoria Contábil. Terceiro (III) Congresso da USP de Controladoria e Contabilidade. POR
Günnel, S and Tödter, K-H (2009). Does Benford's law hold in economic research and forecasting?. Empirica 36, pp. 273-292. DOI:10.1007/s10663-008-9084-1.
Haferkorn, M (2013). Humans vs. Algorithms – Who Follows Newcomb-Benford’s Law Better with Their Order Volume?. Enterprise Applications and Services in the Finance Industry: Lecture Notes in Business Information Processing Volume 135, pp 61-70 . ISSN/ISBN:9783642362187. DOI:10.1007/978-3-642-36219-4_4.
Hafner, EM (1979). Circular slide roulette. IEEE Communications Magazine 17(2), pp. 29-32.
Haigh, J (2003). Benford's Law. pp. 283-286 in: Taking Chances: Winning with Probability, Oxford University Press.
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), pp. 583-593.
Halperin, M and Lusk, EJ (2016). Navigating the Benford labyrinth: A big-data Analytic protocol illustrated using the Academic library Context. Knowledge Management & E-Learning 8(1), pp. 138-157.
Hamadeh, N (2004). Wireless Security and Traffic Modeling Using Benford's Law. Master’s Thesis, University of New Mexico, Albuquerque, NM, 2004 (99 pgs).
Hartmann, S and Brinkert, D (2018). Aufdeckung von Versicherungsbetrug bei Kfz-Schäden mit Hilfe des Benford-Tests [Detecting insurance fraud for vehicle damage using the Benford test]. Zeitschrift für die gesamte Versicherungswissenschaft 107(4), pp. 41-59. DOI:10.1007/s12297-017-0396-8. GER
Hasan, B (2002). Assessing Data Authenticity with Benford’s Law. Information System Control Journal, vol. 6, pp. 41-43.
Hassler, U and Hosseinkouchack, M (2019). Testing the Newcomb-Benford Law: experimental evidence. Applied Economics Letters, pp. 1-8. DOI: 10.1080/13504851.2019.1597248.
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), pp. 575-576.
Haynes, AH (2012). Detecting Fraud in Bankrupt Municipalities Using Benford's Law. Scripps Senior Theses. Paper 42, http://scholarship.claremont.edu/scripps_theses/42; last accessed November 12, 2014.
Hein, J, Zobrist, R, Konrad, C and Schuepfer, G (2012). Scientific fraud in 20 falsified anesthesia papers : detection using financial auditing methods. Der Anaesthesist 61(6), pp. 543-9. DOI:10.1007/s00101-012-2029-x.
Henselmann, K, Ditter, D and Scherr, E (2014). Irregularities in Accounting Numbers and Earnings Management - A Novel Approach Based on SEC XBRL Filings . 22nd Annual Research Workshop on Strategic and Emerging Technologies in Accounting, Auditing, and Tax, AAA Annual Meeting 2013, Anaheim, USA.
Henselmann, K, Ditter, D and Scherr, E (2015). Irregularities in accounting numbers and earnings management - A novel approach based on SEC XBRL filings. Journal of Emerging Technologies in Accounting 12 (1), pp. 117–151. DOI:10.2308/jeta-51247.
Henselmann, K, Scherr, E and Ditter, D (2013). Applying Benford's Law to individual financial reports: An empirical investigation on the basis of SEC XBRL filings. Working Papers in Accounting Valuation Auditing, No. 2012-1 [rev.].
Hesman, T (1999). Randomness rules. The Dallas Morning News, August 9.
Hickman, MJ and Rice, SK (2010). Digital Analysis of Crime Statistics: Does Crime Conform to Benford’s Law?. Journal of Quantitative Criminology 26(3), pp. 333-349. ISSN/ISBN:1573-7799. DOI:10.1007/s10940-010-9094-6.
Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363. ISSN/ISBN:0883-4237.
Hill, TP (1995). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), pp. 322-327. DOI:10.2307/2974952.
Hill, TP (1995). Base-Invariance Implies Benford's Law. Proceedings of the American Mathematical Society 123(3), pp. 887-895. ISSN/ISBN:0002-9939. DOI:10.2307/2160815.
Hill, TP (1996). A note on distributions of true versus fabricated data. Perceptual and Motor Skills 83, pp. 776-778 Part 1. ISSN/ISBN:0031-5215. DOI:10.2466/pms.1996.83.3.776.
Hill, TP (1997). Benford law. Encyclopedia of Mathematics Supplement, vol. 1, pp. 102-103.
Hill, TP (1999). The difficulty of faking data. Chance 12(3), pp. 27-31. DOI:10.1080/09332480.1999.10542154.
Hill, TP and Fox, RF (2016). Hubble’s Law Implies Benford’s Law for Distances to Galaxies. Journal of Astrophysics and Astronomy 37(1), pp. 1-8. ISSN/ISBN:0973-7758. DOI:10.1007/s12036-016-9373-1.
Hobza, T and Vajda, I (2001). On the Newcomb-Benford law in models of statistical data. Revista Matematica Complutense XIV(2), pp. 407-420. ISSN/ISBN:1139-1138.
Holz, CA (2013). The Quality of China's GDP Statistics. Munich Personal RePEc Archive Paper No. 51864; available online at http://mpra.ub.uni-muenchen.de/51864/; last accessed June 23, 2014.
Holz, CA (2014). The quality of China’s GDP statistics. China Economic Review, vol. 30, September 2014, pp. 309–338. DOI:10.1016/j.chieco.2014.06.009.
Hoppe, FM (2016). Benford's Law and Distractors in Multiple Choice Exams. International Journal of Mathematical Education in Science and Technology, 47(4), pp. 606–612. DOI:10.1080/0020739X.2015.1091515.
Horgan, J (2011). An introduction with computer science applications. Section 9.4 of Probability with R pp. 142-144, John Wiley & Sons . ISSN/ISBN:978-0-470-28073-7.
Hoyle, DC, Rattray, M, Jupp, R and Brass, A (2002). Making sense of microarray data distributions. Bioinformatics 18(4), pp. 576-584. ISSN/ISBN:1367-4803. DOI:10.1093/bioinformatics/18.4.576.
Hüngerbühler, N (2007). Benfords Gesetz über führende Ziffern: Wie die Mathematik Steuersündern das Fürchten lehrt. EDUCETH - Das Bildungsportal der ETH Zürich. GER
Hürlimann, W (2003). A generalized Benford law and its application. Advances and Applications in Statistics 3(3), pp. 217-228.
Hürlimann, W (2004). Integer powers and Benford’s law. International Journal of Pure and Applied Mathematics 11(1), pp. 39-46.
Hürlimann, W (2009). Generalizing Benford’s law using power laws: application to integer sequences. International Journal of Mathematics and Mathematical Sciences, Article ID 970284. DOI:10.1155/2009/970284.
Hürlimann, W (2014). A first digit theorem for powers of perfect powers. Communications in Mathematics and Applications 5(3), pp. 91-99. ISSN/ISBN:0975-8607.
Hürlimann, W (2014). A first digit theorem for square-free integer powers. Pure Mathematical Sciences 3(3), pp. 129 - 139. DOI:10.12988/pms.2014.4615.
Hürlimann, W (2015). Prime powers and generalized Benford law. Pioneer Journal of Algebra, Number Theory and its Applications 12/2015; 10(1-2):51-70.
Hürlimann, W (2015). Benford's Law in Scientific Research. International Journal of Scientific & Engineering Research, Volume 6, Issue 7, pp. 143-148. ISSN/ISBN:2229-5518.
Hürlimann, W (2015). A first digit theorem for powerful integer powers. SpringerPlus (2015) 4: 576. DOI:10.1186/s40064-015-1370-3.
Hürlimann, W (2016). First digit counting compatibility for Niven integer powers. Journal of Progressive Research in Mathematics 7(4). ISSN/ISBN:2395-0218.
Hürlimann, W (2016). First digit counting compatibility II: twin prime powers. Journal of Progressive Research in Mathematics(JPRM) 9(1), pp. 1341-1349. ISSN/ISBN:2395-0218.
Hussein, A (2019). An evaluation of last digit-based test as a tool for electoral fraud detection. Bachelor Thesis in Statistics, University of Gothenburg.
Huxley, SJ (1999). Why Benford's Law works and How to do digit analysis on spreadsheets. Presented at the 1999 International Conference of the Decision Sciences Institute.
Iafrate, JR (2014). Benford’s Law and Power Law Behavior in Fragmentation Processes. Undergraduate Honors Thesis, Williams College, Williamstown, MA.
Idrovo, AJ, Bojórquez-Chapela, I, Fernández-Niño, JA and Moreno-Montoya, J (2011). Performance of public health surveillance systems during the influenza A(H1N1) pandemic in the Americas: testing a new method based on Benford's Law. Epidemiol. Infect. 139(12), pp. 1827-34. ISSN/ISBN:1469-4409. DOI:10.1017/S095026881100015X.
Iorliam, A, Tirunagari, S, Ho, ATS, Li, S, Waller, A and Poh, N (2017). "Flow Size Difference" Can Make a Difference: Detecting Malicious TCP Network Flows Based on Benford's Law. arXiv:1609.04214v2 [cs.CR], last accessed February 6, 2017.
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.
Jameson, M, Thorner, J and Ye, L (2014). Benford's Law for Coefficients of Newforms. arXiv:1407.1577 [math.NT]; posted July 7, 2014; last accessed November 10, 2014.
Jang, D, Kang, JU, Kruckman, A, Kudo, J and Miller, SJ (2009). Chains of distributions, hierarchical Bayesian models and Benford's Law. Journal of Algebra, Number Theory: Advances and Applications 1(1), pp. 37-60.
Jann, B (2008). Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples. The Stata Journal 8(2), pp. 147-169.
Janvresse, E (2009). Quel est le début de ce nombre?. Images des Mathématiques, 26 December. FRE
Janvresse, É (2012). Quelques contributions aux probabilités eta la théorie ergodique. Document de synthèse présenté pour l’Habilitation à Diriger des Recherches, l’université de Rouen. FRE
Janvresse, E and De la Rue, T (2003). La loi de Benford. Quadature no. 48, pp. 5-9. FRE
Janvresse, E and de la Rue, T (2004). From Uniform Distributions to Benford’s Law. Journal of Applied Probability 41(4), pp. 1203-1210. ISSN/ISBN: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. DOI:10.2436/20.2002.01.18. CAT
Janvresse, É and de la Rue, T (2012). Averaging along Uniform Random Integers. Uniform Distribution Theory 7(2), pp. 35–60.
Jasak, Z (2011). Benford’s Law and Invariances. Journal of Mathematics and System Science, Volume 1, No.1 (Serial No.1). ISSN/ISBN:2159-5291.
Jasak, Z (2015). Benford's Law and Arithmetic Sequences. Journal of Mathematical Sciences: Advances and Applications, 32, pp. 1-16. ISSN/ISBN:0974-5750.
Jasak, Z (2016). Benford's Law and Hosmer-Lemeshow test. Journal of Mathematical Sciences: Advances and Applications Volume 41, 57-73.
Jasak, Z (2017). Sum invariance testing and some new properties of Benford's law. Doctorial Dissertation, University of Tuzla, Bosnia and Herzegovina.
Jasak, Z (2018). Benford's Law and Wilcoxon Test. Journal of Mathematical Sciences: Advances and Applications 52, pp. 69-81.
Jasak, Z and Banjanovic-Mehmedovic, L (2008). Detecting Anomalies by Benford's Law. In Proceedings of IEEE International Symposium on Signal Processing and Information Technology, 2008. ISSPIT 2008, pp. 453-458 . ISSN/ISBN:978-1-4244-3554-8. DOI:10.1109/ISSPIT.2008.4775660.
Jech, T (1992). The Logarithmic Distribution of Leading Digits and Finitely Additive Measures. Discrete Mathematics 108(1-3), pp. 53-57. ISSN/ISBN:0012-365X. DOI:10.1016/0012-365X(92)90659-4.
Jiang, H, Shen, J-J and Zhao, Y-M (2011). Benford’s Law in nuclear structure physics. Chinese Physics Letters, 28(3), pp. 32101–32104. DOI:10.1088/0256-307X/28/3/032101.
Joannes-Boyau, R, Bodin, T, Scheffers, A, Sambridge, M and May, SM (2015). Using Benford’s law to investigate Natural Hazard dataset homogeneity. Nature -Scientific Reports 5:12046, pp. 1-8 . DOI:10.1038/srep12046.
Joenssen, DW (2014). Testing for Benford's Law: A Monte Carlo Comparison of Methods. Preprint available at SSRN: https://ssrn.com/abstract=2545243; last accessed Mar 24, 2019 . DOI:10.2139/ssrn.2545243.
Joksimović, D, Knežević, G, Pavlović, V, Ljubić, M and Surovy, V (2017). Some Aspects of the Application of Benford’s Law in the Analysis of the Data Set Anomalies. In: Knowledge Discovery in Cyberspace: Statistical Analysis and Predictive Modeling. New York: Nova Science Publishers, pp. 85–120. ISSN/ISBN:978-1-53610-566-7.
Jolion, JM (2001). Images and Benford's Law. Journal of Mathematical Imaging and Vision 14(1), pp. 73-81. ISSN/ISBN:0924-9907. DOI:10.1023/A:1008363415314.
Jolissaint, P (2017). L’étonnante loi de Benford. VSMP Bulletin No. 135, pp. 13-17. FRE
Jordan, CE and Clark, SJ (2011). Detecting Cosmetic Earnings Management Using Benford’s Law. The CPA Journal 81 (2), pp. 32–37.
Judge, G and Schechter, L (2009). Detecting problems in survey data using Benford’s law. J. Human Resources 44, pp. 1-24. DOI:10.3368/jhr.44.1.1.
Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. posted on arXiv 8 March 2009 - arXiv:0901.3047v2.
Kafri, O (2009). The Distributions in Nature and Entropy Principle. CoRR, vol. abs/0907.4852.
Kappal, S (2017). HealthCare Industry’s Savior: Using the Benford's Law (The Law of First Digit) to Debunk the Fraudsters. Blog on Data Science Central, posted on January 16, 2017; last accessed October 15, 2018.
Karavardar, A (2014). Benford’s Law and an Analysis in Istanbul Stock Exchange (BIST). International Journal of Business and Management, 9(4), pp. 160-172. DOI:10.5539/ijbm.v9n4p160.
Kazemitabar, Jal and Kazemitabar, Jav (2019). Measuring the conformity of distributions to Benford's law. Communications in Statistics - Theory and Methods, pp. 1-7. DOI:10.1080/03610926.2019.1590599.
Kha, V and Lam, B (2011). Das Benford’sche Gesetz. Facharbeit Mathematik, Max-von-Laue-Gymnasium Koblenz. GER
Khosravani, A and Rasinariu, C (2013). n-Digit Benford Distributed Random Variables. Advances and Applications in Statistics, 36, pp. 119-130.
Khosravani, A and Rasinariu, C (2018). Emergence of Benford's Law in Classical Music. Unpublished manuscript.
Kienle, S (2015). What Benford Can Tell Us About Cover Pools – An Empirical Analysis. International Business & Economic Research Journal 14(6), pp. 829-834. DOI:10.19030/iber.v14i6.9489.
Kim, S (2012). Benford’s law in non-equilibrium processes: Droplet collisions case. Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 20, pp. 4970–4975. DOI:10.1016/j.physa.2012.05.043.
Klink, S and Henke, M (2004). Das Gesetz der ersten Ziffer. Projektarbeit im Rahmen des Fachwissenschaftlichen Seminars (Leitung: Prof. Dr. Maria Specovius-Neugebauer), Universität Kassel, Germany. GER
Knot, R (2016). The Mathematical Magic of the Fibonacci Numbers. Posted on R. Knot's Fibonacci blog - see Chapter 7; last accessed August 1, 2019.
Knuth, DE (1997). The Art of Computer Programming. pp. 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA.
Kocameşe, M (2006). Benford Kanunu ve Vergi Denetiminde Kullanılabilirliğinin Đncelenmesi [Benford's Law and Review of the Usability of Tax Audit]. Masters Thesis, Marmara University, Institute of Social Sciences, Business Administration, Department Of Accounting. TUR
Kontorovich, AV and Miller, SJ (2005). Benford's Law, Values of L-functions and the 3x+ 1 Problem. Acta Arithmetica 120(3), pp. 269-297. ISSN/ISBN:0065-1036. DOI:10.4064/aa120-3-4.
Kopczewski, T and Okhrimenko, I (2019). Playing with Benford’s Law. E-print posted on http://www.nbp.pl/badania/seminaria/8ii2019.pdf; last accessed June 6, 2019.
Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. posted December 21, 2006 on arXiv:math/0612627.
Kossovsky, AE (2012). Statistician's New Role as a Detective - Testing Data for Fraud. Ciencias Económicas 30(2), pp. 179-200 . ISSN/ISBN:0252-9521.
Kossovsky, AE (2014). Benford's Law: Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications. World Scientific Publishing Company: Singapore. ISSN/ISBN:978-981-4583-68-8.
Kottke, J (2006). Catching cheaters with Benford's Law . http://www.kottke.org/06/02/catching-cheaters-with-benfords-law.
Kozlov, VV (2005). Weighted averages, uniform distribution, and strict ergodicity. Russian Mathematical Surveys 60(6), pp. 1121-1146. ISSN/ISBN:0036-0279. DOI:10.1070/RM2005v060n06ABEH004284.
Krawiec, J (2012). Prawo Benforda jako narzędzie wykrywania manipulacji finansowych [Benford's law as a tool for detecting financial manipulation]. KWARTALNIK NAUK O PRZEDSIĘBIORSTWIE, 2012, 4, pp. 86-91. POL
Kreiner, WA (2002). First digit law. Preprint, Universität Ulm. GER
Kreiner, WA (2003). On the Newcomb-Benford Law. Zeitschrift für Naturforschung Section A - A Journal of Physical Sciences 58(11), pp. 618-622. ISSN/ISBN:0932-0784. DOI:10.1515/zna-2003-1105.
Kreuzer, M, Jordan, D, Antkowiak, B, Drexler, B, Kochs, EF and Schneider, G (2014). Brain electrical activity obeys Benford's law. Anesth. Analg. 118(1), pp. 183-91. DOI:10.1213/ANE.0000000000000015.
Kruger, PS and Yadavalli, VSS (2017). The Power of One: Benford's Law. South African Journal of Industrial Engineering Vol 28(2), pp. 1-13. DOI:10.7166/28-2-1753.
Kumar, K and Bhattacharya, S (2007). Detecting the dubious digits: Benford’s law in forensic accounting. Significance 4(2), pp. 81-83. DOI:10.1111/j.1740-9713.2007.00234.x.
Kundt, TC (2014). Applying "Benford's law" to the Crosswise Model: Findings from an online survey on tax evasion . Helmut-Schnidt-University, Department of Economics, Working Paper, 148/2014.
Kuruppu, N (2019). The Application of Benford’s Law in Fraud Detection: A Systematic Methodology. International Business Research, Canadian Center of Science and Education 12(10), pp. 1-10. DOI:10.5539/ibr.v12n10p1.
Lacasa, L (2019). Newcomb–Benford law helps customs officers to detect fraud in international trade. Proceedings of the National Academy of Sciences 116(1), pp. 11-13. DOI:10.1073/pnas.1819470116.
Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, pp. 289-303. ISSN/ISBN:0024-6107. DOI:10.1112/S0024610706023131.
Lagioia, UCT, de Araújo, IJC, de Figueiredo Alves Filho, B, Barros, MAB and de Almeida Santos, SGO (2011). Aplicabilidade da Lei de Newcomb-Benford nas fiscalizações do Imposto sobre Serviços. Revista de Contabilidade e Finanças –USP, São Paulo, 22 (56) pp. 203-224. ISSN/ISBN: 1519-7077. POR
Lebiere, C (1999). The dynamics of cognition: an ACT-R model of cognitive arithmetic. Kognitionswissenschaft 8(1), pp. 5-19. DOI:10.1007/BF03354932.
Lee, J, Cho, WKT and Judge, G (2010). Stigler’s approach to recovering the distribution of first significant digits in natural data sets. Statistics and Probability Letters 80(2), pp. 82-88. DOI:10.1016/j.spl.2009.09.015.
Lee, J and de Carvalho, M (2019). Technological improvements or climate change? Bayesian modeling of time-varying conformance to Benford’s Law. PLoS ONE 14(4): e0213300. DOI:10.1371/journal.pone.0213300.
Lee, J and Judge, GC (2008). Identifying falsified clinical data. CUDARE working paper 1073, University of California, Berkeley.
Leemann, L and Bochsler, D (2014). A systematic approach to study electoral fraud. Electoral Studies, Vol. 35, Num. 0, pp. 33-47. ISSN/ISBN:0261-3794. DOI:10.1016/j.electstud.2014.03.005.
Lehman, M, Watson, M and Jones, T (2007). Flexing Your (Super) Financial Sleuth Power. Journal of Accountancy, vol. 203, no. 6, pp. 50–54.
Lemons, DS (2019). Thermodynamics of Benford's first digit law. American Journal of Physics 87 (10) pp. 787-790. DOI:10.1119/1.5116005.
Lenci, A (2017). Benford's Law. Senior Essay, Saint Mary’s College of California, Department of Mathematics, Moraga, CA.
Li, F, Han, S, Zhang, H, Ding, J, Zhang, J and Wu, J (2019). Application of Benford’s law in Data Analysis. Journal of Physics: Conference Series 1168, pp. 032133. DOI:10.1088/1742-6596/1168/3/032133.
Li, Q and Fu, Z (2016). Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford’s law. Commun Nonlinear Sci Numer Simulat 33, pp. 91–98. DOI:10.1016/j.cnsns.2015.09.006.
Li, Q, Fu, Z and Yuan, N (2015). Beyond Benford's Law: Distinguishing Noise from Chaos. PLoS ONE, 10, e0129161. DOI:10.1371/journal.pone.0129161.
Li, Z, Cong, L and Wang, H (2004). Discussion on Benford’s law and its application. posted on arXiv:math/0408057, Aug 4, 2004.
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. Journal of the Chinese Institute of Industrial Engineers, 26(5), pp. 337-343. DOI:10.1080/10170660909509148.
Lin, F, Guan, L and Fang, W (2011). Heaping In Reported Earnings: Evidence from Monthly Financial Reports of Taiwanese Firms. Emerging Markets Finance & Trade / January–February 2011, Vol. 47, No. 2, pp. 62–73. ISSN/ISBN:1540-496X. DOI:10.2753/REE1540-496X470205.
Lipovetsky, S (2008). Comparison among different patterns of priority vectors estimation methods. International Journal of Mathematical Education in Science 39(3), pp. 301-311. DOI:10.1080/00207390701639532.
Little, B, Rejesus, R, Schucking, M and Harris, R (2008). Benfords Law, data mining, and financial fraud: A case study in New York State Medicaid data. WIT Transactions on Information and Communication Technologies 40, pp. 195-204. DOI:10.2495/DATA080191.
Liu, XJ, Zhang, XP, Ni, DD and Ren, ZZ (2011). Benford’s law and cross-sections of A(n,α)B reactions. European Physical Journal A: Hadrons and Nuclei, 47(6), p. 78. DOI:10.1140/epja/i2011-11078-3.
Logan, JL and Goudsmit, SA (1978). The First Digit Phenomenon. Proceedings of the American Philosophical Society 122(4), pp. 193-197. ISSN/ISBN:0003-049X.
Lolbert, T (2006). Digital Analysis: Theory and Applications in Auditing. Hungarian Statistical Review 84, Special number 10, p. 148. ISSN/ISBN:0039 0690.
Lolbert, T (2007). Statisztikai eljárások alkalmazása az ellenőrzésben (Applications of statistical methods in monitoring). PhD thesis, Corvinus University, Budapest, Hungary. HUN
Lolbert, T (2008). On the non-existence of a general Benford's law. Mathematical Social Sciences 55(2), pp. 103-106. ISSN/ISBN:0165-4896. DOI:10.1016/j.mathsocsci.2007.09.001.
Lowe, T, Murphy, S and Hayward, J (1999). The first digit law. Preprint.
Lu, OF and Giles, DE (2006). Benford's Law and Psychological Barriers in Certain eBay Auctions. Econometrics Working Paper EWP0606, University of Victoria. ISSN/ISBN:1485-6441.
Lu, OF and Giles, DE (2010). Benford’s law and psychological barriers in certain eBay auctions. Applied Economics Letters, 17, pp. 1005–1008. DOI:10.1080/13504850802631814.
Luo, P and Li, Y (2018). A new quantity for statistical analysis: "Scaling invariable Benford distance''. Preprint in: arXiv:1803.01117 [physics.data-an]; last accessed October 25, 2018.
Luque, B and Lacasa, L (2009). The first-digit frequencies of prime numbers and Riemann zeta zeros. Proc. Royal Soc. A, published online 22Apr09. DOI:10.1098/rspa.2009.0126.
Lusk, EJ and Halperin, M (2014). Detecting Newcomb-Benford digital frequency anomalies in the audit context: Suggested x^2 test possibilities. Accounting and Finance Research 3(2), pp. 191-205. DOI:10.5430/afr.v3n2p191.
Lusk, EJ and Halperin, M (2014). Using the Benford Datasets and the Reddy and Sebastin Results to Form an Audit Alert Screening Heuristic: An Appraisal. The IUP Journal of Accounting Research and Audit Practices, vol. XIII, issue 3, pp. 56-69.
Lusk, EJ and Halperin, M (2014). Detecting Digital Frequency Anomalies as Benchmarked against the Newcomb-Benford Theoretical Frequencies: Calibrating the Chi2 Test: A Note. International Business Research 7(2). ISSN/ISBN:1913-9012. DOI:10.5539/ibr.v7n2p72 .
Makous, W (2011). Biblical Longevities: Empirical Data or Fabricated Numbers?. Perspectives on Science and Christian Faith, Vol. 63, No. 2, pp. 117-130.
Manack, C and Miller, SJ (2015). Leading digit laws on linear Lie groups. Research in Number Theory 1:22. DOI:10.1007/s40993-015-0024-4.
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), pp. 956-961.
Mansilla, R (2006). Análisis de los resultados electorales a partir de la Ley de Benford. preprint UNAM. SPA
Margellou, AG and Pomonis, PJ (2020). Benford's law, Zipf's law and the pore properties in solids. Microporous and Mesoporous Materials 292, p. 109735. DOI:10.1016/j.micromeso.2019.109735.
Martín, AB (2003). Sistematización del proceso de depuración de los datos en estudios con seguimientos. PhD Thesis, Universitat Autònoma de Barcelona, Spain. SPA
Massé, B and Schneider, D (2011). A survey on weighted densities and their connection with the first digit phenomenon. Rocky Mountain Journal of Mathematics 41(5), 1395-1415. ISSN/ISBN:0035-7596. DOI:10.1216/RMJ-2011-41-5-1395.
Massé, B and Schneider, D (2012). Random number sequences and the first digit phenomenon. Electronic Journal of Probability, Vol 17, Article 86, pp. 1-17 . DOI:10.1214/EJP.v17-1900.
Medzihorsky, J (2015). Election Fraud: A Latent Class Framework for Digit-Based Tests. Political Analysis 23(4), pp. 506-517. DOI:10.1093/pan/mpv021.
Mendez, PF, Furrer, R, Ford, R and Ordóñez, F (2008). Scaling laws as a tool of materials informatics. JOM Journal of the Minerals, Metals and Materials Society 60(3), pp. 60-66. ISSN/ISBN:1047-4838. DOI:10.1007/s11837-008-0036-9.
Mendez, PF and Ordóñez, F (2005). Scaling Laws From Statistical Data and Dimensional Analysis. J. Appl. Mech. - Transactions of the ASME 72(5), pp. 648-657. ISSN/ISBN:0021-8936. DOI:10.1115/1.1943434.
Michalski, T and Stoltz, G (2013). Do Countries Falsify Economic Data Strategically? Some Evidence That They Might. The Review of Economics and Statistics, Vol. 95, No. 2, pp. 591-616. DOI:10.1162/REST_a_00274.
Miller, SJ (2015). How a simple observation from the 1800s about patterns in big data sets can fight fraud. Posted on TheConversation website (Science + Technology), December 10; last accessed April 11, 2019.
Miller, SJ (2016). Can math detect fraud? CSI: Math: The natural behavior of numbers. Presentation at Science Cafe, Northampton, September 26; last accessed July 4, 2019.
Miller, SJ and Nigrini, MJ (2006). Order Statistics and Shifted Almost Benford Behavior. Posted on Math Arxiv, January 13, 2006.
Miller, SJ and Nigrini, MJ (2008). The Modulo 1 Central Limit Theorem and Benford's Law for Products. International Journal of Algebra 2(3), pp. 119 - 130.
Miller, SJ (ed.) (2015). Benford's Law: Theory and Applications. Princeton University Press: Princeton and Oxford. ISSN/ISBN:978-0-691-14761-1.
Mir, TA (2011). Law of the leading digits and the ideological struggle for numbers. physics arXiv:1104.3948. DOI:10.1016/j.physa.2011.09.001.
Mir, TA (2012). The law of the leading digits and the world religions. Physica A: Statistical Mechanics and its Applications, 391 (2012), pp. 792-798. DOI:10.1016/j.physa.2011.09.001.
Mir, TA (2012). The leading digit distribution of the worldwide illicit financial flows. arXiv:1201.3432. DOI:10.1007/s11135-014-0147-z.
Mir, TA (2014). The Benford law behavior of the religious activity data. Physica A 408, pp. 1-9. DOI:10.1016/j.physa.2014.03.074.
Mir, TA (2016). Citations to articles citing Benford's law: a Benford analysis. arXiv:1602.01205; posted Feb 3, 2016.
Mir, TA (2016). The leading digit distribution of the worldwide illicit financial flows. Quality & Quantity vol. 50, p. 271-281. DOI:10.1007/s11135-014-0147-z.
Mir, TA and Ausloos, M (2018). Benford's law: a 'sleeping beauty' sleeping in the dirty pages of logarithmic tables. Journal of the Association for Information Science and Technology 69(3) pp. 349–358. DOI:10.1002/asi.23845.
Mir, TA, Ausloos, M and Cerqueti, R (2014). Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions. Eur. Phys. J. B (2014) 87: 261. ISSN/ISBN:1434-6028. DOI:10.1140/epjb/e2014-50525-2.
Mitchell, J (2001). Clustering and psychological barriers: the importance of numbers. Journal of Futures Markets 21(5), pp. 395-428. ISSN/ISBN:0270-7314. DOI:10.1002/fut.2.
Mochty, L (2002). Die Aufdeckung von Manipulationen im Rechnungswesen - Was leistet das Benford's Law?. Die Wirtschaftsprüfung 14, pp. 725-736. GER
Mohammadi, S, Nezhad, BM, Mohammadi, A and Zahmati, F (2015). Benford's Law and its Application in Auditing. International Journal of Industrial Organization 6(2), pp. 13-16. DOI:10.13106/ijidb.2015.vol6.no2.13..
Moin, SS and Islam, S (2017). Benford's law for detecting contrast enhancement. Proceedings of 2017 Fourth International Conference on Image Information Processing (ICIIP), Dec 21-23, pp. 1-4. DOI:10.1109/ICIIP.2017.8313717.
Möller, M (2009). Measuring the Quality of Auditing Services with the Help of Benford’s Law - An Empirical Analysis and Discussion of this Methodical Approach. E-print available at: http://ssrn.com/abstract=1529307; last accessed June 23, 2014. DOI:10.2139/ssrn.1529307.
Morag, S and Salmon-Divon, M (2019). Characterizing Human Cell Types and Tissue Origin Using the Benford Law. Cells 8(9), p. 1004. DOI:10.3390/cells8091004.
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), pp. 1597-1604. ISSN/ISBN:0129-1831. DOI:10.1142/S0129183106010054.
Moret, MA, de Senna, V, Santana, MC and Zebende, GF (2009). Geometric Structural Aspects of Proteins and Newcomb-Benford Law. International Journal of Modern Physics C 20(12), pp. 1981-1988. DOI:10.1142/S0129183109014874.
Morrison, KE (2010). The Multiplication Game. Mathematics Magazine 83, pp. 100-110. ISSN/ISBN:0025-570X. DOI:10.4169/002557010X482862.
Mörters, P (2001). Benford’s Gesetz über die Verteilung der Ziffern. Habilitationsvorlesung. Kaiserslauten und Bath. GER
Morton, E (2019). Corporate Tax Transparency Reporting and Benford’s Law. Australian Tax Forum 34(1).
Morzy, M, Kajdanowicz, T and Szymański, BK (2016). Benford’s Distribution in Complex Networks. Scientific Reports 6:34917. DOI:1038/srep34917.
Motahari, AM (2013). Benford’s Law and the numerical structure of Quran. accessed August 23, 2016 at: http://submission.org/Benford.html.
Nagasaka, K (2008). Benford’s Law to Base g of Order r in the Sense of a Certain Density. Short talk at: Colloque international sur la répartition uniforme, Marseille, January 2008.
Nebel, J-C and Pezzulli, S (2012). Distribution of Human Genes Observes Zipf's Law. Kingston University Research & Innovation Reports (KURIR), Vol. 8, 2012. ISSN/ISBN:1749-5652.
Nguyen, TQ (2019). What Influence Earnings Management By Share-Financed Acquirers Prior To Deal Announcements?. PhD Thesis for University of East London. DOI:10.15123/uel.86y35.
Ni, D and Ren, Z (2008). Benford’s law and half-lives of unstable nuclei. Eur. Phys. J. A 38, 251–255. DOI:10.1140/epja/i2008-10680-8.
Ni, D, Wei, L and Ren, Z (2009). Benford's Law and β-Decay Half-Lives. Commun. Theor. Phys. 51, 713-716. DOI:10.1088/0253-6102/51/4/25.
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). Digital Analysis and the Reduction of Auditor Litigation Risk. Proceedings of the 1996 Deloitte & Touche / University of Kansas Symposium on Auditing Problems, ed. M. Ettredge, University of Kansas, Lawrence, KS, pp. 69-81.
Nigrini, MJ (1999). Peculiar patterns of first digits. IEEE Potentials 18(2), pp. 24-27. DOI:10.1109/45.755849.
Nigrini, MJ (2001). Digital Analysis Using Benford's Law: Tests and Statistics for Auditors. EDPACS - The EDP Audit, Control, and Security Newsletter 28(9), pp. 1-2. DOI:10.1201/1079/43266.28.9.20010301/30389.4.
Nigrini, MJ (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection . John Wiley & Sons: Hoboken, New Jersey. ISSN/ISBN:978-1-118-15285-0. DOI:10.1002/9781119203094.
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), pp. 1-14. DOI:10.2202/1935-1690.1449.
O'Brien, C (2003). Working Group on Methods on Fish Stock Assessments. ICES CM 2003/D:03 Ref. ACFM, G.
Oleksy, M (2010). Data Mining und Benford's Law als Controllinginstrumente. Band 45, Wismarer Schriften zu Management und Recht, Europäischer Hochschulverlag, Bremen. ISSN/ISBN:978-3867414-40. GER
Orita, M, Hagiwara, Y, Moritomo, A, Tsunoyama, K, Watanabe, T and Ohno, K (2013). Agreement of drug discovery data with Benford's law. Expert Opinion on Drug Discovery 8(1), pp. 1-5. DOI:10.1517/17460441.2013.740007.
Orita, M, Moritomo, A, Niimi, T and Ohno, K (2010). Use of Benford's law in drug discovery data. Drug Discovery Today, Vol. 15, Nos. 9–10, pp. 328–331. ISSN/ISBN:1359-6446. DOI:10.1016/j.drudis.2010.03.003.
Ozawa, K (2019). Continuous Distributions on (0, ∞) Giving Benford’s Law Exactly. Preprint arXiv:1905.02031 [math.PR]; last accessed June 6, 2019.
Özer, G and Babacan, B (2013). Benford's Law and Digital Analysis: Application on Turkish Banking Sector. Business & Economics Research Journal Vol. 4 Issue 1, pp. 29-41. ISSN/ISBN:1309-2448.
Pain, J-C (2008). Benford’s law and complex atomic spectra. Physical Review E 77(1): Art. No. 012102. ISSN/ISBN:1539-3755. DOI:10.1103/PhysRevE.77.012102.
Pain, J-C (2013). Regularities and symmetries in atomic structure and spectra. High Energy Density Physics, Vol. 9, No. 3, pp. 392–401. DOI:10.1016/j.hedp.2013.04.007.
Pan, D, Shao, L and Ma, BQ (2010). Benford's Law in Statistical Physics. Wolfram Online Demonstrations Projects.
Park, JA, Kim, M and Yoon, S (2016). Evaluation of Large-scale Data to Detect Irregularity in Payment for Medical Services. Methods of Information in Medicine 55(03), pp. 284-291. DOI:10.3414/ME15-01-0076.
Park, JH, Choi, CH and Cho, EH (2016). Preliminary Study to Detect Match-Fixing: Benford’s Law in Badminton Rally Data. Journal of Physical Education and Sports Management, 3(1), pp. 64-77. ISSN/ISBN:2373-2156. DOI:10.15640/jpesm.v3n1a5.
Pavlović, V, Knežević, G, Joksimović, M and Joksimović, D (2019). Fraud Detection in Financial Statements Applying Benford's Law with Monte Carlo Simulation. Acta oeconomica 69(2), pp.217-239. DOI:10.1556/032.2019.69.2.4.
Pérez-González, F, Heileman, G and Abdallah, CT (2007). A generalization of Benford’s Law and its application to images. European Control Conference’2007, Kos, Greece, July 2007, pp. 3613 - 3619. ISSN/ISBN:9783952417386.
Pericchi, L and Torres, DA (2011). Quick anomaly detection by the Newcomb-Benford law, with applications to electoral processes data from the USA, Puerto Rico and Venezuela. Statistical Science 26(4), pp. 502-16. DOI:10.1214/09-STS296.
Peterson, I (1998). First Digits. Science News Online, Ivars Peterson's MathTrek, 27 June.
Phatarfod, R (2013). Some aspects of the Benford law of leading significant digits. The Mathematical Scientist, Applied Probability Trust, 38 (2), pp 73-85. ISSN/ISBN:03123685.
Phillips, T (2009). Simon Newcomb and "Natural Numbers" (Benford's Law). American Mathematical Society Feature Column, Monthly Essays on Mathematical Topics.
Pickover, C (2012). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones). Sterling Publishing: New York. See: Benford's Law (1881). ISSN/ISBN:978-1-4027-5796-9.
Pietronero, L, Tosatti, E, Tosatti, V and Vespignani, A (1998). The Uneven Distribution of Numbers in Nature. Arxiv preprint cond-mat/9808305, 1998 - arxiv.org.
Pietronero, L, Tosatti, E, Tosatti, V and Vespignani, A (2001). Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf. Physica A - Statistical Mechanics and its Applications 293(1-2), 297-304. ISSN/ISBN:0378-4371. DOI:10.1016/S0378-4371(00)00633-6.
Pimbley, JM (2014). Benford’s Law and the Risk of Financial Fraud. Global Association of Risk Professionals (garp.org). Last retrieved 20 April 2018.
Pimbley, JM (2014). Benford’s Law as a Logarithmic Transformation. Maxwell Consulting Archives. Last retrieved 20 April 2018.
Pinilla, J, López-Valcárcel, BG, González-Martel, C and Peiro, S (2018). Pinocchio testing in the forensic analysis of waiting lists: using public waiting list data from Finland and Spain for testing Newcomb-Benford’s Law. BMJ open,8(5), pp. 1-6. ISSN/ISBN:2044-6055. DOI:10.1136/bmjopen-2018-022079.
Pippenger, N (2002). Expected acceptance counts for finite automata with almost uniform input. Algorithms and Computation, Proceedings. Lecture Notes in Computer Science 2518, pp. 636-646. ISSN/ISBN:0302-9743. DOI:10.1007/3-540-36136-7_56.
Pippenger, N (2004). Entropy and expected acceptance counts for finite automata. IEEE Transactions on Information Theory 50(1), pp. 78-88. ISSN/ISBN:0018-9448. DOI:10.1109/TIT.2003.821997.
Pocheau, A (2006). The significant digit law: a paradigm of statistical scale symmetries . European Physical Journal B 49(4), pp. 491-511. ISSN/ISBN:1434-6028. DOI:10.1140/epjb/e2006-00084-2.
Poekl, G (2016). Newcomb-Benford's Law ohne Limits. 03.16 ZRFC Risk, Fraud & Compliance, Erich-Schmid-Verlag, Berlin, Germany, pp. 115-120. GER
Pollach, G, Brunkhorst, F, Mipando, M, Namboya, F, Mndolo, S and Luiz, T (2016). The "first digit law" - A hypothesis on its possible impact on medicine and development aid. Medical Hypotheses 97, pp. 102-106. DOI:10.1016/j.mehy.2016.10.021.
Porta Mana, PGL, Månsson, A and Björk, G (2007). The Laplace-Jaynes approach to induction. arXiv preprint.
Posch, PN (2004). Ziffernanalyse in der Fälschungsaufspürung. Benford’s Gesetz und Steuererklärungen in Theorie und Praxis. Unpublished manuscript; link no longer available. GER
Posch, PN (2008). A Survey on Sequences and Distribution Functions satisfying the First-Digit-Law. Journal of Statistics & Management Systems 11(1), pp. 1-19. DOI:10.1080/09720510.2008.10701294.
Posch, PN (2010). Ziffernanalyse mit dem Newcomb-Benford Gesetz in Theorie und Praxis. VEW Verlag Europäische Wirtschaft: Munich 2nd edition. GER
Posch, PN (2013). Benford Or Not-Benford? How To Test For The First-Digit-Law. JP Journal of Fundamental and Applied Statistics 4(1/2), pp. 1-22.
Posch, PN and Kreiner, WA (2005). A general approach to digital analysis exemplified by stock market indices. Online unpublished manuscript; link broken; copy available upon request.
Posch, PN and Kreiner, WA (2006). Analysing digits for portfolio formation and index tracking. Journal of Asset Management 7(1), pp. 69-80. DOI:10.1057/palgrave.jam.2240203.
Qadir, G, Zhao, X and Ho, ATS (2010). Estimating JPEG2000 Compression for Image Forensics Using the Benford’s Law. Proc. of SPIE Vol. 7723, pp. 77230J1 -77230J10. DOI:10.1117/12.855085.
Qadir, G, Zhao, X, Ho, ATS and Casey, M (2011). Image forensic of glare feature for improving image retrieval using Benford's Law. Proceedings of 2011 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2661--2664. ISSN/ISBN:0271-4302. DOI:10.1109/ISCAS.2011.5938152.
Qu, H, Steinberg, R and Burger, R (2019). Abiding by the Law? Using Benford's Law to Examine the Accuracy of Nonprofit Financial Reports. Nonprofit and Voluntary Sector Quarterly. DOI:10.1177/0899764019881510.
Quick, R and Wolz, M (2005). Benford’s law in German financial statements. Finance India, 19 (4), 1285-1302. ISSN/ISBN:09703772.
Raimi, RA (1985). The First Digit Phenomenon Again. Proceedings of the American Philosophical Society 129(2), pp. 211-219. ISSN/ISBN:0003-049X.
Rajagopal, AK, Uppuluri, VRR, Scott, DS, Iyengar, SS and Yellayi, M (1984). New structural properties of strings generated by leading digits of 2^N. Applied Mathematics and Computation 14(3), pp. 221-244. DOI:10.1016/0096-3003(84)90023-7.
Rane, AD, Mishra, U, Biswas, A, De, AS and Sen, U (2014). Benford's law gives better scale exponents in phase transitions of quantum XY models. Phys. Rev. E 90(2), p. 022144 (previously available from http://arxiv.org/abs/1405.2744). DOI:10.1103/PhysRevE.90.022144.
Rauch, B, Brähler, G, Engel, S and Göttsche, M (2011). Fact and Fiction in EU-Governmental Economic Data. German Economic Review 12(3), pp. 243-255. DOI:10.1111/j.1468-0475.2011.00542.x.
Rauch, B, Göttsche, M, Brähler, G, Geidel, FA and Pietras, T (2014). Assessing the Accountability Reports of Political Parties in Germany using Benford's Law. Betriebswirtschaftliche Forschung und Praxis 66(2).
Rauch, B, Göttsche, M and El Mouaaouy, F (2013). LIBOR Manipulation – Empirical Analysis of Financial Market Benchmarks Using Benford's Law. Posted December 5, 2013. Available at SSRN: https://ssrn.com/abstract=2363895. Last accessed May 15, 2017. DOI:10.2139/ssrn.2363895.
Rauch, B, Göttsche, M and Langenegger, S (2014). Detecting Problems in Military Expenditure Data Using Digital Analysis. Defence and Peace Economics 25(2), pp. 97-111. DOI:10.1080/10242694.2013.763438.
Regan, KW (2012). Benford’s Law and Baseball. Gödel’s Lost Letter and P=NP website, last accessed April 1, 2019.
Ribeiro, JC, Monteiro, GB, dos Santos, J and Galvao, KdS (2005). Aplicação da Lei de Newcomb-Benford na Auditoria. Caso notas de empenho dos Municípios do Estado da Paraíba. 2o Congresso USP Iniciação cientifica em contabilidade. POR
Riccioni, J and Cerqueti, R (2018). Regular paths in financial markets: Investigating the Benford’s law. Chaos, Solitons and Fractals 107, pp. 186-194. DOI:10.1016/j.chaos.2018.01.008.
Richter, R (2015). Em busca de transparência: a Lei de Benford aplicada às despesas eleitorais. Monografia (Bacharelado em Ciências Econômicas)- Universidade de Brasília, Brasília. POR
Rieger, J (1993). Das Rätsel der ersten Ziffern. Frankfurter Allgemeine Zeitung, Oktober 20. GER
Rodriguez, RJ (2004). First Significant Digit Patterns from Mixtures of Uniform Distributions. American Statistician 58(1), pp. 64-71. ISSN/ISBN:0003-1305. DOI:10.1198/0003130042782.
Romero-Rochin, V (2009). A derivation of Benford's Law ... and a vindication of Newcomb. preprint arXiv:0909.3822.
Roukema, BF (2009). Benford's Law Anomalies in the 2009 Iranian presidential election. preprint arXiv:0906.2789.
Roukema, BF (2014). A first-digit anomaly in the 2009 Iranian presidential election. Journal of Applied Statistics 41(1), pp. 164-199. DOI:10.1080/02664763.2013.838664.
Rücker, G (2003). Benford's Law in Medical Data Sets. In Proceedings of 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, pp. 615-617.
Ryder, P (2009). Multiple origins of the Newcomb-Benford law: rational numbers, exponential growth and random fragmentation. Staats- und Universitätsbibliothek Bremen, Germany.
Sadaf, R (2016). Benford’s Law in the Case of Hungarian Whole-Sale Trade Sector. SEA – Practical Application of Science 12, pp. 561-566.
Sadaf, R (2017). Advanced Statistical Techniques For Testing Benford'S Law. Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pp. 229-238.
Safiri S, Rahimi-Movaghar, A, Mansournia, MA, Yunesian, M, Shamsipour, M, Sadeghi-Bazargani, H and Fotouhi, A (2019). Sensitivity of Crosswise Model to Simplistic Selection of Nonsensitive Questions: An Application to Estimate Substance Use, Alcohol Consumption and Extramarital Sex Among Iranian College Students. Substance Use and Misuse 54(4), pp. 601-611. DOI:10.1080/10826084.2018.1528462.
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/ISBN:2010-3484.
Sambridge, M, Tkalčić, H and Jackson, A (2010). Benford's law in the Natural Sciences. Geophysical Research Letters 37: L22301. DOI:10.1029/2010GL044830.
Sanches, J and Marques, JS (2006). Image reconstruction using the Benford law. Proceedings of the IEEE International Conference on Image Processing, Atlanta, GA, October 2006, pp. 2029-2032. ISSN/ISBN:1522-4880. DOI:10.1109/ICIP.2006.312845.
Sánchez, JLH (2002). Analisis de la megacefalia demografica urbana mediante leyes de Zipf y de potencia (Urban demographic analysis by using Zipf and potence laws). Theoria 11, 21-26. ISSN/ISBN:0717-196X. SPA
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/ISBN:1634-2941. DOI:10.3917/popu.204.0761.
Santiwipanont, T, Sumetkijakan, S and Wiriyakraikul, T (2019). Benfordness of Chains of Truncated Beta Distributions via a Piecewise Constant Approximation. In: Kreinovich V., Sriboonchitta S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham, pp. 342-351. DOI:10.1007/978-3-030-04263-9_26.
Saville, A (2003). Using Benford's Law to predict data error and fraud. An examination of companies listed on the JSE securities exchange. E-print online. Last accessed 26Mar2015.
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/ISBN:1015-8812.
Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. ISSN/ISBN:0863-0593.
Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN/ISBN:0167-7152. DOI:10.1016/S0167-7152(97)00142-9.
Scheidt, JK and Schelin, CW (1987). Distributions of floating point numbers. Computing 38(4), 315-324. ISSN/ISBN:0010-485X. DOI:10.1007/BF02278709.
Schetnikov, AL and Schetnikova, AB (2002). Teaching and Research Seminar "The distribution of the first significant digits". Matematicheskoe obrazovanie (Mathematical Education), № 2(21), 2002, p. 107–123. (in Russian). RUS
Schiavo, M (2010). Analisi statistica sulla legge di benford. Tesi di Laurea, Facoltà di Scienze Statistiche, Universita' degli studi di padova. ITA
Schilling, MF (1992). Sequential Partitioning. American Mathematical Monthly 99(9), 846-855. ISSN/ISBN:0002-9890.
Schneider, RU (2006). Das Rätsel der abgegriffenen Seiten [The riddle of the worn pages]. NZZ Folio: Die Zeitschrift der Neuen Zürcher Zeitung, Statistik / Januar 2006. GER
Schräpler, 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. DOI:10.2139/ssrn.1562574.
Schräpler, J-P 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.
Schündeln, M (2018). Multiple Visits and Data Quality in Household Surveys. Oxford Bulletin of Economics and Statistics 80(2), pp. 380-405. DOI:10.1111/obes.12196.
Schüpfer, G, Hein, J, Casutt, M, Steiner, L and Konrad, C (2012). Vom Finanz- sum Wissenschaftsbetrug [From financial to scientific fraud : methods to detect discrepancies in the medical literature]. Der Anaesthesist 61(6):537-42. ISSN/ISBN:0003-2417. DOI:10.1007/s00101-012-2028-y. GER
Schürger, K (2008). Extensions of Black-Scholes processes and Benford's law. Stochastic Processes and their Applications 118(7), 1219-1243. ISSN/ISBN:0304-4149. DOI:10.1016/j.spa.2007.07.017.
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.
Seaman, RS (2002). The relevance of Benford's Law to background field errors in data assimilation. Australian Meteorological Magazine 51(1), 25-33. ISSN/ISBN:0004-9743.
Seibert, J and Zahrádka, J (2014). First Digit Law and its Application. Scientific Papers of the University of Pardubice Series D, Faculty of Economics and Administration Vol. XXI, No. 30, pp. 75 - 82. CZE
Sen, A and Sen, U (2011). Benford's law detects quantum phase transitions similarly as earthquakes. EPL (Europhysics Letters) 95(5), 50008, 1-6. DOI:10.1209/0295-5075/95/50008.
Shao, L and Ma, BQ (2009). First Digit Distribution of Hadron full width. Modern Physics Letters A, 24(40), 3275-3282. ISSN/ISBN:0217-7323. DOI:10.1142/S0217732309031223.
Shao, L and Ma, BQ (2010). Empirical mantissa distributions of pulsars. Astroparticle Physics 33, 255-262. DOI:10.1016/j.astropartphys.2010.02.003.
Shao, L and Ma, BQ (2010). The significant digit law in statistical physics. Physica A 389, 3109-3116. DOI:10.1016/j.physa.2010.04.021.
Shao, L and Ma, BQ (2010). First-digit law in nonextensive statistics. Physical Review E 82, 041110. DOI:10.1103/PhysRevE.82.041110.
Sheynin, OB (1984). On the History of the Statistical Method in Astronomy. Archive for History of Exact Sciences 29(2), 151-199. ISSN/ISBN:2782843 (0003-9519). DOI:10.1007/BF00348245.
Shi, J, Ausloos, M and Zhu, T (2018). Benford's law is the first significant digit and distribution distances for testing the reliability of financial reports in developing countries. Physica A: Statistical Mechanics and its Applications 492(1), pp. 878-888. DOI:10.1016/j.physa.2017.11.017.
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/ISBN:978-3-642-04437-3. DOI:10.1007/978-3-642-04438-0_37.
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.
Shukla, A, Pandey, AK and Pathak, A (2017). Benford’s distribution in extrasolar world: Do the exoplanets follow Benford’s distribution?. Journal of Astrophysics and Astronomy JOAA-D-16-00138, 38(7). DOI:10.1007/s12036-017-9427-z.
Shulzinger, E, Legchenkova, I and Bormashenko, E (2018). Co-occurrence of the Benford-like and Zipf Laws Arising from the Texts Representing Human and Artificial Languages. Preprint arXiv:1803.03667 [cs.CL]; last accessed April 6, 2019.
Simonet, S, Monteleone, S and Diego, A (2007). Analyse von Bildflächen auf Benfordverteilung am Beispiel von Northern Blots. ETH Zuerich sociology working paper. GER
Singleton, TW (2011). Understanding and applying Benford’s Law. ISACA Journal, v.3 pp.1-4.
Slepkov, AD, Ironside, KB and DeBattista, D (2013). Benford's Law: Textbook Exercises and Multiple-choice Testbanks. Preprint posted on physics arXiv - submitted 19 November 2013.
Slepkov, AD, Ironside, KB and DiBattista, D (2015). Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks. PLoS ONE 10(2): e0117972. DOI:10.1371/journal.pone.0117972.
Slijepčević, S and Blašković, B (2014). Statistical detection of fraud in the reporting of Croatian public companies. Financial Theory and Practice, 38(1), pp. 81-96. DOI:10.3326/fintp.38.1.4.
Smith, AC (2013). Benford-Newcomb Subsequences for Fraud Detection. Preprint arXiv:1301.6086v1 [math.ST]; last accessed March 25, 2019.
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/ISBN:1063-651X. DOI:10.1103/PhysRevE.64.026222.
Soffer, BH and Lynch, DK (1999). Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision. American Journal of Physics 67(11), 946-953. DOI:10.1119/1.19170.
Stigler, SM (1978). Mathematical Statistics in the Early States. Annals of Statistics 6(2), 239-265. ISSN/ISBN:0090-5364.
Stoessiger, R (2013). Benford’s Law and why the integers are not what we think they are. Australian Senior Mathematics Journal, Vol. 27, No. 1, pp. 29-46. ISSN/ISBN:0819-4564.
Stoschek, EP and Schönfeld, D (2002). Benford's Law - Places of interest near Benford's Law. Module 45 of: Workshop on Design of Algorithms. GER
Strzałka, D (2010). On some properties of Benford's law. Journal of the Korean Math. Soc. 47(5), pp. 1055-1075.
Stückemann, S and Pflanzer, M (2010). Das Benfordsche Gesetz. Papermint 1/Juli 2010, pp. 31-34. GER
Suzuki, T, Kamimasu, T, Nakatoh, T and Hirokawa, S (2018). Identification of Unnatural Subsets in Statistical Data. 7th International Congress on Advanced Applied Informatics (IIAI-AAI), pp. 74-80. DOI:10.1109/IIAI-AAI.2018.00024.
Szymanowski, J (2010). Fenomen rozkładu Benforda [The phenomenon of Benford distribution]. Online - last accessed May 2, 2015. POL
Tabachnikov, S (2005). Geometry and Billiards. AMS Student Mathematical Library vol.30, pp. 23-25. ISSN/ISBN:978-0-8218-3919-5.
Tarantola, A (2006). Benford Effect. Elements for Physics: Quantities, Qualities, and Intrinsic Theories, Springer, pp 111-113. ISSN/ISBN: 978-3-540-25302-0.
Thomas, JK (1989). Unusual Patterns in Reported Earnings. Accounting Review 64(4), 773-787. ISSN/ISBN:0001-4826.
Tijms, H (2012). Understanding Probability . 3rd Ed., Cambridge University Press, see Chapter 5 "Falsified data and Benford's law", pp. 196-202. ISSN/ISBN:9781107658561.
Tirunagari, S, Abasolo, D, Iorliam, A, Ho, ATS and Poh, N (2017). Using Benford’s Law to Detect Anomalies in Electroencephalogram: An Application to Detecting Alzheimer’s Disease. In: Proceedings of 2017 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), Manchester, 2017, pp. 1-6. DOI:10.1109/CIBCB.2017.8058547.
Tödter, K-H (2007). Das Benford-Gesetz und die Anfangsziffern von Aktienkursen. Wirtschaftswissenschaftliches Studium 36(2), pp. 93-97. DOI:10.15358/0340-1650-2007-2-93. GER
Tödter, K-H (2009). Benford's Law as an Indicator of Fraud in Economics. German Economic Review 10(3), 339-351. DOI:10.1111/j.1468-0475.2009.00475.x.
Toledo, PA, Riquelme, SR and Campos, JA (2015). Earthquake source parameters that display the first digit phenomenon. Nonlin. Processes Geophys., 22(5), pp. 625–632. DOI:10.5194/npg-22-625-2015.
Tolle, CR, Budzien, JL and LaViolette, RA (2000). Do dynamical systems follow Benford's law?. Chaos, 10(2), 331-336. ISSN/ISBN:1054-1500. DOI:10.1063/1.166498.
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/ISBN:0143-0807. DOI:10.1088/0143-0807/28/3/N04.
Tsagbey, S, de Carvalho, M and Page, GL (2017). All Data are Wrong, but Some are Useful? Advocating the Need for Data Auditing . The American Statistician, 71, pp. 231--235. DOI:10.1080/00031305.2017.1311282.
Tseng, H-C, Huang, W-N and Huang, D-W (2017). Modified Benford’s law for two-exponent distributions. Scientometrics 110(3), pp. 1403–1413. DOI:DOI 10.1007/s11192-016-2217-6.
Tucson, M (2000). Numerical Structure of the Quran - An Approach Based on Benford's Law. Submitters Perspective Vol 16, No. 7.
Tunalioglu, N and Erdogan, B (2019). Usability of the Benford’s law for the results of least square estimation. Acta Geodaetica et Geophysica, pp. 1-17. DOI:10.1007/s40328-019-00259-3.
Türkyener, CM (2007). Benford Yasası ve Mali Denetimde Kullanımı. Sayıştay Dergisi Sayi: 64, pp. 111-122. TUR
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/ISBN:978-1-875900-63-3.
Uhlig, N (2016). Rundum das Benfordsche Gesetz. Diploma thesis, University of Leipzig, Fakultät für Mathematik und Informatik. GER
Uyar, A and Uzuner, MT (2014). Benford Yasasinin Sermaye Piyasasinda Faaliyet Gosteren Araci Kurumlarin Konsolide Bilancolarina Uygulanmasi. Trakya University Journal of Social Science Vol. 16 Issue 1, pp. 95-106. TUR
Valadier, M (2012). The Benford phenomenon for random variables. Discussion of Feller's way. Math arXiv:1203.2518; posted 19 Apr 2012.
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.
Van Caneghem, T (2016). NPO Financial Statement Quality: An Empirical Analysis Based on Benford’s Law. International Journal of Voluntary and Nonprofit Organizations 27(6), pp. 2685–2708. DOI:10.1007/s11266-015-9629-4.
Villa-Boas, S, Fu, Q and Judge, G (2015). Is Benford’s Law a Universal Behavioral Theory?. Econometrics 3(4), pp. 698–708. DOI:10.3390/econometrics3040698.
Villas-Boas, SB, Fu, Q and Judge, G (2017). Benford’s law and the FSD distribution of economic behavioral micro data . Physica A: Statistical Mechanics and its Applications Volume 486, pp. 711-719. DOI:10.1016/j.physa.2017.05.093.
Volcic, A (1996). The First Digit Problem and Scale-Invariance. In: P. Marcellini, G. Talenti and E. Vesentini (eds), Partial differential equations and applications: collected papers in honor of Carlo Pucci. Marcel Dekker, pp. 329-340 .
Wallace, WA (2002). Assessing the quality of data used for benchmarking and decision- making. The Journal of Government Financial Management 51(3), pp. 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. DOI:10.1007/s11846-008-0019-9.
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).
Whyman, G, Ohtori, N, Shulzinger, E and Bormashenko, E (2016). Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?. Physica A: Statistical Mechanics and its Applications Volume 461, pp. 595-601. DOI:10.1016/j.physa.2016.06.054.
Whyman, G, Shulzinger, E and Bormashenko, E (2016). Intuitive considerations clarifying the origin and applicability of the Benford law. Results in Physics Volume 6, pp. 3-6 . DOI:10.1016/j.rinp.2015.11.010.
Wikipedia (2018). Benfordsches Gesetz. Posted on German Wikipedia website; last accessed April 30, 2019. GER
Wilkinson, L (2006). Revising the Pareto chart. American Statistician 60(4), 332-334. ISSN/ISBN:0003-1305. DOI:10.1198/000313006X152243.
Williamson, J (2000). Random probability functions. Preprint.
Winter, C, Schneider, M and Yannikos, Y (2011). Detecting Fraud Using Modified Benford Analysis. Advances in Digital Forensics VII, 7th IFIP WG 11.9 International Conference on Digital Forensics, Orlando, FL, USA, January 31 – February 2, 2011, Revised Selected Papers. Gilbert Peterson and Sujeet Shenoi (Editors). IFIP Advances in Information and Co. ISSN/ISBN:1868-4238. DOI:10.1007/978-3-642-24212-0_10.
Winter, C, Schneider, M and Yannikos, Y (2012). Model-Based Digit Analysis for Fraud Detection overcomes Limitations of Benford Analysis. Availability, Reliability and Security (ARES 2012), Seventh International Conference, August 20–24, 2012, Prague, Czech Republic. IEEE CS volume E4775, pages 255–261. IEEE Computer Society. ISSN/ISBN:978-1-4673-2244-7 . DOI:10.1109/ARES.2012.37.
Wist, H (2019). Assessing The Conformity Of Cryptocurrency Market Data With Benford’s Law. Masters thesis, University of Vaasa, Faculty of Business Studies, Department of Accounting and Finance .
Wojcik, MR (2013). Notes on scale-invariance and base-invariance for Benford's Law. arXiv:1307.3620 [math.PR].
Wojcik, MR (2014). A characterization of Benford’s law through generalized scale-invariance. Mathematical Social Sciences, Volume 71, September 2014, pp. 1–5. DOI:10.1016/j.mathsocsci.2014.03.006.
Wong, SCY (2010). Testing Benford’s Law with the first two significant digits. Master's Thesis, University of Victoria, Canada.
Wroński, K (2012). Zastosowanie Rozkładu Benforda do Analizy Plików Dźwiękowych [Benford Distribution Application to the Analysis of Sound File] . Bachelor Thesis, Krakow Academy, Faculty of Economics and Management. POL
Yan, X, Yang, S-G, Kim, BJ and Minnhagen, P (2017). Benford's Law and First Letter of Word. Physica A: Statistical Mechanics and its Applications 512, pp. 305-315. DOI:10.1016/j.physa.2018.08.133.
Yang, D (2016). Characterization of noise in airborne transient electromagnetic data using Benford's law. SEG Technical Program Expanded Abstracts 2016, pp. 1043-1047. ISSN/ISBN:1949-4645. DOI:10.1190/segam2016-13972000.1.
Yücel, R and Özevin, O (2016). The Application Of Benford Analysis On Balance Sheet Items Of Companies Traded In Bist. Papers On Social Science 2016, pp. 83-97. TUR
Zhao, S and Wu, W (2010). Does Chinese Stock Indices Agree with Benford's Law?. 2010 International Conference on Management and Service Science (MASS), 24-26 Aug. 2010, Wuhan, Page(s): 1 - 3. ISSN/ISBN:978-1-4244-5325-2. DOI:10.1109/ICMSS.2010.5575999.

Cross Reference Up

Newcomb, S (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics 4(1), pp. 39-40.

Note that this list may be incomplete, and is currently being updated. Please check again at a later date.