Benford Online Bibliography

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

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Abrantes-Metz, RM, Kraten, M, Metz, AD and Seow, G (2012). Libor Manipulation?. Journal of Banking & Finance 36(1), pp. 136-150. ISSN/ISBN:0378-4266. DOI:10.1016/j.jbankfin.2011.06.014.
Afanasiev, S, Smirnova, A and Kotereva, D (2021). Itsy Bitsy SpiderNet: Fully Connected Residual Network for Fraud Detection. Preprint arXiv:2105.08120 [cs.LG]; last accessed May 24, 2021.
Aggarwal, V and Dharni, K (2020). Deshelling the Shell Companies Using Benford’s Law: An Emerging Market Study. Vikalpa 45(3), pp. 160-169. DOI:10.1177/0256090920979695.
Agyemang, EF, Nortey, ENN, Minkah, R and Asah-Asante, K (2023). The unfolding mystery of the numbers: First and second digits based comparative tests and its application to ghana’s elections. Model Assisted Statistics and Applications 18(2), pp. 183-192. DOI:10.3233/MAS-221418.
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
Alagöz, A and Ay, M (2001). Muhasebe denetiminde Benford kanunu temelli dijital analiz [Benford's law-based digital analysis in auditing]. Selçuk Üniversitesi Sosyal ve Ekonomik Araştırmalar Dergisi 4, pp. 59-76. TUR
Alexander, J (2009). Remarks on the use of Benford's law. Social Science Research Network (November 13, 2009). Available at SSRN: http://ssrn.com/abstract=1505147 or . DOI:10.2139/ssrn.1505147.
Alexopoulos, T and Leontsinis, S (2014). Benford's Law in Astronomy. Journal of Astrophysics and Astronomy, 35(4), pp. 639-648. ISSN/ISBN:0250-6335. DOI:10.1007/s12036-014-9303-z.
Alipour, A and Alipour, S (2019). Application of Benford’s Law in Analyzing Geotechnical Data. Civil Engineering Infrastructures Journal 52(2), pp. 323 – 334. DOI:10.22059/ceij.2019.272005.1534.
Alshaikh, L (2022). Benford's Law on Social Media. Young Scientists Journal, posted January 16, 2022, last accessed January 31, 2022.
Alves, AD, Yanasee, HH and Soma, NY (2016). An analysis of bibliometric indicators to JCR according to Benford’s law. Scientometrics 107(3), pp. 1489–1499. DOI:10.1007/s11192-016-1908-3.
Alves, AD, Yanasse, HH and Soma, NY (2014). Benford's Law and articles of scientific journals: comparison of JCR® and Scopus data. Scientometrics 98, pp. 173-184. ISSN/ISBN:0138-9130. DOI:10.1007/s11192-013-1030-8.
Amanda Bowman, A (2016). Contributions to the Testing of Benford's Law. Masters Thesis, McMaster University, Hamilton, Canada.
Anab, F, Khaliq, A and Younas, I (2021). A Statistical Analysis of Covid-19 Data of Pakistan by Applying Benford’s Law. Journal of Applied Pharmacy 13, pp. 55-60.
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.
Andriotis, P, Oikonomou, G and Tryfonas, T (2013). JPEG steganography detection with Benford's law. Digital Investigation 9(3-4), pp. 246-57. DOI:10.1016/j.diin.2013.01.005.
Antunes, AM, Teixeira, D and Sousa, F (2023). Benford’s Law: the fraud detection’s left hand. Proceedings of 18th Iberian Conference on Information Systems and Technologies (CISTI), Aveiro, Portugal, pp. 1-6. DOI:10.23919/CISTI58278.2023.10211738.
Arezzo, MF and Cerqueti, R (2023). A Benford’s Law view of inspections’ reasonability. Physica A: Statistical Mechanics and its Applications 632, Part 1, pp. 129294. DOI:10.1016/j.physa.2023.129294.
Arita, M (2005). Scale-freeness and biological networks. Journal of Biochemistry, 138 (1): 1-4. ISSN/ISBN:0021-924X. DOI:10.1093/jb/mvi094.
Ausloos, M, Castellano, R and Cerqueti, R (2016). Regularities and discrepancies of credit default swaps: a data science approach through Benford's law. Chaos, Solitons & Fractals 90, pp. 8-17. DOI:10.1016/j.chaos.2016.03.002.
Ausloos, M, Cerqueti, R and Lupi, C (2017). Long-range properties and data validity for hydrogeological time series: The case of the Paglia river. Physica A: Statistical Mechanics and its Applications 470, pp. 39-50. DOI:10.1016/j.physa.2016.11.137.
Ausloos, M, Cerqueti, R and Mir, TA (2017). Data science for assessing possible tax income manipulation: The case of Italy. Chaos, Solitons and Fractals 104, pp. 238–256. DOI:10.1016/j.chaos.2017.08.012.
Ausloos, M, Ficcadenti, V, Dhesi, G and Shakeel, M (2021). Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity. Physica A: Statistical Mechanics and its Applications 574, pp. 125969. DOI:10.1016/j.physa.2021.125969.
Ausloos, M, Ficcadenti, V, Dhesi, G and Shakeel, M (2021). Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity. Preprint arXiv:2104.07962 [q-fin.ST]; last accessed April 30, 2021. To appear in: Physica A: Statistical Mechanics and its Applications, 574. DOI:10.1016/j.physa.2021.125969.
Ausloos, M, Herteliu, C and Ileanu, B-V (2015). Breakdown of Benford’s law for birth data. Physica A: Statistical Mechanics and its Applications Volume 419, pp. 736–745. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2014.10.041.
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.
Aybars, A and Ataunal, L (2016). An application of Benford’s law to fundamental accounting figures reported by Borsa Istanbul (BIST) companies. Journal of Economics, Finance and Accounting 3(3), pp. 234-243. DOI:10.17261/Pressacademia.2016321991.
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.
Baer, MB (2006). Rényi to Rényi - Source Coding under Siege. Proceedings of 2006 IEEE International Symposium on Information Theory, Seattle, WA, pp. 1258--1262. DOI:10.1109/ISIT.2006.262027.
Baer, MB (2006). Prefix coding under Siege. Preprint on CoRR archive: arXiv cs/0605099; last updated 28 March 2009.
Baer, MB (2007). Reserved-Length Prefix Coding. Proceedings of 2008 IEEE International Symposium on Information Theory, {ISIT}, Toronto, ON, Canada, July 6-11, 2008, pp. 2469--2473. DOI:10.1109/ISIT.2008.4595435.
Baer, MB (2007). Bounds on Generalized Huffman Codes. Preprint on CoRR archive: arXiv cs/0702059; last updated 7 Oct 2010.
Balado, F and Silvestre, GCM (2021). Benford's Law: Hammering a Square Peg Into a Round Hole?. 29th European Conference on Signal Processing (EUSIPCO), Dublin, Ireland, August, 2021, pp. 796-800. ISSN/ISBN: 978-9-0827-9707-7.
Balado, F and Silvestre, GCM (2024). General Distributions of Number Representation Elements. Probability in the Engineering and Informational Sciences 38(3), pp. 594-616 . DOI:10.1017/S0269964823000207.
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.
Baláž, V, Nagasaka, K and Strauch, O (2010). Benford's law and distribution functions of sequences in (0, 1). Mathematical Notes, 2010, Vol. 88, No. 4, pp 449–463. Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 4, pp. 485–501. ISSN/ISBN:0001-4346. DOI:10.1134/S0001434610090178.
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, 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.
Barabesi, L and Pratelli, L (2020). On the Generalized Benford law. Statistics & Probability Letters 160, 108702 . DOI:10.1016/j.spl.2020.108702.
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.
Bartulović, M and Mitrović, M (2020). Application of Benford's Law in Forensic Accounting. Conference Proceedings of Contemporary Issues in Economy & Technology CIET 2020, Split.
Baryła, M (2012). Some Remarks about Benford's Distribution. Mathematical Economics 8(15), pp. 5-15.
Baryła, M and Pociecha, J (2019). Euclidean distance as a measure of conformity to Benford's law in digital analysis for fraud detection. Book of Short Papers, Proceedings of the 12th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS), pp. 75-78.
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.
Baumeister, J and Macedo, TG (2011). Von den Zufallszahlen und ihrem Gebrauch. Stand: 21, November 2011. GER
Becker, PW (1982). Patterns in Listings of Failure-Rate and MTTF Values and Listings of Other Data. IEEE Transactions on Reliability 31(2), 132-134. ISSN/ISBN:0018-9529.
Becker, T, Burt, D, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J, Strauch, FW and Talbut, B (2018). Benford's Law and Continuous Dependent Random Variables. Annals of Physics 388, pp. 350–381. DOI:10.1016/j.aop.2017.11.013.
Becker, T, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J and Strauch, FW (2013). Benford's Law and Continuous Dependent Random Variables. Preprint arXiv:1309.5603 [math.PR]; last accessed October 23, 2018. DOI:10.1016/j.aop.2017.11.013.
Beer, TW (2009). Terminal digit preference: beware of Benford's law. Journal of Clinical Pathology 62(2), p. 192. DOI:10.1136/jcp.2008.061721.
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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.
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Berger, A (2015). Most linear flows on ℝ^d are Benford . Journal of Differential Equations 259(5), pp. 1933–1957. DOI:10.1016/j.jde.2015.03.016.
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Berger, A and Eshun, G (2016). A characterization of Benford's law in discrete-time linear systems. Journal of Dynamics and Differential Equations 28(2), pp. 432-469. ISSN/ISBN:1040-7294. DOI:10.1007/s10884-014-9393-y.
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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.
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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 and Morrison, KE (2008). Scale-Distortion Inequalities for Mantissas of Finite Data Sets. Journal of Theoretical Probability 21(1), pp. 97-117. ISSN/ISBN:0894-9840.
Berger, A and Xu, C (2018). Best Finite Approximations of Benford’s Law. Journal of Theoretical Probability. DOI:10.1007/s10959-018-0827-z.
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Burns, BD (2020). Do people fit to Benford’s law, or do they have a Benford bias?. Proceedings of the 42nd Annual Virtual Meeting of the Cognitive Science Society, pp. 1729-1735.
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Cross Reference Up

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

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