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Fairthorne, RA (1969). Progress in Documentation - Empirical Hyperbolic Distributions (Bradford-Zipf-Mandelbrot) for Bibliometric Description and Prediction. Journal of Documentation 25(4), pp. 319-343; reprinted 2005 in Journal of Documentation 61(2), pp. 171-193. ISSN/ISBN:0022-0418. DOI:10.1108/00220410510585179. View Complete Reference Online information Works that this work references Works that reference this work
Fairweather, WR (2017). Sensitivity and Specificity in the Application of Benford’s Law to Explore for Potential Fraud. Journal of Forensic & Investigative Accounting 9(3), Special Issue, pp. 953-961. View Complete Reference Online information Works that this work references Works that reference this work
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 View Complete Reference Online information Works that this work references No Bibliography works reference this work
Falk, BH, Tsoulalas, G and Zhang, N (2023). Crypto Wash Trading: Direct vs. Indirect Estimation. Preprint arXiv:2311.18717 [econ.GN]; last accessed January 4, 2024. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fallico, D (2023). Searching Applications of Benford’s Law to Investigate Beam Jitter. Presentation for Teacher Research Associate (TRAC) Program at Fermilab. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fang, G (2022). Investigating Hill’s question for some probability distributions. AIP Advances 12, 095004. DOI:10.1063/5.0100429. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fang, X, Miller, SJ, Sun, M and Verga, A (2024). Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference No online information available Works that this work references Works that reference this work
Farhadi, N (2021). Can we rely on COVID-19 data? An assessment of data from over 200 countries worldwide. Science Progress 104(2). DOI:10.1177/00368504211021232. View Complete Reference Online information Works that this work references Works that reference this work
Farhadi, N and Lahooti, H (2021). Are COVID-19 Data Reliable? A Quantitative Analysis of Pandemic Data from 182 Countries. COVID 1, pp. 137–152. DOI:10.3390/covid1010013. View Complete Reference Online information Works that this work references Works that reference this work
Farhadi, N and Lahooti, H (2021). Pandemic Growth and Benfordness: Empirical Evidence from 176 Countries Worldwide. COVID 1(1), pp. 366-383. DOI:10.3390/covid1010031. View Complete Reference Online information Works that this work references Works that reference this work
Farhadi, N and Lahooti, H (2022). Forensic Analysis of COVID-19 Data from 198 Countries Two Years after the Pandemic Outbreak. COVID 2(4), pp. 472-484. DOI:10.3390/covid2040034. View Complete Reference Online information Works that this work references Works that reference this work
Farhadi, N and Lahooti, H (2022). In Data We Trust: Proving Market Manipulation on the Tehran Stock Exchange. International Journal of Business and Management 17(4). DOI:10.5539/ijbm.v17n4p1. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Farkas, J and Gyürky, G (2010). The significance of using the Newcomb-Benford law as a test of nuclear half-life calculations. Acta Physica Polonica B 41(6), pp. 1213-1221. ISSN/ISBN:PL 0587-4254. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Farris, M, Luntzlara, N, Miller, SJ, Shao, L and Wang, M (2021). Recurrence Relations and Benford's Law. Statistical Methods & Applications 30, pp. 797–817. DOI:10.1007/s10260-020-00547-1. View Complete Reference Online information Works that this work references Works that reference this work
Farris, M, Luntzlara, N, Miller, SJ, Zhao, L and Wang, M (2019). Recurrence Relations and Benford’s Law. Preprint arXiv:1911.09238 [math.PR]; last accessed December 8, 2019. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Favaretto, F (2007). Verificacao da qualidade de dados atraves da lei de Benford. Proceedings of XXVII Brazilian National Conference on Engineering, October 2007. View Complete Reference Online information Works that this work references Works that reference this work
Feldstein, A and Goodman, R (1976). Convergence Estimates for Distribution of Trailing Digits. Journal of the Association for Computing Machinery 23(2), pp. 287-297. ISSN/ISBN:0004-5411. DOI:10.1145/321941.321948. View Complete Reference Online information Works that this work references Works that reference this work
Feldstein, A and Turner, P (1986). Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction. IMA Journal of Numerical Analysis 6, pp. 241-251. DOI:10.1093/imanum/6.2.241. View Complete Reference Online information Works that this work references Works that reference this work
Feldstein, A and Turner, PR (1996). Overflow and underflow in multiplication and division. Applied Numerical Mathematics 21(3), pp. 221-239. ISSN/ISBN:0168-9274. DOI:10.1016/0168-9274(96)00010-4. View Complete Reference Online information Works that this work references Works that reference this work
Feldstein, A and Turner, PR (2006). Gradual and tapered overflow and underflow: A functional differential equation and its approximation. Applied Numerical Mathematics 56(3-4), pp. 517-532. ISSN/ISBN:0168-9274. DOI:10.1016/j.apnum.2005.04.018. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Feller, W (1971). An Introduction to Probability Theory and Its Applications. 2nd ed., J. Wiley (see p 63, vol 2). View Complete Reference No online information available Works that this work references Works that reference this work
Fellman, J (2014). The Benford paradox. Journal of statistical and econometric methods 3(4), pp. 1-20. ISSN/ISBN:2241-0384 . View Complete Reference Online information Works that this work references Works that reference this work
Fellman, J (2016). En statistisk paradox. Quintensen No.2, pp. 15-17. SWE View Complete Reference Online information Works that this work references Works that reference this work
Fellman, J (2017). Benfordparadoxen. Arkhimedes 2017(4), pp. 26-33. SWE View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fernandes, P and Antunes, M (2023). Benford’s law applied to digital forensic analysis. Forensic Science International: Digital Investigation 45, p. 301515. DOI:10.1016/J.FSIDI.2023.301515. View Complete Reference Online information Works that this work references Works that reference this work
Fernandes, P, Ó Ciardhuáin, S and Antunes, M (2024). Uncovering Manipulated Files Using Mathematical Natural Laws. In: Vasconcelos, V., Domingues, I., Paredes, S. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2023. Lecture Notes in Computer Science, vol 14469. Springer, Cham . DOI:10.1007/978-3-031-49018-7_4. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Ferreira, KB and Levy, S (2022). Characterizing Memory Failures Using Benford's Law. Proceedings of Euro-Par 2021: Parallel Processing Workshops. Lecture Notes in Computer Science, vol 13098. Springer, Cham. DOI:10.1007/978-3-031-06156-1_25. View Complete Reference Online information Works that this work references Works that reference this work
Ferreira, KB and Levy, S (2023). Using Benford's Law to Identify Unusual Failure Regions. Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis, pp. 516–519 . DOI:10.1145/3624062.3624121. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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 View Complete Reference Online information Works that this work references Works that reference this work
Ferrero, JM, Ballesteros, BC and Milani Filho, MAF (2015). The link between earnings management and digital pattern. Revista de Administração, Contabilidade e Economia, 14(1), pp. 351-382. DOI:10.18593/race.v14i1.4065 . View Complete Reference Online information Works that this work references Works that reference this work
Fewster, RM (2009). A Simple Explanation of Benford's Law. American Statistician 63(1), pp. 26-32. DOI:10.1198/tast.2009.0005. View Complete Reference Online information Works that this work references Works that reference this work
Filho, DF, Silva, L and Carvalhoa, E (2022). The forensics of fraud: Evidence from the 2018 Brazilian presidential election. Forensic Science International: Synergy, p. 100286. ISSN/ISBN:2589-871X. DOI:10.1016/j.fsisyn.2022.100286. View Complete Reference Online information Works that this work references Works that reference this work
Filho, DF, Silva, L and Medeiros, H (2022). “Won’t get fooled again”: statistical fault detection in COVID-19 Latin American data. Globalization and Health 18, pp.105. DOI:10.1186/s12992-022-00899-1. View Complete Reference Online information Works that this work references Works that reference this work
Filho, MAFM (2013). A Confiabilidade dos Dados Financeiros de Hospitais Filantrópicos Canadenses: Um Estudo Empírico Baseado na Lei de Benford [The reliability of financial information of charitable organizations: an exploratory study based on the Benford’s Law]. Sociedade, Contabilidade e Gestão 8(2), pp. 47-63. POR View Complete Reference Online information Works that this work references Works that reference this work
Filho, MAFM, Poker, JH, Belli, MM and Segura, LC (2016). Bolsas de Valores dos BRICS: Uma Análise das Informações Financeiras Baseada na Lei de Benford [BRICS Stock Exchanges: An Analysis of Financial Information Based on Benford's Law]. Revista Contabilidade Vista e Revista, Universidade Federal de Minas Gerais, 64 Belo Horizonte 27(2), mai/ago. ISSN/ISBN: 0103-734X. POR View Complete Reference Online information Works that this work references No Bibliography works reference this work
Filho, RNA (2016). Fraude em licitações e a Lei de Benford – aplicação em perícias de engenharia civil do DPF. In: Seminário de Perícias de Engenharia da Polícia Federal 8, Maceió. POR View Complete Reference No online information available No Bibliography works referenced by this work. Works that reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Filipponi, P (1994). Fn and Ln cannot have the same initial digit. Pi Mu Epsilon Journal 10.1, pp. 5-6. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Filipponi, P and Menicocci, R (1995). Some Probabilistic Aspects of the Terminal Digits of Fibonacci Numbers. Fibonacci Quarterly 33(4), pp. 325-331. ISSN/ISBN:0015-0517. View Complete Reference Online information Works that this work references Works that reference this work
Finch, S (2011). Newcomb-Benford Law. Online publication - last accessed July 16, 2018. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fisher, AM and Zhang, X (2023). Uniform distribution mod 1 for sequences of ergodic sums and continued fractions. Preprint arXiv:2307.14843 [math.DS]; last accessed August 5, 2023 . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fisher, D (2014). The Simple Mathematical Law That Financial Fraudsters Can't Beat. Forbes.com, May 30. View Complete Reference Online information Works that this work references Works that reference this work
Fisher, L (2009). The Perfect Swarm: The Science of Complexity in Everyday Life. Basic Books, pp. 159-162, 168, 242-243. ISSN/ISBN:978-0-465-01884-0. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Flam, F (2000). Math formula could help spot tax cheats. The Pittsburg Post-Gazette, 19 April. View Complete Reference No online information available No Bibliography works referenced by this work. No Bibliography works reference this work
Flayyih, HH (2013). Using Benford Law in Detecting Earnings Management and its Reflection on the audit quality : In application on a sample of listed companies in the Iraq stock Exchange. Master Thesis, College of Administration and Economics, University of Baghdad. ARA View Complete Reference Online information Works that this work references Works that reference this work
Flayyih, HH, Noorullah, AS, Jari, AS and Hasan, AM (2020). Benford Law: A Fraud Detection Tool Under Financial Numbers Game: A Literature Review. Social Science and Humanities Journal 4(5), pp. 1909-1914. View Complete Reference Online information Works that this work references Works that reference this work
Flehinger, BJ (1966). On the Probability that a Random Integer has Initial Digit A. American Mathematical Monthly 73(10), pp. 1056-1061. ISSN/ISBN:0002-9890. DOI:10.2307/2314636. View Complete Reference Online information Works that this work references Works that reference this work
Flenghi, R and Jourdain, B (2023). Convergence to the uniform distribution of vectors of partial sums modulo one with a common factor. Preprint arXiv:2308.01874 [math.PR]; last accessed August 24, 2023. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Florack, LMJ (1999). Visual representations embodying spacetime structure. Technical Report, University Utrecht, UU-CS-1999-07. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Ford, C (2016). Earthquake data and Benford’s Law. Posted on blog "Statistics you can probably trust" . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Forgan, D (2013). Benford’s Law – Can you detect fraud by the first digit?. Research the HeadLines website; last accessed Dec 6, 2019. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Forster, RP (2006). Auditoria contábil em entidades do terceiro setor : uma aplicação da Lei Newcomb-Benford. Universidade de Brasília, Brasília. POR View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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 View Complete Reference Online information Works that this work references Works that reference this work
Franel, J (1917). A propos des tables de logarithmes. Festschrift der Naturforschenden Gesellschaft in Zürich, Vierteljahrsschrift 62, pp. 286-295. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Frank, A (2006). Benford's law. Reason-and-Rhyme Blog. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Freeman, RB (2018). Benford's Law. Lecture 17 notes for Economics 1818 course, Harvard University. View Complete Reference Online information Works that this work references Works that reference this work
Freidank, C-C and Kusch, A (2008). Das Benfordsche Gesetz als Instrument zur Aufdeckung von Unregelmäßigkeiten im Rahmen der Jahresabschlussprüfung. Wirtschaftswissenschaftliches Studium, Vol. 37, No. 2, pp. 100-102. ISSN/ISBN:0340-1650. GER View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Frick, RA , Liu, H and Steinebach, M (2020). Detecting double compression and splicing using benfords first digit law. ARES '20: Proceedings of the 15th International Conference on Availability, Reliability and SecurityAugust, Article No. 47, pp. 1–9. DOI:10.1145/3407023.3409200. View Complete Reference Online information Works that this work references Works that reference this work
Friedberg, SH (1984). The Distribution of First Digits. College Mathematics Journal 15(2), pp. 120-125. ISSN/ISBN:0049-4925. DOI:10.2307/2686516. View Complete Reference Online information Works that this work references Works that reference this work
Frieden, BR (1999). F-Information, a Unitless Variant of Fisher Information. Foundations of Physics 29(10), pp. 1521-1541. ISSN/ISBN:0015-9018. DOI:10.1023/A:1018806603833. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Friedman, E, Kolakaluri, R and Rege, M (2020). Benford’s Law Applied to Precinct Level Election Data. Issues in Information Systems 21(2), pp. 238-247. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Frost, J (2023). Benford’s Law Explained with Examples. Posted on Statistics by Jim blog; last accessed June 28, 2023. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Fu, Q, Fang, Z, Villas-Boas, SB and Judge, G (2014). An Investigation of the Quality of Air Data in Beijing. Unpublished manuscript. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Fuchs, A and Letta, G (1984). Sur le problème du premier chiffre décimal. Bollettino dell'Unione Matematica Italiana, VI. Ser., B 3, pp. 451-461. FRE View Complete Reference No online information available Works that this work references Works that reference this work
Fuchs, A and Letta, G (1996). Le problème du premier chiffre décimal pour les nombres premiers. The Electronic Journal of Combinatorics 3(2), R25. FRE View Complete Reference Online information Works that this work references Works that reference this work
Fuchs, A and Nanopoulos, P (1985). Mesures invariantes par translation, classes de Dynkin first-digit problem. Advances in Mathematics 55, pp. 24-74. DOI:10.1016/0001-8708(85)90004-0. FRE View Complete Reference Online information Works that this work references Works that reference this work
Furlan, LV (1946). Das Harmoniegesetz der Statistik: Eine Untersuchung ueber die metrische Interdependenz der sozialen Erscheinungen. Basel, Verlag fuer Recht und Gesellschaft AG, xiii:504p. DOI:10.1111/j.1467-6435.1948.tb00591.x. GER View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Furry, WH and Hurwitz, H (1945). Distribution of numbers and distribution of significant figures. Nature 155(3924), pp. 52-53. DOI:doi:10.1038/155052a0. View Complete Reference Online information Works that this work references Works that reference this work

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