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.
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.
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
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.
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.
Brock, T (2014). Benford's law and elections - part 1. Posted on Datatodisplay.com blog; last accessed April 25, 2019.
Brown, MS (2012). Does the Application of Benford's Law Reliably Identify Fraud on Election Day? . Masters thesis, Georgetown University.
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.
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.
Buyse, M, George, SL, Evans, S, Geller, NL, Edler, L and Hutton, J (1999). The Role of Biostatistics in the Prevention, Detection and Treatment of Fraud in Clinical Trials. Statistics in Medicine 18 (24), pp. 3435-3451. ISSN/ISBN:0277-6715. DOI:10.1002/(SICI)1097-0258(19991230)18:24<3435::AID-SIM365>3.0.CO;2-O.
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.
Cakebread, K (2011). Detecting Manipulations in Data with Benford's Law – A C# Class. Posted on codeproject.com; last accessed Jun 8, 2019.
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.
Canessa, E (2003). Theory of analogous force on number sets. Physica A 328, pp. 44-52. DOI:10.1016/S0378-4371(03)00526-0.
Cantu, F and Saiegh, SM (2010). A Supervised Machine Learning Procedure to Detect Electoral Fraud Using Digital Analysis. Preprint posted on SSRN; last accessed August 5, 2021. DOI:10.2139/ssrn.1594406.
Cantu, F and Saiegh, SM (2011). Fraudulent Democracy? An Analysis of Argentina’s Infamous Decade Using Supervised Machine Learning. Political Analysis 19 (4), pp. 409-433. DOI:10.1093/pan/mpr033.
Capalbo, F, Galati, L, Lupi, C and Smarra, M (2022). The Impact of Elections on the Quality of Financial Statements in Municipally Owned Entities. University of Molise Economics and Statistics Discussion Paper n. 078/22.
Capalbo, F, Galati, L, Lupi, C and Smarra, M (2023). Local elections and the quality of financial statements in municipally owned entities: A Benford analysis. Chaos, Solitons and Fractals 173 p. 113752. DOI:10.1016/j.chaos.2023.113752.
Capalbo, F, Galati, L, Lupi, C and Smarra, M (2023). Proportional appropriation systems and financial statement quality in municipally owned entities: empirical evidence from Italy. Journal of Public Budgeting, Accounting & Financial Management. DOI:10.1108/JPBAFM-01-2023-0015.
Carreira, P and da Silva, CG (2016). Assessing the omission of records from a data set using Benford’s law. Journal of Financial Crime 23(4), pp. 798-805. DOI:10.1108/JFC-10-2015-0060.
Castañeda, G (2011). La ley de Benford y su aplicabilidad en el análisis forense de resultados electorales [Benford’s Law and its Applicability in the Forensic Analysis of Electoral Results]. Política y gobierno 18(2), pp. 297-329. SPA
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.
Cerqueti, R and Lupi, C (2022). Severe testing of Benford’s law. Preprint arXiv:2202.05237 [stat.ME]; last accessed February 21, 2022.
Cerqueti, R and Lupi, C (2023). Severe testing of Benford's law. TEST 32(2), pp. 677-694. DOI:10.1007/s11749-023-00848-z.
Cerqueti, R and Maggi, M (2021). Data validity and statistical conformity with Benford’s Law. Chaos, Solitons & Fractals 144, p. 110740 . DOI:10.1016/j.chaos.2021.110740.
Cerqueti, R, Maggi, M and Riccioni, J (2022). Statistical methods for decision support systems in finance: how Benford’s law predicts financial risk. Annals of Operations Research. DOI:10.1007/s10479-022-04742-z.
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.
Chanda, T, Das, T, Sadhukhan, D, Pal, AK, Sen(De), A and Sen, U (2015). Statistics of leading digits leads to unification of quantum correlations. Europhysics Letters 114(3). DOI:10.1209/0295-5075/114/30004.
Chenavier, N, Massé, B and Schneider, D (2018). Products of random variables and the first digit phenomenon. Preprint arXiv:1512.06049 [math.PR]; last accessed January 9, 2019.
Chi, D (2020). First Digit Phenomenon in Number Generation Under Uncertainty: Through the Lens of Benford’s Law. Master's thesis, School of Psychology, University of Sydney.
Chiverton, J and Wells, K (2006). Mixture effects in FIR low-pass filtered signals. IEEE Signal Processing Letters 13(6), pp. 369-372. ISSN/ISBN:1070-9908. DOI:10.1109/LSP.2006.871710.
Cho, MJ, Eltinge, JL and Swanson, D (2003). Inferential methods to identify possible interviewer fraud using leading digit preference patterns and design effect matrices. Proceedings of the American Statistical Association 2003 Joint Statistical Meetings - Section on Survey Research Methods.
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.
Cinelli, C (2017). Benford analysis for data validation and Forensic analytics. Online software R package benford.analysis V. 0.1.4.1.
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.
Cong, M, Li, C and Ma, B-Q (2019). First digit law from Laplace transform. Phys. Lett. A, 383(16), pp. 1836-1844. DOI:10.1016/j.physleta.2019.03.017 .
Cong, M and Ma, B-Q (2019). A Proof of First Digit Law from Laplace Transform. Chinese Physics Letters, 36, 7, 070201. DOI:10.1088/0256-307X/36/7/070201.
Corazza, M, Ellero, A and Zorzi, A (2008). What sequences obey Benford's law?. Working Paper n. 185/2008, November 2008, Department of Applied Mathematics, University of Venice. ISSN/ISBN:1828-6887.
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 (2011). Análise de Conformidade nos Gastos Públicos dos Entes Federativos: Estudo de Caso de uma Aplicação da Lei de Newcomb-Benford para o Primeiro e Segundo Dígito em Dois Estados Brasileiros [Conformity Analysis In The Public Expenditure Of Federative Entities. In: Congresso De Controladoria E Cont Abilidade USP , 11., 2011. São Paulo. POR
Costa, JI, da Silva, WB, Travassos, SK and dos Santos, J (2013). Análise de Conformidade da Lei de Newcomb-Benford no Ambiente de Auditoria Contínua: Uma Proposta de Identificação de Desvios no Tempo. In Proceedings of Anais do 37o Encontro Nacional da Associação Nacional de Pós-Graduação e Pesquisa em Administração, Rio de Janeiro, RJ, Brasil. POR
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, Henriques, DBB, Melo, S and dos Santos, J (2012). Análise de métodos contabilométricos para determinação de conformidade da Lei Newcomb-Benford aplicados à auditoria contábil. [An analysis of Benford’s law conformity contabilometric methods applied to audit accounting] . Revista Gestão Pública: Práticas e Desafios, Recife, v. III, n. 6, pp. 292-314. POR
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.
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.
Cuenca, AV (2023). La Ley de Benford, Del Primer Dígito Significativo. Trabajo Fin de Grado en Matemáticas, Universidad de Valladolid . SPA
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 (2013). Aplicações da lei Newcomb-Benford à auditoria de obras públicas [Applications of the Newcomb-Benford Law on Audit of Public Works]. Masters Thesis, University of Brasilia. POR
da Silva, AJ, Floquet, S, Santos, DOC and Lima, RF (2020). On the validation of the Newcomb-Benford Law and the Weibull distribution in neuromuscular transmission. Physica A 553, 1 September 2020, 124606. DOI:10.1016/j.physa.2020.124606.
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 .
Dang, CT, Burger, R and Owens, T (2019). Do better-performing nongovernmental organizations report more accurately? Evidence from financial accounts in Uganda. Economic Development and Cultural Change, forthcoming. DOI:10.1086/703099.
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.
Davic, RD (2022). Correspondence of Newcomb-Benford law with ecological processes . Posted on bioRxiv preprint server of Cold Springs Harbor Laboratory June 27, 2022 . DOI:10.1101/2022.06.27.497806.
de Jong, J, de Bruijne, J and De Ridder, J (2020). Benford’s law in the Gaia universe. Preprint arXiv:2008.12271 [astro-ph.GA]; last accessed August 8, 2022. Published Astron. & Astrophys. 642, A205.
De Marchi, S and Hamilton, JT (2006). Assessing the accuracy of self-reported data: An evaluation of the toxics release inventory. Journal of Risk and Uncertainty 32(1), pp. 57-76. ISSN/ISBN:0895-5646. DOI:10.1007/s10797-006-6666-3.
de Oliveira, JAJ, Francischetti, CE, Galeano, R, Padoveze, CL and Filho, MAFM (2018). Aplicações da Lei de Newcomb-Benford nas Demonstrações Financeiras da Petrobrás [Applications of the Newcomb-Benford on Financial statements of Petrobrás]. Enfoque Reflexão Contábil 37(1), pp. 21-38. DOI:10.4025/enfoque.v37i1.35608. POR
de Vocht, F and Kromhout, H (2013). The use of Benford's law for evaluation of quality of occupational hygiene data. Ann Occup Hyg. 57(3), pp. 296-304. DOI:10.1093/annhyg/mes067.
Debreceny, RS and Gray, GL (2010). Data mining journal entries for fraud detection: An exploratory study. International Journal of Accounting Information Systems, Vol. 11, No. 3, pp. 157–181. DOI:10.1016/j.accinf.2010.08.001.
Del Acebo, E and Sbert, M (2005). Benford's Law for Natural and Synthetic Images. Proc. of the First Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, Eds., Girona, Spain, May 2005, pp. 169–176. ISSN/ISBN:1816-0859. DOI:10.2312/COMPAESTH/COMPAESTH05/169-176.
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.
DeMatteis, JM, Young, LJ, Dahlhamer, J, Langley, RE, Murphy, J, Olson, K and Sharma, S (2020). Falsification in Surveys. Tech Report prepared for AAPOR Council and the Executive Committee of the American Statistical Association by the members of the Task Force on Data Falsification.
Demidenko, E (2020). Advanced Statistics with Applications in R. Wiley: Hoboken, NJ (Chapter 2.16). ISSN/ISBN:1118387988.
Demir, B and Javorcik, B (2017). Forensics, Elasticities and Benford’s Law: Detecting Tax Fraud in International Trade. E-print posted on semantic scholar.org, Dec 22, 2017.
Demir, B and Javorcik, B (2018). Using Benford’s Law to detect tax fraud in international trade. VOX CEPR Policy Portal, posted on September 27, 2018; last accessed June 8, 2019.
Demir, B and Javorcik, B (2020). Trade Policy Changes, Tax Evasion and Benford’s Law. Journal of Development Economics, 144. DOI:10.1016/j.jdeveco.2020.102456.
Demirdöven, K (2019). Adli Muhasebeciler İçin Benford’un Hukukunun Etkinliğinin Bir Araştirma Araci Olarak Değerlendirilmesi [Evaluation of the Effectiveness of Benford's Law as a Research Tool for Forensic Accountants]. Masters Project, Istanbul Esenyurt University. TUR
Depken, CA (2008). Benford, Zipf and the blogosphere. Applied Economics Letters, 15(9), pp. 689–692. ISSN/ISBN:1350-4851. DOI:10.1080/13504850600735270.
Diaconis, P (2002). G.H. Hardy and Probability ???. Bulletin of the London Mathematical Society 34(4), pp. 385-402. DOI:10.1112/S002460930200111X.
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.
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.
Dogan, AH, Altuntas, C, Gui, C, Tunalioglu, N and Erdogan, B (2023). Statistical Analysis of Covid-19 Outbreak with Benford’s Law. Journal of Management and Economics Research 21(2), pp. 120-133. DOI:10.11611/yead.1078847 .
Dorfleitner, G and Klein, C (2009). Psychological barriers in European stock markets: Where are they?. Global Finance Journal 19(3), pp. 268-285. DOI:10.1016/j.gfj.2008.09.001.
Dorrestijn, J (2008). Graphing conformity of distributions to Benford’s Law for various bases. MSc thesis, Universiteit Utrecht, The Netherlands.
dos Santos, CC (2014). Aplicação da Lei de Benford na auditoria : estudo de caso [Application of Benford's Law in Auditing - Case Study] . Masters thesis, Instituto Politécnico de Leiria. POR
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
Drew, JH, Evans, DL, Glen, AG and Leemis, LM (2017). Products of Random Variables. In:Computational Probability: Algorithms and Applications in the Mathematical Sciences, Springer International Publishing, pp. 73-86. ISSN/ISBN:978-3-319-43323-3. DOI:10.1007/978-3-319-43323-3.
Drew, JH, Evans, DL, Glen, AG and Leemis, LM (2017). Other Applications. In: Computational Probability. International Series in Operations Research & Management Science, vol 246. Springer, Cham, pp. 301-321. ISSN/ISBN:978-3-319-43323-3. DOI:10.1007/978-3-319-43323-3_15.
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.
Durmić, I (2022). Benford Behavior of a Higher Dimensional Fragmentation Processes. Undergraduate thesis, Williams College, Williamstown, Massachusetts.
Durmić, I and Miller SJ (2023). Benford Behavior of a Higher-Dimensional Fragmentation Process. Preprint arXiv:2308.07404 [math.PR]; last accessed August 24, 2023.
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.
Dutta, A, Choudhury, MR and De, AK (2022). A Unified Approach to Fraudulent Detection. International Journal of Applied Engineering Research 17(2), pp. 110-124. ISSN/ISBN:0973-4562.
Dutta, A, Voumik, LC, Kumarasankaralingam, L, Rahaman, A and Zimon, G (2023). The Silicon Valley Bank Failure: Application of Benford’s Law to Spot Abnormalities and Risks. Risks 11(7), p. 120. DOI:10.3390/risks11070120.
Egbunike, FC and Amakor, CI (2013). Fraud & auditors analytical procedure: A test of Benford’s law. EBS Journal of Management Sciences 1(1), pp. 14-31.
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.
Elba, F (2020). Dati Covid 2019 e legge di Benford. Preprint arXiv:2008.05884 [physics.soc-ph]; last accessed August 29, 2020. ITA
Eliazar, II (2013). Benford's Law: A Poisson Perspective. Physica A 392(16) pp. 3360–3373. DOI:10.1016/j.physa.2013.03.057.
Endress, MB (2014). Benford's law and humanly generated prices in auction houses and buyout systems of virtual worlds. Masters Thesis, Dept. of Mathematics & Computer Science, Texas Woman's University .
Engel, HA and Leuenberger, C (2003). Benford's law for exponential random variables. Statistics & Probability Letters 63, pp. 361-365. ISSN/ISBN:0167-7152.
Ensminger, J and Leder-Luis, J (2022). Measuring Strategic Data Manipulation: Evidence from a World Bank Project. Preprint, submitted for publication.
Ensminger, J and Leder-Luis, J (2022). Detecting Fraud in Development Aid. Preprint.
Erdoğan, M (2001). Muhasebe Hilelerinin Ortaya Çıkarılmasında Benford Yasası. Muhasebe ve Denetime Bakış, Yıl:1 (3), Ankara: Ocak, pp. 1-8. TUR
Erti̇ki̇n, K (2017). Hile Denetimi: Benford Yasası’nın Bilgisayar Destekli Kullanımına Yönelik Bir Hizmet İşletmesi Örneği [Fraud auditing: a services business example for computer-aided Use of Benford’s law]. The World of Accounting Science 19(3), pp. 696-726. TUR
Etim, ES, Daferighe, EE, Inyang, AB and Ekikor, ME (2023). Application of Benford’s Law and the Detection of Accounting Data Fraud in Nigeria. International Journal of Auditing and Accounting Studies 5(2) pp. 119-163. DOI:10.47509/IJAAS.2023.v05i02.01.
Ettredge, ML and Srivastava, RP (1999). Using digital analysis to enhance data integrity. Issues in Accounting Education 14(4), pp. 675-690. DOI:10.2308/iace.1999.14.4.675.
Eutsler, J, Harris, MK, Williams, LT and Cornejo, OE (2023). Accounting for partisanship and politicization: Employing Benford's Law to examine misreporting of COVID-19 infection cases and deaths in the United States. Accounting, Organizations and Society, in press. DOI:10.1016/j.aos.2023.101455.
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
Fang, G (2022). Investigating Hill’s question for some probability distributions. AIP Advances 12, 095004. DOI:10.1063/5.0100429.
Fang, G and Chen, Q (2019). Several common probability distributions obey Benford’s law. Physica A: Statistical Mechanics and its Applications, 123129 . DOI:10.1016/j.physa.2019.123129.
Fang, X, Miller, SJ, Sun, M and Verga, A (2023). Generalized Continuous and Discrete Stick Fragmentation and Benford’s Law. Preprint arXiv:2309.00766 [math.PR]; last accessed September 12, 2023.
Fang, X, Miller, SJ, Sun, M and Verga, A (2024). Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition. Preprint.
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.
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 (2017). Benfordparadoxen. Arkhimedes 2017(4), pp. 26-33. SWE
Fernández-Gracia, J and Lacasa, L (2018). Bipartisanship Breakdown, Functional Networks, and Forensic Analysis in Spanish 2015 and 2016 National Elections. Complexity 2018, Article ID 9684749. DOI:10.1155/2018/9684749.
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, TMR, Mendes, JFF, Lucio, ML and Moret, MA (2022). Reliability of COVID-19 data and government policies. Preprint arXiv:2208.11226 [physics.soc-ph]; last accessed August 31, 2022.
Filho, TMR, Mendes, JFF, Lucio, ML and Moret, MA (2023). COVID-19 data, mitigation policies and Newcomb–Benford law. Chaos, Solitons and Fractals 174 p. 113814. DOI:10.1016/j.chaos.2023.113814.
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.
Francischetti, CE (2007). Aplicação da lei dos números anômalos ou Lei de Newcomb- Benford para o controle das demonstrações financeiras das organizações [Application of the law of anomalous numbers or the Newcomb-Benford Act to control the financial statements of organizations]. Masters thesis, Universidade Metodista de Piracicaba, Brasil. POR
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.
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.
Friar, JL, Goldman, T and Pérez–Mercader, J (2012). Genome Sizes and the Benford Distribution. PLoS ONE 7(5): e36624. DOI:10.1371/journal.pone.0036624.
Frunza, M-C (2016). Solving Modern Crime in Financial Markets: Analytics and Case Studies. Academic Press, New York, (Chapter 2K) 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.
Galati, L (2020). Do Municipally Owned Utilities Round Earnings Before Elections? An Application of the Benford's Law. Unpublished Master's Dissertation, University of Molise. DOI:10.13140/RG.2.2.36384.51204.
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.
Gamermann, D and Antunes, FL (2018). Statistical analysis of Brazilian electoral campaigns via Benford’s law. Physica A: Statistical Mechanics and its Applications 496, pp. 171-188. DOI:10.1016/j.physa.2017.12.120.
Gámez, RAM and Rivera, CEA (2009). Ley de Benford y sus aplicaciones. Undergraduate Thesis, . SPA
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.
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
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.
Giannakis, N and Burlac, L (2021). Benford’s Law: Analysis of the trustworthiness of COVID-19 reporting in the context of different political regimes. Bachelor’s Degree Project in Mathematics, Division of Mathematics and Physics Mälardalen University, Sweden.
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.
Giles, DE (2013). Exact Asymptotic Goodness-of-Fit Testing for Discrete Circular Data, With Applications. Chilean Journal of Statistics 4(1), pp.19-34. ISSN/ISBN:0718-7912.
Glogić, E and Jasak, Z (2021). Benford's Law in Forensic Analysis of Registered Turnover. Journal of Forensic Accounting Profession 1(1), pp. 50-60. DOI:10.2478/jfap-2021-0004.
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.
Golbeck, J (2015). Benford’s Law Applies to Online Social Networks. PLoS ONE 10(8): e0135169. DOI:10.1371/journal.pone.0135169.
Gönen, S and Rasgen, M (2016). Hile Denetiminde Benford Yasası: Borsa İstanbul Örneği [Benford's Law in Fraud Control: The Case of Borsa İstanbul]. Journal of International Trade, Finance and Logistics 1(1), pp. 93-113 . TUR
González, F (2019). Detecting Anomalous Data in Household Surveys: Evidence for Argentina. Journal of Social and Economic Statistics 8(2), pp. 1-10. DOI:10.2478/jses-2019-0001.
González, F (2020). Self-reported income data: are people telling the truth?. To appear in Journal of Financial Crime. DOI:10.1108/JFC-08-2019-0113.
Gonzalez-Garcia, J and Pastor, G (2009). Benford’s Law and Macroeconomic Data Quality. International Monetary Fund Working Paper WP/09/10, Statistics Department, January 2009.
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.
Grabiński, T, Farbaniec, M, Zabłocki, B and Zając,W (2012). Application of the First Digit Law in Credibility Evaluation of the Financial-Accounting Data Based on Particular Cases. Auditor Journal for Theory and Practice, Revisor, Godina XV - br. 59 - septembar. ISSN/ISBN:1450-7005.
Grabiński, T (2010). Benford's Law. W: Poland – Serbia. The Challenges of the Scientific Cooperation. (red.) Zbigniew Paszek. Kraków: Society for Education, pp. 73-86.
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.
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.
Grime, J (2011). Benford's Law - How mathematics can detect fraud!. singingbanana.com youtube channel; last accessed July 28, 2018.
Guha, D, Mahapatra, PK, Misra, RP and Singh, Y (2020). Exploring the Applicability of Benford’s Law in Data Quality Management. Unpublished manuscript.
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
Guillou, A and Hall, P (2001). A diagnostic for selecting the threshold in extreme value analysis. Journal of the Royal Statistical Society Series B - Statistical Methodology 63(2), pp. 293-305. ISSN/ISBN:1369-7412.
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.
Güttler, 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
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).
Harrington, JE (2005). Detecting Cartels. Economics Working Paper 526, Johns Hopkins University; also in: Paolo Buccirossi (Ed.): Handbook of antitrust economics. Cambridge, Mass: MIT Press, pp. 213-258 (2008).
Hasan, B (2002). Assessing Data Authenticity with Benford’s Law. Information System Control Journal, vol. 6, pp. 41-43.
Hashemi, S and Hariri, A (2017). The analysis of Benford’s law ability to identify and predict financial fraud detection. Accounting and Auditing Review 24 (2), pp. 283–302. DOI:10.22059/ACCTGREV.2017.220346.1007490. PER
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 (2008). Benford's Law. pp. 190-200 in: Impossible? Surprising solutions to counterintuitive conundrums, Princeton University Press, USA. ISSN/ISBN:978-0-691-13131.
Heilig, F and Lusk, EJ (2017). A robust Newcomb-Benford account screening profiler: An audit decision support system. International Journal of Financial Research 8(3), pp. 27-39. DOI:10.5430/ijfr.v8n3p27.
Heilig, F and Lusk, EJ (2018). Testing the Small Size Effect Bias for Benford Screening: The False Negative Signaling Error. Business Management Dynamics 8(6), pp. 23-34.
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.
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 (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 (1998). The First-Digit Phenomenon. American Scientist 86 (4), pp. 358-363. ISSN/ISBN:0003-0996. DOI:10.1511/1998.4.358.
Hill, TP (1999). Le premier chiffre significatif fait sa loi. La Recherche Hors Serie 316, pp. 72-74. FRE
Hill, TP (1999). The difficulty of faking data. Chance 12(3), pp. 27-31. DOI:10.1080/09332480.1999.10542154.
Hill, TP (2001). Response to "Benfords Gesetz", Brief an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 3/2001, p 4. GER
Hill, TP and Schürger, K (2005). Regularity of digits and significant digits of random variables. Journal of Stochastic Processes and their Applications 115(10), pp. 1723-1743. ISSN/ISBN:0304-4149. DOI:10.1016/j.spa.2005.05.003.
Hindls, R and Hronová, S (2015). Benford’s Law and Possibilities for Its Use in Governmental Statistics. Statistika 95( 2), pp. 54-64.
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.
Hofmacher, P and Hornik, K (2013). First Significant Digits and the Credit Derivative Market During the Financial Crisis. Contemporary Economics 7(2), pp. 21-29. DOI:10.5709/ce.1897-9254.80.
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.
Horton, J, Kumar, DK and Wood, A (2020). Detecting academic fraud using Benford law: The case of Professor James Hunton. Research Policy 49(8), 104084 . DOI:10.1016/j.respol.2020.104084.
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.
Huang, SM, Yen, DC, Yang, LW and Hua, JS (2008). An investigation of Zipf's Law for fraud detection. Decision Support Systems 46(1), pp. 70-83. DOI:10.1016/j.dss.2008.05.003.
Huang, Y, Niu, Z and Yang, C (2020). Testing firm-level data quality in China against Benford’s Law. Economics Letters 192, 109182. DOI:10.1016/j.econlet.2020.109182.
Huber, H (2023). Explanations of Benford’s Law. Undergraduate research paper, William and Mary.
Hüllemann, S , Schüpfer, G and Mauch, J (2017). Application of Benford's law: a valuable tool for detecting scientific papers with fabricated data?. Der Anaesthesist vol. 66(10), pp. 795--802 . DOI:10.1007/s00101-017-0333-1.
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 (2015). Benford's Law in Scientific Research. International Journal of Scientific & Engineering Research, Volume 6, Issue 7, pp. 143-148. ISSN/ISBN:2229-5518.
Iafrate, JR (2014). Benford’s Law and Power Law Behavior in Fragmentation Processes. Undergraduate Honors Thesis, Williams College, Williamstown, MA.
Iorliam, A (2016). Application of power laws to biometrics, forensics and network traffic analysis. PhD Thesis, University of Surrey.
Iorliam, A, Ho, AT, Poh, N, Zhao, X and Xia, Z (2017). Benford's law for classification of biometric images. In: User-Centric Privacy and Security in Biometrics, Claus Vielhauer (Ed.). ISSN/ISBN:9781785612077. DOI:10.1049/PBSE004E_ch11.
Iorliam, A, Ho, ATS, Poh, N and Shi, YQ (2014). Do Biometric Images Follow Benford's Law?. Proceedings of the 22nd European Signal Processing Conf.(Eusipco). DOI:10.1109/IWBF.2014.6914261.
Iorliam, A, Ho, ATS, Poh, N, Tirunagari, S and Bours, P (2015). Data forensic techniques using  Benford’s law and Zipf’s law for keystroke dynamics. In: Proceedings of 3rd International Workshop on  Biometrics and Forensics (IWBF 2015). IEEE, pp. 1–6. DOI:10.1109/IWBF.2015.7110238.
Iorliam, A, Ho, ATS, Waller, A and Zhao, X (2017). Using Benford's Law Divergence and Neural Networks for Classification and Source Identification of Biometric Images. In: Shi Y., Kim H., Perez-Gonzalez F., Liu F. (eds) Digital Forensics and Watermarking. IWDW 2016. Lecture Notes in Computer Science, vol 10082. Springer, Cham, pp. 88-105. DOI:10.1007/978-3-319-53465-7_7.
Iorliam, A and Shangbum, FC (2017). On the Use of Benford’s Law to Detect JPEG Biometric Data Tampering. Journal of Information Security 8, pp. 240-256. DOI:10.4236/jis.2017.83016.
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.
Irwin, J (2015). The Effective Use of Benford’s Law to Assist in Detecting Fraud in U.S. Environmental Protection Agency (EPA) Toxics Release Inventory (TRI) Data. Faculty Forum, Issue No. 21, Spring 2015, The University of South Carolina Salkehatchie Campus.
Isaković-Kaplan, S, Demirović, L and Proho, M (2021). Benford’s Law in Forensic Analysis of Income Statements of Economic Entities in Bosnia and Herzegovina. Croatian Economic Survey 23(1), pp. 31-61. DOI:10.15179/ces.23.1.2.
Iudica, F (2012). Benford’s Law: Mathematical Properties and Forensic Accounting Applications. Master’s Thesis, Luiss Guido Carli University, Rome, Italy, 2012.
İlkdoğan, S (2020). İç denetimin hileye yaklaşımında Benford Kanunu’nun uygulanması [Application of Benford's Law in internal audit's approach to fraud]. Masters Thesis, Balikesir University Institute of Social Sciences, Balikesir. TUR
Jafaridargiri, A and Rostami, M (2021). A Survey on Benford Law in Tehran Stock Exchange . Management Research in Iran 17(1), pp. 95-110. PER
Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG.
Jammalamadaka, SR and SenGupta, A (2001). Topics in Circular Statistics. Chapter 3, Section 3.4.4, pp. 78-79, World Scientific Press, Singapore. ISSN/ISBN:9810237782. DOI:10.1142/4031.
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.
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
Jasak, Z (2010). Benfordov zakon i reinforcement učenje (Benford's Law and reinforcment learning) . MSc Thesis, University of Tuzla, Bosnia. SRP
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 (2017). Sum invariance testing and some new properties of Benford's law. Doctorial Dissertation, University of Tuzla, Bosnia and Herzegovina.
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.
Jiang, C, Zhang, X and Hu, B (2024). Government reporting credibility as immunity: Evidence from a public health event. Journal of Multinational Financial Management 73. DOI:10.1016/j.mulfin.2024.100847.
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.
Jianu, Io and Jianu, Iu (2021). Reliability of Financial Information from the Perspective of Benford’s Law. Entropy 23(5), article no. 557. DOI:10.3390/e23050557.
Joenssen, DW (2013). Two digit testing for Benford's Law. Proceedings of the ISI World Statistics Congress, 59th Session in Hong Kong.
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.
Johnson, GG and Weggenmann, J (2013). Exploratory Research Applying Benford’s Law to Selected Balances in the Financial Statements of State Governments. Academy of Accounting & Financial Studies Journal 17 (3), pp. 31-44.
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.
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.
Kıvraklar, K and Demirci, M (2019). Benford Yasası’nın Mali Denetim Alanında Kullanımı Üzerine Bir Uygulama [An Application On The Use Of Benford Law In The Field Of Financial Inspection]. Muhasebe ve Vergi Uygulamaları Dergisi 12(2), pp. 289-316. DOI:10.29067/muvu.340793. TUR
Kafri, O (2007). The Second Law as a Cause of the Evolution. Preprint arXiv: 0711.4507, 2007 - arxiv.org.
Kafri, O (2008). Sociological Inequality and the Second Law. http://arxiv.org/abs/0805.3206.
Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. posted on arXiv 8 March 2009 - arXiv:0901.3047v2.
Kaiser, M (2019). Benford’s Law As An Indicator Of Survey Reliability—Can We Trust Our Data?. Journal of Economic Surveys Vol. 00, No. 0, pp. 1–17. DOI:10.1111/joes.12338.
Kak, S (2018). Variations on the Newcomb-Benford Law. Preprint arXiv:1806.06695 [physics.soc-ph]; last accessed January 31, 2022.
Kak, S (2022). The Iterated Newcomb-Benford Distribution for Structured Systems. International Journal of Applied and Computational Mathematics 8, p. 51. DOI:10.1007/s40819-022-01251-2.
Kalaichelvan, M and Jie, SLK (2012). A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford's Law. International Research Journal of Finance and Economics 95, pp. 196-210. ISSN/ISBN:1450-2887.
Kapoor, M, Malani, A, Ravi, S and Agarwal, A (2020). Authoritarian Governments Appear to Manipulate COVID Data. Preprint arXiv:2007.09566 [econ.GN]; last accessed August 29, 2020.
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.
Kaşikci, B and Dalgar, H (2021). Muhasebe hi̇leleri̇ni̇n ortaya çikarilmasinda benford yasasi’nin kullanilmasina yöneli̇k bi̇r uygulama [An application on Benford’s Law usage for revealing accounting frauds] . Süleyman Demirel University Visionary Journal 12(32), pp. 1196-1211. ISSN/ISBN:1308-9552. DOI:10.21076/vizyoner.872157.
Kaushik, R (2022). Using benford’s law and RMSE to predict financial fraud using firm-reported data. PREPRINT (Version 1) available at Research Square. DOI:10.21203/rs.3.rs-2270360/v1.
Kazemitabar, J (2021). Double-Crossing Benford's Law. Preprint arXiv:2105.09812 [stat.AP]; last accessed May 31, 2021.
Kazemitabar, J (2022). A general framework for constructing distributions satisfying Benford’s law. Communications in Statistics - Simulation and Computation. DOI:10.1080/03610918.2022.2032153.
Kazemitabar, Jal and Kazemitabar, Jav (2020). Measuring the conformity of distributions to Benford's law. Communications in Statistics - Theory and Methods 49(14), pp. 3530-3536. DOI:10.1080/03610926.2019.1590599.
Kazemitabar, Jav and Kazemitabar, Jal (2022). Benford Test Based on Logarithmic Property. International Journal of Auditing Technology 4(4), pp. 279-291. DOI:10.1504/IJAUDIT.2022.10047587.
Kellerman, L (2014). Evaluating the effectiveness of Benford’s law as an investigative tool for forensic accountants. Masters thesis (Magister Commercii) in Forensic Accountancy at the Potchefstroom Campus of the North-West University.
Kendal, WS (2004). Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models. Ecological Complexity 1(3), pp. 193-209.
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.
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-mentor 80(3), pp. 34−44 .
Kordestani, G and Tatli, R (2016). The review of earnings management in different level of conservatism and institutional investors base Benford law. The Iranian Accounting and Auditing Review 23 (1), pp. 73–96. DOI:10.22059/ACCTGREV.2016.58467. PER
Köse, E and Özdemir, M (2019). Muhasebe Denetiminde Benford Kanunu ve Ölçekten Bağımsızlık Yönteminin Test Edilmesi [Testing of Benford's Law and Non-Scale Method in Auditing]. Kırklareli University Journal of Social Sciences 3(3), pp. 271-287. TUR
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.
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 (2022). First Digits’ Shannon Entropy. Entropy 24(10), pp. 1413. DOI:10.3390/e24101413.
Kreiner, WA (2022). Non-Newcomb-Benford Distributions. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. DOI:10.18725/OPARU-46416.
Krengel, U (2005). Die Anfangszifferverteilung. pp. 136-137 in: Einführung in die Wahrscheinlichkeitstheorie und Statistik, 8th ed, Vieweg und Sohn, Wiesbaden. ISSN/ISBN:3-8348-0063-5. GER
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.
Kubaščíková, Z and Pakšiová, R (2014). Applying Benford’s Law. European Financial Systems 2014 - Proceedings of the 11th International Scientific Conference, V.Kajurová, O. Deev, and J. Krajíček (Editors), pp. 359-363.
Kulikova, AA and Prokhorov, YV (2005). Completely asymmetric stable laws and Benford’s law. Theory of Probability and its Application 49(1), pp. 163-169. DOI:10.1137/S0040585X97980944.
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.
Kuruppu, N (2020). Uncovering Financial Shenanigans: Benford’s Law as a Computer Assisted Analytical Procedure. International Journal of Business and Management 15(7), pp. 37-47. DOI:10.5539/ijbm.v15n7p37.
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.
Lacasa, L and Fernández-Gracia, J (2019). Election Forensics: Quantitative methods for electoral fraud detection. Forensic Science International 294, pp. e19-e22. DOI:10.1016/j.forsciint.2018.11.010.
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.
Lai, H-Y and Wei, J-J (2024). First Digit Distributions of Gamma-Ray Bursts. Preprint arXiv:2401.10609 [astro-ph.HE];last accessed January 25, 2024.
Lanham, SW (2019). Analyzing Big Data with Benford’s Law: A Lesson for the Classroom. American Journal of Business Education 12(2), pp. 33-42. DOI:10.19030/ajbe.v12i2.10285.
Le, T and Lobo, GJ (2022). Audit Quality Inputs and Financial Statement Conformity to Benford’s Law. Journal of Accounting, Auditing & Finance 37(3), pp. 586–602 . DOI:10.1177/0148558X20930467.
Lebert, S, Mohrmann, U and Stefani, U (2019). Rounding Up Performance Measures in German Firms: Earnings Cosmetics or Earnings Management on a Larger Scale? . Available at SSRN: https://ssrn.com/abstract=2882741 . DOI:10.2139/ssrn.2882741.
Lebert, S, Mohrmann, U and Stefani, U (2021). Rounding up performance measures in German firms: Earnings cosmetics or earnings management on a larger scale?. Journal of Business Finance & Accounting 48(3-4), pp. 564-586. DOI:10.1111/jbfa.12494.
Leder-Luis, J (2020). The Economics of Fraud and Corruption. PhD Thesis, Massachusetts Institute of Technology.
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.
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.
Leemis, LM, Schmeiser, BW and Evans, DL (2000). Survival Distributions Satisfying Benford's Law. American Statistician 54(4), pp. 236-241. ISSN/ISBN:0003-1305. DOI:10.2307/2685773.
Lemons, DS, Lemons, N and Peter, W (2021). First Digit Oscillations. Stats 4(3), pp. 595-601. DOI:10.3390/stats4030035.
Lesperance, M, Reed, WJ, Stephens, MA, Tsao, C and Wilton, B (2016). Assessing Conformance with Benford’s Law: Goodness-Of-Fit Tests and Simultaneous Confidence Intervals. PLoS One 11(3): e0151235; published online 2016 Mar 28. DOI:10.1371/journal.pone.0151235.
Levičar, S (2020). Potential of Benford's Law and Machine Learning Based Verification in Agricultural Logistics. Proceedings of XIV. International Conference on Logistics in Agriculture. DOI:10.18690/978-961-286-406-4.4.
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, Lin, L-J, Yeh, C-C and Wang-T-S (2018). Does the board of directors as Fat Cats exert more earnings management? Evidence from Benford's law. The Quarterly Review of Economics and Finance 68, pp. 158-170. DOI:10.1016/j.qref.2017.09.005.
Lin, F, Wu, CM, Fang, TY and Wun, JC (2014). The relations among accounting conservatism, institutional investors and earnings manipulation. Economic Modelling, 37, pp. 164-174. DOI:10.1016/j.econmod.2013.10.020.
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.
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.
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, F (2007). Uncovering Fraud in Direct Marketing Data with a Fraud Auditing Case Builder. Lecture Notes in Computer Science 4702, pp. 540-547. ISSN/ISBN:978-3-540-74975-2. DOI:10.1007/978-3-540-74976-9_56.
Lu, F and Boritz, JE (2005). Detecting Fraud in Health Insurance Data: Learning to Model Incomplete Benford’s Law Distributions. Machine Learning: ECML 2005 (Proceedings). Lecture Notes in Artificial Intelligence 3270, pp. 633-640. ISSN/ISBN:0302-9743.
Lu, F, Boritz, JE and Covvey, D (2006). Adaptive Fraud Detection Using Benford’s Law. Advances in Artificial Intelligence Lecture Notes in Computer Science Volume 4013, pp. 347-358. ISSN/ISBN:978-3-540-34628-9. DOI:10.1007/11766247_30.
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). Test of Proportions Screening for the Newcomb-Benford Screen in the Audit Context: A Likelihood Triaging Protocol. Journal of Accounting and Finance Research 3(4), pp. 166-180. DOI:10.5430/afr.v3n4p166.
Lusk, EJ and Halperin, M (2015). Testing the mixing property of the Newcomb-Benford Profile: Implications for the audit context. International Journal of Economics & Finance 7(6), pp. 42-50. DOI:10.5539/ijef.v7n6p42.
Lusk, EJ and Halperin, M (2015). Account Screening Based Upon Digital Frequency Profiling in the Internal Audit Context: A Cartesian Distance Likelihood Triaging Protocol. Business Management Dynamics 5(3), pp.12-17.
Luty, P, Petković, M and Vavrek, R (2022). Applying Benfordʼs Law on assessing the reliability of financial information in European companies from the rental and leasing sector before and after the adoption of IFRS 16. The Theoretical Journal of Accounting 46(4), pp. 51-68. ISSN/ISBN:1641-4381 .
Macías, ALO and Ogua, ST (2018). Encontrando datos anómalos en la tributación. Aplicación de la Ley de Benford en el Impuesto a la Renta en Ecuador [Finding anomalous data in taxation. Application of the Benford Law on Income Tax in Ecuador]. SaberEs 10(2), pp. 173-188. SPA
Mack, V (2016). The Fingerprints of Fraud: An In-depth Study of Election Forensics with Digit Tests. PhD Thesis, Universitat Konstanz.
Madahali, L and Hall, M (2020). Application of the Benford’s law to Social bots and Information Operations activities. International Conference on Cyber Situational Awareness, Data Analytics and Assessment (CyberSA), Dublin, Ireland, pp. 1-8. DOI:10.1109/CyberSA49311.2020.9139709.
Mainusch, NM (2020). On Benford's law - Computing a Bayes factor with the Savage-Dickey method to quantify conformance of numerical data to Benford's law. Bachelor's Thesis, University of Osnabrueck, Institute of Cognitive Science, Germany.
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.
Manoochehrnia, P, Rachidi, F, Rubinstein, M, Diendorfer, G and Schulz, W (2009). Do lightning data obey the Benford's law?. Proceedings of X International Symposium on Lightning Protection (SIPDA), Curitiba, Brazil.
Manoochehrnia, P, Rachidi, F, Rubinstein, M, Schultz, W and Diendorfer, G (2010). Benford’s law and lightning data. Proceedings of the 30th International Conference on Lightning Protection (ICLP), Cagliari, Italy, 13–17 September; pp. 1–3 . DOI:10.1109/ICLP.2010.7845921.
Marcel, M (2017). Benford_py: a Python Implementation of Benford's Law Tests. GitHub repository; last accessed October 8, 2021.
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
Masters, AB (2020). Benford’s Law and Election Data. Blog posted on Medium, Nov 15.
Mataković, IC (2019). The empirical analysis of financial reports of companies in Croatia: Benford distribution curve as a benchmark for first digits. Croatian Review of Economic, Business and Social Statistics (CREBSS) 5(2), pp. 90-100 . DOI:10.2478/crebss-2019-0014.
Mataković, H (2021). Tourism Data in Croatia Assessed by Benford's Law. Journal of Public Administration, Finance and Law 19, pp. 166-184. DOI:10.47743/jopafl-2021-19-13.
Máté, D, Sadaf, R, Tarnóczi, T and Fenyves, V (2017). Fraud Detection by Testing the Conformity to Benford’s Law in the Case of Wholesale Enterprises. Polish Journal Of Management Studies, 16(1), pp.115-126. DOI:10.17512/pjms.2017.16.1.10 .
Mayo, R (2022). Hidden Risk: Detecting Fraud in Chinese Banks’ Non-performing Loan Data. nternational Journal of Finance & Banking Studies (2147-4486), 11(1), pp. 98–106. DOI:10.20525/ijfbs.v11i1.1550.
Maza-Quiroga, R, Thurnhofer-Hemsi, K, López-Rodríguez, D and López-Rubio, E (2023). Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit . Axioms 12, pp. 1117 . DOI:10.3390/axioms12121117.
McDonald, BD and Goodman, CB (2020). The Truth about Honesty in the Nonprofit Sector. SocArXiv 48g5c, Center for Open Science. DOI:10.31219/osf.io/48g5c.
Mebane, WR Jr (2006). Detecting Attempted Election Theft: Vote Counts, Voting Machines and Benford’s Law. Paper prepared for the 2006 Annual Meeting of the Midwest Political Science Association, Chicago, IL.
Mebane, WR Jr (2006). Election Forensics: The Second-digit Benford’s Law Test and Recent American Presidential Elections. pp 161-181 in: Alvarez, RM, Hall, TE and Hyde, SD (eds.), Election Fraud: Detecting and Deterring Electoral Manipulation. Brookings Press, Washington DC. ISSN/ISBN:9780815701606.
Mebane, WR Jr (2006). Election Forensics: Vote Counts and Benford’s Law. Proceedings of the Summer Meeting of the Political Methodology Society, UC-Davis, July, pp. 20-22.
Mebane, WR Jr (2006). Election Forensics: The Second-digit Benford’s Law Test and Recent American Presidential Elections. Proceedings of the Election Fraud Conference, Salt Lake City, Utah, September 29-30, 2006.
Mebane, WR Jr (2007). Election Forensics: Statistical Interventions in Election Controversies. Prepared for presentation at the 2007 Annual Meeting of the American Political Science Association, Chicago, August 30–Sept 2.
Mebane, WR Jr (2010). Fraud in the 2009 presidential election in Iran?. Chance 23(1), pp. 6-15. DOI:10.1080/09332480.2010.10739785.
Mebane, WR Jr (2010). Election Fraud or Strategic Voting? Can Second-digit Tests Tell the Difference?. Prepared for Presentation at the 2010 Summer Meeting of the Political Methodology Society. University of Iowa.
Mebane, WR Jr (2012). Second-digit Tests for Voters’ Election Strategies and Election Fraud. Prepared for presentation at the 2012 Annual Meeting of the Midwest Political Science Association, Chicago, April 12–15; last accessed Apr 11, 2019.
Mebane, WR Jr (2013). Election Forensics: The Meanings of Precinct Vote Counts’ Second Digits. Prepared for presentation at the 2013 Summer Meeting of the Political Methodology Society, University of Virginia, July 18–20.
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.
Merberg, A and Miller, SJ (2008). The Cramér-Rao Inequality. Course Notes for Math 162: Mathematical Statistics.
Michalski, T and Stoltz, G (2013). Do Countries Falsify Economic Data Strategically? Some Evidence That They Might. The Review of Economics and Statistics 95(2), pp. 591-616. DOI:10.1162/REST_a_00274.
Miller, SJ (2007). When the Cramér-Rao Inequality provides no information. Communications in Information and Systems 7(3), pp. 265-272.
Miller, SJ (2008). Benford’s Law and Fraud Detection, or: Why the IRS Should Care About Number Theory!. Presentation for Bronfman Science Lunch Williams College, October 21.
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 and Nigrini, MJ (2008). Order Statistics and Benford's Law. International Journal of Mathematics and Mathematical Sciences, Art. ID 382948. ISSN/ISBN:0161-1712. DOI:10.1155/2008/382948.
Miller, SJ and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. ISSN/ISBN:978-0691120607.
Miller, SJ and Takloo-Bighash, R (2007). Introduction to Random Matrix Theory. In: An Invitation to Modern Number Theory, Princeton University Press. ISSN/ISBN:9780691120607.
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 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.
Mir, TA, Darzi, MA, Ishtiaq, PM and Mufti, S (2023). Benford’s law: an application to sunspot data. Preprint posted on Research Square. DOI:10.21203/rs.3.rs-3372099/v1.
Misiolek, E (2003). Swarm simulations of the power law distribution models. Poster session submission.
Mochty, L (2002). Die Aufdeckung von Manipulationen im Rechnungswesen - Was leistet das Benford's Law?. Die Wirtschaftsprüfung 14, pp. 725-736. GER
Mocnik, F-J (2021). Benford's law and geographical information - the example of OpenStreetMap. International Journal of Geographical Information Science 35, pp. 1746-1772. DOI:10.1080/13658816.2020.1829627.
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..
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.
Montenegro, MALO (2006). Policing Pollution Control in the Philippines: Issues and Prospects. Research Proposal.
Morales, HR, Diaz, CB and Castello, RJ (2018). La Ley de Benford Aplicada a Una Base de Datos. Posible Indicador de Riesgo Inherente de La Información Contenida. 47º Jornadas Argentinas De Informática - JAIIO Simposio Argentino de GRANdes DAtos (AGRANDA 2018), pp. 32-45. ISSN/ISBN:2451-7569. SPA
Morales, HR, Porporato, M and Epelbaum, N (2021). Benford’s law for integrity tests of high-volume databases: a case study of internal audit in a state-owned enterprise. Journal of Economics, Finance and Administrative Science. DOI:10.1108/JEFAS-07-2021-0113.
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.
Morrow, J (2010). Benford's Law, Families of Distributions and a Test Basis. E-print formerly published on www.johnmorrow.info; last accessed Mar 10, 2021. .
Morrow, J (2014). Benford’s Law, Families of Distributions and a Test Basis. Center for Economic Performance Discussion Paper No 1291.
Morzy, M, Kajdanowicz, T and Szymański, BK (2016). Benford’s Distribution in Complex Networks. Scientific Reports 6:34917. DOI:1038/srep34917.
Mourraille, AMR (2012). Las elecciones presidenciales de Colombia 2010 a la luz de la Ley de Newcomb-Benford. Undergraduate Thesis, Pontificia Universidad Javeriana, Bogotá, Colombia. SPA
Mucko, P and Adamczyk, A (2023). Does the bankrupt cheat? Impact of accounting manipulations on the effectiveness of a bankruptcy prediction. PLoS ONE 18(1), e0280384. ISSN/ISBN:1932-6203. DOI:10.1371/journal.pone.0280384.
Mumic, N and Filzmoser, P (2021). A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data. Statistical Methods & Applications 30, 819–840. DOI:10.1007/s10260-021-00582-6.
Munther, E and Wright, R (2021). Did 2001 Mark the Beginning of a More Manipulated Market? An Analysis of Financial Markets via Benford’s Law. Bachelor’s Degree Project in Mathematics, Division of Mathematics and Physics Mälardalen University, Sweden .
Murtagh, J (2023). What Is Benford’s Law? Why This Unexpected Pattern of Numbers Is Everywhere. Scientific American May 8, 2023.
Nasser, L (2020). Digits. Netflix series - Connected: The Hidden Science of Everything, Episode 4.
Nguyen, HT, Kreinovich, V and Longpré, L (2003). Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals. The 12th IEEE International Conference on Fuzzy Systems. FUZZ’03. Fuzzy Systems 1, pp. 67-73. DOI:10.1109/FUZZ.2003.1209339.
Nguyen, HT, Kreinovich, V and Longpré, L (2004). Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Innite Intervals. Reliable Computing 10(2), 83-106. DOI:10.1023/B:REOM.0000015848.19449.12.
Nguyen, L, Nguyen, TT, Le, T and Mai, N (2023). Applying Benford’s Law to examine earnings management: Evidence from emerging ASEAN-5 countries. Journal of Financial Reporting and Accounting (in press).
Nguyen, TT (2019). Three essays on earnings quality. PhD Thesis, University of East London. DOI:10.15123/uel.86yq8.
Nguyen, TT, Duong, C and Nguyen, N (2018). Benford’s Law, earnings management, and accounting conservatism: The UK evidence. Proceedings of European Financial Management Association (EFMA) Annual Meeting, Milan.
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 (1999). Peculiar patterns of first digits. IEEE Potentials 18(2), pp. 24-27. DOI:10.1109/45.755849.
Nigrini, MJ (2005). An Assessment of the Change in the Incidence of Earnings Management Around the Enron-Andersen Episode. Review of Accounting and Finance 4, pp. 92-110. DOI:10.1108/eb043420.
Nigrini, MJ (2011). Forensic Analytics: Methods and Techniques for Forensic Accounting Investigations. John Wiley & Sons: Hoboken, New Jersey; (2nd edition published in 2020, isbn 978-1-119-58576-3). ISSN/ISBN:978-0-470-89046-2.
Nigrini, MJ (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection . John Wiley & Sons: Hoboken, New Jersey. ISSN/ISBN:978-1-118-15285-0. DOI:10.1002/9781119203094.
Nigrini, MJ (2017). Audit Sampling Using Benford's Law: A Review of the Literature With Some New Perspectives. Journal of Emerging Technologies in Accounting Vol. 14, No. 2, pp. 29–46. DOI:10.2308/jeta-51783.
Nigrini, MJ and Mittermaier, LJ (1997). The use of Benford's Law as an aid in analytical procedures. Auditing - A Journal of Practice & Theory 16(2), 52-67. ISSN/ISBN:0278-0380.
Nye, J and Moul, C (2007). The Political Economy of Numbers: On the Application of Benford's Law to International Macroeconomic Statistics. The BE Journal of Macroeconomics 7(1), 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.
Odueke, A and Weir, GRS (2012). Triage in Forensic Accounting using Zipf's Law. Issues in Cybercrime, Security and Digtal Forensics. Edited by G. R. S. Weir and A. Al-Nemrat. Glasgow. University of Strathclyde Publishing, pp. 33-43.
Oleksy, M (2010). Data Mining und Benford's Law als Controllinginstrumente. Band 45, Wismarer Schriften zu Management und Recht, Europäischer Hochschulverlag, Bremen. ISSN/ISBN:978-3867414-40. GER
Ollén, ER and Wennberg, J (2021). Assessing practicalities of Benford's Law: A study of the law's potential to detect fraud in transactional data. Bachelor thesis, Dept. of Economics, Lund University.
Oriol, JC (2007). Formation à la statistique par la pratique d'enquêtes par questionnaires et la simulation: étude didactique d'une experience d'enseignment dans u department d'IUT. Ph.D. Thesis, Université Lumière, Lyon, France. FRE
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.
Otey, ME (2006). Approaches to Abnormality Detection with Constraints. PhD thesis, The Ohio State University, USA.
Ou, F-Z, Wang, Y-G and Zhu, G (2019). A Novel Blind Image Quality Assessment Method Based On Refined Natural Scene Statistics. IEEE International Conference on Image Processing (ICIP), Taipei, Taiwan, pp. 1004-1008. DOI:10.1109/ICIP.2019.8803047.
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.
Özkan, K (2021). Benford Kanunu ve Genelleştirilmiş Benford Kanunu ile ekosistem doğallığının hesaplanması [Estimating ecosystem naturalness using Benford’s Law and Generalized Benford’s Law]. Turkish Journal of Forestry 22(2), pp. 73-82 . DOI:10.18182/tjf.907217. TUR
Özkundakci, D and Pingram, MA (2019). Nature favours “one” as the leading digit in phytoplankton abundance data. Limnologica 78, p. 125707 . DOI:10.1016/j.limno.2019.125707.
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.
Palacios, NT (2020). Benford's Law. History, mathematical justification and applications. Degree in Statistics Final Degree Project, Universidad de Valladolid. Facultad de Ciencias.
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.
Parker, MC and Jeynes, C (2023). A Maximum Entropy Resolution to the Wine/Water Paradox. Posted on Preprints.org 2023061551; last access June 28. 2023. DOI:10.20944/preprints202306.1551.v1.
Parnak, A, Baleghi, Y, Kazemitabar, J and (2020). A Novel Forgery Detection Algorithm Based on Mantissa Distribution in Digital Images. Proceedings of 6th Iranian Conference on Signal Processing and Intelligent Systems (ICSPIS), pp. 1-4. DOI:10.1109/ICSPIS51611.2020.9349611.
Parnes, D (2022). Banks’ Off-Balance Sheet Manipulations. Quarterly Review of Economics and Finance. DOI:10.1016/j.qref.2022.07.011.
Păunescu, M, Nichita, E-M, Lazăr, P and Frățilă, A (2023). Applying Benford’s Law to Detect Fraud in the Insurance Industry—A Case Study from the Romanian Market. Proceedings of Fostering Recovery Through Metaverse Business Modelling. DOI:10.1007/978-3-031-28255-3_4.
Pericchi, LR and Torres, DA (2004). La Ley de Newcomb-Benford y sus aplicaciones al Referendum Revocatorio en Venezuela. Reporte Técnico-definitivo 2a. versión: Octubre 01,2004. SPA
Pericchi, LR 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.
Perrotta, D, Cerasa, A, Barabesi, L and Menegatti, M (2019). Contamination And Manipulation Of Trade Data: The Two Faces Of Customs Fraud . 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. 394-397.
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.
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.
Plaček, M (2013). Is data of Znojmo reliable?. New Trends 2013 - Proceedings of 8th international scientific conference. Private College of Economics Studies Znojmo, p.52-57. ISSN/ISBN: 978-80-87314-54-8 . CZE
Plaček, M (2014). Aplikace Benfordova zákona na vládní makroekonomická data: případ obchodní bilance. Trendy ekonomiky a managementu VIII, č. 19, pp. 45-51. ISSN/ISBN:1802-8527. CZE
Plaček, M (2014). Applying Benford’s law by testing the government macroeconomics data. Acta academica karviniensia 14(3), pp. 148-160. DOI:10.25142/aak.2014.056.
Plaček, M and Krápek, M (2014). The applications of Benford´s law to macroeconomic data – Current Experience . New Trends 2014 - Proceedings of 9th international scientific conference. Private College of Economic Studies Znojmo, pp. 428-432. ISSN/ISBN:2336–7431 . CZE
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.
Popescu, II (2002). On the Lavelette’s nonlinear Zipf’s law. Online pre-print; link is broken. Copy of article is available on request.
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 (2005). Ziffernanalyse in Theorie und Praxis. Testverfahren zur Fälschungsaufspürung mit Benfords Gesetz. Diploma thesis, Universität Bonn, Germany, 2003. Published by Shaker Verlag, Aachen. 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.
Prasetyo, KA and Djufri_M (2020). Penggunaan Benford’s Law Untuk Menentukan Prioritas Audit Pajak Pertambahan Nilai [Using Benford's Law to Determine Value Added Tax Audit Priorities]. Scientax: Jurnal Kajian Ilmiah Perpajakan Indonesia 1(2), pp. 167–183. DOI:10.52869/st.v1i2.40 . IND
Pröger, L, Griesberger, P, Hackländer, K, Brunner, N and Kühleitner, M (2021). Benford’s Law for Telemetry Data of Wildlife. Stats 4(4), pp. 943–949. DOI:10.3390/ stats4040055.
Prudêncio, ARG (2015). Aplicação da Lei de Benford para o controlo das demonstrações financeiras de entidades bancárias [Application of Benford's Law for the control of the financial statements of banking entities]. Masters Thesis, Universidade de Lisboa. Instituto Superior de Economia e Gestão. POR
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 (2020). Abiding by the Law? Using Benford's Law to Examine the Accuracy of Nonprofit Financial Reports. Nonprofit and Voluntary Sector Quarterly 49(3), pp. 548-570. 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.
Rad, M, Amiri, A, Ranjbar, MH and Salari, H (2021). Predictability of financial statements fraud-risk using Benford’s Law. Cogent Economics & Finance 9(1), p. 1889756 . DOI:10.1080/23322039.2021.1889756.
Radiah, O and Ameer, R (2020). Benford Law and Earnings Analysis: International Comparison. Ch. 18 in: Handbook of Research on Accounting and Financial Studies, L. Farinha, A. Baltazar Cruz and J.R. Sebastião, IGI Global: Hershey, PA, pp. 381-404 . ISSN/ISBN:9781799821366. DOI:10.4018/978-1-7998-2136-6.ch018.
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.
Rasgen, M (2016). Hile Denetiminde Benford Yasası'nın Kullanımına İlişkin Bir Uygulama [An Application for the Use of Benford's Law in Fraud Control] . Yüksek Lisans Tezi. Dokuz Eylül Üniversitesi Sosyal Bilimler Enstitüsü ĠĢletme Anabilim Dalı, Izmir. TUR
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, G, Brähler, G and Kronfeld, T (2014). Deficit versus Social Statistics: Empirical Evidence for the Effectiveness of Benford’s Law. Applied Economics Letters 21(3), pp. 147-151. DOI:10.1080/13504851.2013.844319.
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, El Mouaaouy, F and Geidl, F (2013). Empirical methods in competition analysis – Applying Benford’s law to the Western Australian petroleum market. Available at SSRN: https://ssrn.com/abstract=2364384; last accessed Dec 7, 2019. DOI:10.2139/ssrn.2364384.
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.
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.
Rodriguez, RJ (2004). Reducing False Alarms in the Detection of Human Influence on Data. Journal of Accounting, Auditing & Finance 19(2), pp. 141-158. DOI:10.1177/0148558X0401900202.
Ross, KA (2011). Benford's Law, a growth industry. American Mathematical Monthly 118 (7), pp. 571-583. ISSN/ISBN:0002-9890. DOI:10.4169/amer.math.monthly.118.07.571.
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.
Rubin, AE (2021). Benford’s law: Applications to ordinary-chondrite mass distributions. Meteoritics & Planetary Science, pp. 1-14. DOI:10.1111/maps.13626.
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 (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.
Safaei, F, Akbar, R and Moudi, M (2022). Efficient methods for computing the reliability polynomials of graphs and complex networks. Journal of Supercomputing. DOI:10.1007/s11227-021-04216-2.
Said, T and Mohammed, K (2020). Detection of anomaly in socio-economic databases, by Benford probability law. 2020 IEEE 6th International Conference on Optimization and Applications (ICOA), Beni Mellal, Morocco, 2020, pp. 1-4. DOI:10.1109/ICOA49421.2020.9094466.
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.
Sampaio, AdH, Figueiredo, PS and Loiola, E (2022). Public Procurement In Brazil: Evidence of Frauds Using the Newcomb-Benford Law. The Public Management and Citizenship Journal 27(86). DOI:10.12660/cgpc.v27n86.82760.
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.
Sarkar, T (2018). What is Benford’s Law and why is it important for data science?. Posted on: towardsdatascience.com, last accessed September 3, 2019.
Sarkar, T (2023). What Is Benford‘s law and why is it important?. Possted on BuiltIn.com; last accessed June 28, 2023.
Satapathy, G, Bhattacharya, G, Puhan, NB and Ho, ATS (2020). Generalized Benford’s Law for Fake Fingerprint Detection. Proceedings of 2020 IEEE Applied Signal Processing Conference (ASPCON), Kolkata, pp. 242-246. DOI:10.1109/ASPCON49795.2020.9276660.
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.
Schäfer, C, Bömermann, H, Nauenburg, R, Wenzel, K, Müller, KR and Wagner, GG (2006). Qualitätssicherung des Faktors Interviewer für den Mikrozensus. pp 209-216 in: Kehlenbach, J, Rockmann, U (eds.): Amtliche Mikrodaten für die Sozial- und Wirtschaftswissenschaften, Forschungsdatenzentrum der Statistischen Landesämter: Beiträge zu den Nutzerkonferenzen des FDZ der Statistischen Landesämter 2005. GER
Schäfer, C, Schräpler, J-P and Müller, KR (2004). Identification, Characteristics and Impact of Faked and Fraudulent Interviews in Surveys. Proceedings of European Conference on Quality and Methodology in Official Statistics.
Schäfer, C, Schräpler, J-P, Müller, KR and Wagner GG (2004). Automatic Identification of Faked and Fraudulent Interviews in Surveys by Two Different Methods. Discussion paper 441, DIW Berlin (German Institute for Economic Research). ISSN/ISBN:1619-4535.
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.
Schatte, P (2001). Briefe an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 2/2001, pp 6-7.
Schiavo, M (2010). Analisi statistica sulla legge di benford. Tesi di Laurea, Facoltà di Scienze Statistiche, Universita' degli studi di Padova. ITA
Scholes, CA (2023). Applying the significant-digit law to simplify grading of chemical engineering students design projects. Australasian Journal of Engineering Education. DOI:10.1080/22054952.2023.2247292.
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 (2011). Benford's Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP). Jahrbücher für Nationalökonomie und Statistik 231(5-6). DOI:10.1515/jbnst-2011-5-609.
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.
Seaman, RS (2002). Benford’s law and and background field errors in data assimilation. Preprint, Bureau of Meteorology Research Centre, Melbourne, Australia.
Seenivasan, P, Easwaran, S, Sridhar, S and Sinha, S (2016). Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models. Frontiers in Physiology 6, p. 390. DOI:10.3389/fphys.2015.00390.
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.
Sharif, SN and Jaaman-Sharman, SH (2023). Robustness of Extended Benford’s Law Distribution and Its Properties. Proceedings of International Conference on Management Engineering, Software Engineering and Service Sciences (ICMSS 2022), N. Wahi et al. (Eds.), ACSR 98, pp. 195–204.
Sheng, G, Li, T, Su, Q, Chen, B and Tang, Y (2017). Detection of content-aware image resizing based on Benford’s law. Soft Computing 21, pp. 5693–5701. DOI:10.1007/s00500-016-2146-6.
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.
Silva, A, Floquet, S and Lima, R (2023). Newcomb-Benford Law in Neuromuscular Transmission: Validation at Hyperkalemic Conditions. Preprint arXiv:2309.06965 [physics.bio-ph]; last accessed September 21, 2023.
Silva, A, Floquet, S and Lima, R (2023). Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions. Stats 6(4), pp. 1053-1071 . DOI:10.3390/stats6040066.
Silva, AdeA and Gouvêa, MA (2023). Study on the effect of sample size on type I error, in the first, second and first-two digits excessmad tests. International Journal of Accounting Information Systems 48, p. 100599. DOI:10.1016/j.accinf.2022.100599.
Silva, S (2023). Benford’s Law to Detect Fake Data. Posted on DataDrivenInvestor.com; last accessed April 29, 2023.
Singh, K and Best, P (2020). Implementing Benford’s law in continuous monitoring applications. Journal of Accounting and Management Information Systems 2, pp. 379-404.
Singh, SS (2016). Using Benford’s Law in Audit. E-print from Regional Training Institute Kolkata, Indian Audit & Accounts Department .
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.
Spichal, L (2021). Benfordův zákon. Unpublished manuscript. CZE
Starunova, OA, Rudney, SG, Ivanova, AE, Semenova, VG and Starodubov, VI (2022). Application of Benford's Law for Quality Assessment of Preventive Screening Data. Mathematical Biology and Bioinformatics 17(2), pp. 230-249. DOI:10.17537/2022.17.230. RUS
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
Stückemann, S and Pflanzer, M (2010). Das Benfordsche Gesetz. Papermint 1/Juli 2010, pp. 31-34. GER
Sun, L, Ho, A, Xia, Z, Chen, J and Zhang, M (2019). Development of an Early Warning System for Network Intrusion Detection Using Benford’s Law Features. In: Meng W., Furnell S. (eds) Security and Privacy in Social Networks and Big Data. SocialSec 2019. Communications in Computer and Information Science, vol 1095. Springer, Singapore. DOI:10.1007/978-981-15-0758-8_5.
Sun, L, Ho, ATS, Xia, Z, Chen, J, Huang, X and Zhang, Y (2017). Detection and Classification of Malicious Patterns In Network Traffic Using Benford’s Law. 2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), Kuala Lumpur, pp. 864-872. DOI:10.1109/APSIPA.2017.8282154.
Swanson, D, Cho, MJ and Eltinge, J (2003). Detecting possibly fraudulent or error-prone survey data using Benford’s law. pp 4172-4177 in: 2003 Joint Statistical Meetings - Section on Survey Research Methods, Proceedings of the American Statistical Association.
Szabo, JK, Forti, LR and Callaghan, CT (2023). Large biodiversity datasets conform to Benford's law: Implications for assessing sampling heterogeneity. Biological Conservation 280, pp. 109982. DOI:10.1016/j.biocon.2023.109982.
Szymanowski, J (2010). Fenomen rozkładu Benforda [The phenomenon of Benford distribution]. Online - last accessed May 2, 2015. POL
Talwar, S and Mehta, K (2014). Devising a Model for Accounting Fraud Detection Based on Benford's Law. IOSR Journal of Economics and Finance Volume 2 - Simsr International Finance Conference (SIFICO), pp. 1-9. ISSN/ISBN:2321-5933.
Taylor, J (2005). Too many ties? An empirical analysis of the Venezuelan recall referendum counts. unpublished manuscript, Stanford University, USA.
Theodoro, R, Bonarim, CAG and Costa, DRdM (2021). Identifying Discretionary Actions Taken by Managers in Credit Unions: An Application of Benford's Law. Journal of Accounting, Management and Governance 24(3), pp. 331-348. DOI:10.51341/1984-3925_2021v24n3a5.
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 (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.
Tong, SF, Yang, YH and Xie, YJ (2013). Distinguishing Computer Graphics from Natural Images Based on Statistical Characteristics. Applied Mechanics and Materials, Vols. 380-384, pp. 1306-1309. DOI:10.4028/www.scientific.net/AMM.380-384.1306.
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.
Tsung, F, Zhou, Z and Jiang, W (2007). Applying manufacturing batch techniques to fraud detection with incomplete customer information. IIE Transactions 39(6), pp. 671-680. DOI:10.1080/07408170600897510.
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
Us, D (2021). Benford's Law: An Empirical Analysis of Reported Covid-19 Cases and Institutional Structures Around the Globe . Undergraduate Thesis, Università commerciale Luigi Bocconi, Milan. DOI:10.13140/RG.2.2.28839.88488.
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.
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.
Vovor-Dassu, KC (2021). Tests d'adéquation à la loi de Newcomb-Benford comme outils de détection de fraudes. PhD Thesis L’Universite de Montpellier. DOI:10.13140/RG.2.2.12559.25764. FRE
Waaldijk, F (2005). On the foundations of constructive mathematics - Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10(3), 249-324. DOI:10.1007/s10699-004-3065-z.
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.
Wang, D, Chen, F, Mao, J, Liu, N and Rong, F (2022). Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries . Energy Economics, p. 106310. DOI:10.1016/j.eneco.2022.106310.
Wang, L and Ma, B-Q (2023). A concise proof of Benford’s law. Fundamental Research . DOI:10.1016/j.fmre.2023.01.002.
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).
Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2007). Quantifying the Partial Volume Effect in PET Using Benford's Law. IEEE Transactions on Nuclear Science 54(5), pp. 1616-1625 Part 1. ISSN/ISBN:0018-9499. DOI:10.1109/TNS.2007.903182.
Whyman, G (2021). Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies. Applied Mathematics 12, pp. 578-586. ISSN/ISBN:2152-7385. DOI:10.4236/am.2021.127041.
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.
Williamson, J (2000). Random probability functions. Preprint.
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 .
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
Xu, X and Zeng, Z (2020). Did Alibaba Fake the Tmall “Double Eleven” Data? Evidence from Benford’s Law. In: Xu J., Duca G., Ahmed S., García Márquez F., Hajiyev A. (eds) Proceedings of the Fourteenth International Conference on Management Science and Engineering Management. ICMSEM 2020. Advances in Intelligent Systems and Computing, vol 1190. Springer, Cham. DOI:10.1007/978-3-030-49829-0_39.
Yang, Y (2021). Evaluation and correction of electricity consumption statistics based on Benford-Zipf. IOP Conf. Series: Earth and Environmental Science 692 pp. 022008. DOI:10.1088/1755-1315/692/2/022008.
Zenkov, AV (2015). Deviation from Benford’s law and identification of author peculiarities in texts . Computer Research and Modeling, vol. 7, no. 1, pp. 197–201 (in Russian). ISSN/ISBN:2076-7633. RUS
Zenkov, AV (2017). A New Statistical Method of Text Attribution. International Journal of Professional Science, 2017, No. 1, pp. 6–21. ISSN/ISBN:2542-1085.
Zenkov, AV (2017). A Method of Text Attribution Based on the Statistics of Numerals. Journal of Quantitative Linguistics, pp. 256-270; published online: 20 Sep 2017. ISSN/ISBN:0929-6174 (Print), 1. DOI:10.1080/09296174.2017.1371915.
Zenkov, AV (2021). Stylometry and Numerals Usage: Benford’s Law and Beyond. Stats 4(4), pp. 1051-1068. ISSN/ISBN:2571-905X. DOI:10.3390/stats4040060.
Zhao, C and Wang, CA (2021). A cross‐site comparison of online review manipulation using Benford’s law. Electronic Commerce Research. DOI:10.1007/s10660-020-09455-8.

Cross Reference Up

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

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