Benford Online Bibliography

Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363.

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.

Akkaş, 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
Akkaş, ME (2015). Altın Getirileri Dağılımının Newcomb-Benford Kanunu İle Testi [Testing Distribution of Gold Returns by Newcomb-Benford Law]. Uluslararası Sosyal Araştırmalar Dergisi 8(40), pp. 577-584. DOI:10.17719/jisr.20154013940. TUR
Al-Rawashdeh, F (2017). Applying Benford's law into Jordanian insurance companies to identify earning's manipulations. Business and Economic Horizons 13(2), pp. 210-223. DOI:10.15208/beh.2017.16.
Alali, FA and Romero, S (2013). Benford’s Law: Analyzing a decade of financial data. Journal of Emerging Technologies in Accounting Vol. 10, No. 1, pp. 1-39. DOI:10.2308/jeta-50749.
Albrecht, CC (2008). Fraud and forensic accounting in a digital environment. White Paper for The Institute for Fraud Prevention, Brigham Young University.
Aldous, D and Phan, T (2009). When Can One Test an Explanation? Compare and Contrast Benford's Law and the Fuzzy CLT. Class project report, Statistics Department, UC Berkeley.
Aldous, D and Phan, T (2010). When Can One Test an Explanation? Compare and Contrast Benford's Law and the Fuzzy CLT. The American Statistician 64(3), pp. 221–227. ISSN/ISBN:0003-1305. DOI:10.1198/tast.2010.09098.
Aleksandrova, EB, Lavrova, DS and Yarmak, AV (2019). Benford’s Law in the Detection of DoS Attacks on Industrial Systems. Automatic Control and Computer Sciences 53(8), pp. 954–962. DOI:10.3103/S0146411619080030.
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.
Amanda Bowman, A (2016). Contributions to the Testing of Benford's Law. Masters Thesis, McMaster University, Hamilton, Canada.
Amiram, D, Bozanic, Z and Rouen, E (2015). Financial statement errors: evidence from the distributional properties of financial statement numbers. Review of Accounting Studies 20(4), pp. 1540–1593. DOI:10.1007/s11142-015-9333-z.
Amouzegar, M and Moshirvaziri, K (2018). Information Security and Benford’s Law . Posted on Decision Sciences Institute blog May 3; last accessed October 11, 2019.
Amouzegar, MA, Moshirvaziri, K and Snyder, D (2018). Benford's Law And Its Application To Modern Information Security. Proceedings of 47th Annual Meeting of WDSI (Western Decision Sciences Institute) .
Anderson, KM, Dayaratna, K, Gonshorowski, D and Miller, SJ (2022). A New Benford Test for Clustered Data with Applications to American Elections. Stats 5(3), pp. 841–855. DOI:10.3390/stats5030049 .
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.
Aris, NA, Othman, R, Bukhori, MAM, Arif, SMM and Malek, MAA (2017). Detecting Accounting Anomalies Using Benford’s Law: Evidence from the Malaysian Public Sector. Management & Accounting Review 16(2), pp. 73-100.
Arshadi, L and Jahangir, AH (2014). Benford's law behavior of Internet traffic. Journal of Network and Computer Applications, Volume 40, April 2014, pp. 194–205. ISSN/ISBN:1084-8045. DOI:10.1016/j.jnca.2013.09.007.
Aschwanden, D and Diekmann, A (2011). Analyse der Schweizer Nationalratswahlen von 2007 mit dem Benford’schen Gesetz. Gruppenarbeit an der ETH Zürich, betreut von Prof. Andreas Diekmann. GER
Ay, B and Efrem, N (2021). Benford’s law applied to sale prices on the Swedish housing market. Bachelor thesis, Department of Statistics Nr 2021:13, Stockholms Universitet.
Azevedo, CdS, Gonçalves, RF, Gava, VL and Spinola, MdM (2021). A Benford’s Law based methodology for fraud detection in social welfare programs: Bolsa Familia analysis. Physica A 567, p. 125626. DOI:10.1016/j.physa.2020.125626.
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.
Bailly, N (2006). Prominence trend in maximum lengths recorded for fishes: a preliminary analysis. In: Palomares, MLD, Stergiou, KI, and Pauly, D (eds.), Fishes in databases and ecosystems. Proceedings of the 2006 FishBase Symposium. Fisheries Centre Research Reports, 2006, Vol. 14, No. 4, pp. 12-17. ISSN/ISBN:1198-6727.
Baiocchi, G (2004). Using Perl for Statistics: Data Processing and Statistical Computing. Journal of Statistical Software 11(1), pp. 1-75. DOI:10.18637/jss.v011.i01.
Balanzario, EP (2015). Benford’s law for mixtures. Communications in Statistics - Theory and Methods 44(4), pp. 698-709. DOI:10.1080/03610926.2012.752849.
Balashov, VS, Yan, Y and Zhu, X (2020). Who Manipulates Data During Pandemics? Evidence from Newcomb-Benford Law. Preprint arXiv:2007.14841 [econ.GN]; last accessed March 10, 2021.
Balashov, VS, Yan, Y and Zhu, X (2021). Using the Newcomb–Benford law to study the association between a country’s COVID-19 reporting accuracy and its development. Scientific Reports 11, pp. 22914. DOI:10.1038/s41598-021-02367-z.
Bannier, C, Ewelt-Knauer, C, Lips, J and Winker, P (2020). Benford’s Law and Its Application to Detecting Financial Fraud and Manipulation. Ch. 18 in: Corruption and Fraud in Financial Markets: Malpractice, Misconduct and Manipulation, C. Alexander and D. Cumming (Eds.), John Wiley & Sons: Chichester, U.K., pp. 473-504. ISSN/ISBN:978-1-119-42177-1.
Bannier, C, Ewelt-Knauer, C, Winker, P and Lips, J (2019). Benford’s law and its application to detecting financial fraud and manipulation. Chapter 5 of Econometric Modelling of Energy & Financial Markets, Doctoral Thesis of Johannes Lips, Justus-Liebig University Gießen .
Bao, Y, Heilig, F, Lee, C-H and Lusk, EJ (2018). Full range testing of the small size effect bias for Benford screening: A note. International Journal of Economics and Finance 10(6), pp. 47-52. DOI:10.5539/ijef.v10n6p47.
Bao, Y, Lee, C-H, Heilig, F and Lusk, EJ (2018). Empirical information on the small size effect bias relative to the false positive rejection error for Benford test-screening. International Journal of Economics and Finance 10(2), pp. 1-9. DOI:10.5539/ijef.v10n2p1.
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.
Barabesi, L, Cerasa, A, Cerioli, A and Perrotta, D (2021). On characterizations and tests of Benford’s law. Journal of the American Statistical Association. DOI:10.1080/01621459.2021.1891927.
Barabesi, L, Cerioli, A and Di Marzio, M (2023). Statistical models and the Benford hypothesis: a unified framework. TEST. DOI:10.1007/s11749-023-00881-y.
Barabesi, L, Cerioli, A and Perrotta, D (2021). Forum on Benford’s law and statistical methods for the detection of frauds. Statistical Methods & Applications 30, pp. 767–778. DOI:10.1007/s10260-021-00588-0.
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 (2017). The First Significant Digit Distribution Analysis of Financial Data of Selected Companies from Media Sector Listed on the Warsaw Stock Exchange. Res. Pap. Wrocław Univ. Econ. 469, pp. 11–20. DOI:10.15611/pn.2017.469.01. POL
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.
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.
Benedito-Nunes, AM, Gamper, J, Chapman, SC, Friel, M and Gjerloev, JW (2023). Newcomb-Benford Law characterization of solar wind magnetic field and geomagnetic indices. Posted on Authorea; last accessed April 29, 2023. DOI:10.22541/essoar.168121593.35845953/v1.
Benedito-Nunes, AM, Gamper, J, Chapman, SC, Friel, M and Gjerloev, JW (2023). Newcomb-Benford Law as a generic flag for changes in the derivation of long-term solar terrestrial physics timeseries. RAS Techniques and Instruments, pp. rzad041. DOI:10.1093/rasti/rzad041.
Bera, A, Mishra, U, Roy, SS, Biswas, A, Sen, A and Sen, U (2018). Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better. Physics Letters A 382(25), pp. 1639–1644 . DOI:10.1016/j.physleta.2018.04.020.
Berger, A (2005). Benford’s Law in power-like dynamical systems. Stochastics and Dynamics 5, pp. 587-607. ISSN/ISBN:0219-4937. DOI:10.1142/S0219493705001602.
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, 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 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 and Hill, TP (2019). The Mathematics of Benford's Law--A Primer. Preprint arXiv:1909.07527 [math.ST]; last accessed September 22, 2019.
Berger, A and Hill, TP (2020). The mathematics of Benford’s law: a primer. Statistical Methods & Applications 30, pp. 779-795. DOI:10.1007/s10260-020-00532-8.
Berger, A, Hill, TP, Kaynar, B and Ridder, A (2011). Finite-state Markov Chains Obey Benford's Law. SIAM Journal of Matrix Analysis and Applications 32(3), pp. 665-684. DOI:10.1137/100789890.
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 Siegmund, S (2007). On the distribution of mantissae in nonautonomous difference equations. Journal of Difference Equations and Applications 13(8-9), pp. 829-845. ISSN/ISBN:1023-6198. DOI:10.1080/10236190701388039.
Berger, A and Xu, C (2018). Best Finite Approximations of Benford’s Law. Journal of Theoretical Probability. DOI:10.1007/s10959-018-0827-z.
Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Turnage-Butterbaugh, C and Weinstein, M (2014). Benford Behavior of Zeckendorf Decompositions. Fibonacci Quarterly 52(5), pp. 35–46.
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.
Betti, L, Durmić, I, McDonald, Z, Miller, JB and Miller, SJ (2023). Benfordness of Measurements Resulting from Box Fragmentation. Preprint arXiv:2304.08335 [math.PR]; last accessed April 29, 2023.
Bharath, HM (2012). Benford’s Law: A theoretical explanation for base 2. Preprint arXiv:1211.7008 [stat.OT]; last accessed February 15, 2019.
Bi, Z, Durmić, I and Miller, SJ (2022). Benfordness of the Generalized Gamma Distribution. Preprint arXiv:2201.10514 [math.PR]; last accessed January 31, 2022. Published in The PUMP Journal of Undergraduate Research 5, pp. 89–104.
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 (2020). Limits of Benford’s Law in Experimental Field. International Journal of Applied Mathematics 33(4), pp. 685-695. DOI:10.12732/ijam.v33i4.12.
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.
Bolton, RJ and Hand, DJ (2002). Statistical Fraud Detection: a review. Statistical Science 17(3), pp. 235-249.
Bonache, A, Moris, K and Maurice, J (2009). Risque associé à l'utilisation de la loi de Benford pour détecter les fraudes dans le secteur de la mode [Risk of Reviews based on Benford Law in the Fashion Sector]. Munich Personal RePEc Archive (MPRA) Paper No. 15352, posted 26 May 2009. FRE
Bonache, AB, Moris, K and Maurice, J (2010). Détection de fraudes et loi de Benford: Quelques risques associés [Fraud detection and Benford’s law: some linked risks]. Revue Française de Comptabilité n°431, pp. 24-27. FRE
Bond, KD, Conrad, CR, Moses, D and Simmons, JW (2021). Detecting anomalies in data on government violence. Political Science Research and Methods, pp. 1-8. DOI:10.1017/psrm.2021.40.
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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
Branets, S (2019). Detecting money laundering with Benford’s law and machine learning . Masters Thesis, University of Tartu.
Bredl, S, Storfinger, N and Menold, N (2011). A literature review of methods to detect fabricated survey data. Discussion Paper, No. 56, Justus-Liebig- Universität Gießen, Zentrum für Internationale Entwicklungs- und Umweltforschung (ZEU), Giessen. Also appears in: Interviewers’ deviations in surveys. Ed. by N. Menold, P. Winker, and R. Porst. Schriften zur empir.
Bredl, S, Winker, P and Kötschau, K (2012). A statistical approach to detect interviewer falsification of survey data. Survey Methodology, Vol. 38, No. 1, pp. 1-10.
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Brown, MS (2012). Does the Application of Benford's Law Reliably Identify Fraud on Election Day? . Masters thesis, Georgetown University.
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Burgos, A and Santos, A (2021). The Newcomb–Benford law: Scale invariance and a simple Markov process based on it (Previous title: The Newcomb–Benford law: Do physicists use more frequently the key 1 than the key 9?). Preprint arXiv:2101.12068 [physics.pop-ph]; last accessed August 8, 2022; Published Am. J. Phys. 89, pp. 851-861.
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Caldwell, CK (2008). Does Benford's law apply to prime numbers?. From: The Prime Pages (prime number research, records and resources) FAQ.
Campanelli, L (2022). On the Euclidean distance statistic of Benford’s law. Communications in Statistics - Theory and Methods, pp. 1-24. DOI:10.1080/03610926.2022.2082480}.
Campanelli, L (2022). A Statistical Cryptanalysis of the Beale Ciphers. Cryptologia. DOI:10.1080/01611194.2022.2116614.
Campanelli, L (2022). Testing Benford's Law: from small to very large data sets. Spanish Journal of Statistics 4(1), pp. 41-54. DOI:10.37830/SJS.2022.1.03.
Campanelli, L (2022). Monkeypox Obeys the (Benford's) Law: A Dynamic Analysis of Daily Case Counts in the United States of America. Preprint submitted to Statistics in Tran- sition new series..
Campanelli, L (2022). Tuning up the Kolmogorov-Smirnov test for testing Benford’s law. Preprint on ResearchGate.
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.
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Cerasa, A (2022). Testing for Benford’s Law in very small samples: Simulation study and a new test proposal. PLoS ONE 17(7), pp. e0271969. DOI:10.1371/journal.pone.0271969.
Cerioli, A, Barabesi, L, Cerasa, A, Menegatti, M and Perrotta, D (2019). Newcomb-Benford law and the detection of frauds in international trade. Proceedings of the National Academy of Sciences 116(1), pp. 106-115. DOI:10.1073/pnas.1806617115.
Cerqueti, R and Lupi, C (2021). Some New Tests of Conformity with Benford's Law. Stats 4(3), pp. 745-761. DOI:10.3390/stats4030044.
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Cerri, J (2018). A fish rots from the head down: how to use the leading digits of ecological data to detect their falsification. Preprint, bioRxiv p. 368951. DOI:10.1101/368951.
Chamberlain, A and Yanus, AB (2021). Evaluating Federated Voluntary Associations’ Membership Data: An Application of Benford's Law. Social Science Quarterly pp. 1– 12. DOI:10.1111/ssqu.13015.
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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.
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Cross Reference Up

Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363.

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