Abate, GT, de Brauw, A, Gibson, J, Hirvonen, K and Wolle, A (2020). Telescoping causes overstatement in recalled food consumption: Evidence from a survey experiment in Ethiopia. IFPRI Discussion Paper 1976. Washington, DC: International Food Policy Research Institute (IFPRI). DOI:10.2499/p15738coll2.134161.
|
|
|
|
|
Abdulazizov, H (2021). Real Unemployment Measurement in Azerbaijan. Baku Research Institute September 27.
|
|
|
|
|
Abrantes-Metz, RM and Bajari, P (2009). Screens for Conspiracies and Their Multiple Applications. Antitrust 24(1), pp. 66-71. ISSN/ISBN:2162-996X.
|
|
|
|
|
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.
|
|
|
|
|
Abrantes-Metz, RM and Villas-Boas, SB (2010). Tracking the Libor Rate. Available at SSRN: https://ssrn.com/abstract=1646600. DOI:10.2139/ssrn.1646600.
|
|
|
|
|
Abrantes-Metz, RM, Villas-Boas, SB and Judge, G (2011). Tracking the Libor rate. Applied Economics Letters 18(10), pp. 893-899. ISSN/ISBN:1466-4291. DOI:10.1080/13504851.2010.515197.
|
|
|
|
|
Abumrad, J and Krulwich, R (2009). From Benford to Erdős. WNYC Radiolab, Season 6, Episode 5, October 9, 2009.
|
|
|
|
|
ACL Services Ltd. (2012). About Benford analysis. Software documentation website (last retrieved 24Jan2014).
|
|
|
|
|
Adam, A and Tsarsitalidou, S (2022). Data misreporting during the COVID19 crisis: The role of political institutions. Economics Letters 213, p. 110348. DOI:10.1016/j.econlet.2022.110348.
|
|
|
|
|
Adam, I, Fazekas, M, Kazmina, Y, Teremy, Z, Tóth, B, Villamil, IR and Wachs, J (2022). Public procurement cartels: A systematic testing of old and new screens. Government Transparency Institute Working Paper series: GTI-WP/2022:01, Budapest, Hungary.
|
|
|
|
|
Adhikari, AK (1969). Some Results on Distribution of Most Significant Digit. Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), pp. 413-420. ISSN/ISBN:0581-5738.
|
|
|
|
|
Adhikari, AK and Sarkar, BP (1968). Distribution of most significant digit in certain functions whose arguments are random variables. Sankhya-The Indian Journal of Statistics Series B, no. 30, pp. 47-58. ISSN/ISBN:0581-5738.
|
|
|
|
|
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, R and Lucey, BM (2007). Psychological barriers in gold prices?. Review of Financial Economics 16, pp. 217–230. DOI:10.1016/j.rfe.2006.04.001.
|
|
|
|
|
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, Mensah, JA and Nyarko, E (2023). How dependable is World Continental COVID-19 data? Disclosure of Inconsistencies in Daily Reportage Confirmed Cases, Recovered and Deaths During First Wave. Preprint – submitted to Heliyon. DOI:10.2139/ssrn.4516032.
|
|
|
|
|
Agyemang, EF, Nortey, ENN, Minkah, R and Asah-Asante, K (2023). Baseline comparative analysis and review of election forensics: Application to Ghana’s 2012 and 2020 presidential elections. Heliyon 9 p. e18276. DOI:10.1016/j.heliyon.2023.e18276.
|
|
|
|
|
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.
|
|
|
|
|
Ahmad, S, Latif, DA, Mahmood, DM, Aslam, R, Abiddin, ZU, Mumtaz, H, Ahmed, K, Mehdi, W and begum, W (2022). Terminal digit preference and the accuracy of breast cancer diameter reporting based on Benford's law. Annals of Medicine and Surgery. DOI:10.1016/ j.amsu.2022.103993.
|
|
|
|
|
Akinadewo, IS and Akinkoye, EY (2020). Tax Evasion Detection in Nigeria: Analysis of the Specific Forensic Accounting Techniques Used. The Business and Management Review 11(1), pp. 131-139.
|
|
|
|
|
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-Bandawi, H and Deng, G (2018). Blind image quality assessment based on Benford's law. IET Image Processing 12(11), pp. 1983 – 1993. DOI:10.1049/iet-ipr.2018.5385 .
|
|
|
|
|
Al-Bandawi, H and Deng, G (2019). Classification of image distortion based on the generalized Benford’s law. Multimedia Tools and Applications, pp. 1-18. DOI:10.1007/s11042-019-7668-3.
|
|
|
|
|
Al-Marzouki, S, Evans, S, Marshall, T and Roberts, I (2005). Are these data real? Statistical methods for the detection
of data fabrication in clinical trials. Brit. Med. J 331, pp. 267-270. DOI:10.1136/bmj.331.7511.267.
|
|
|
|
|
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.
|
|
|
|
|
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
|
|
|
|
|
Alagöz, Ali ve Mustafa Ay and Ay, M (2001). Denetimde Benford Kanunu'nun Uygulanması [Application of Benford's Law in Audit]. Gazi Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 9(1), p. 63.
TUR
|
|
|
|
|
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.
|
|
|
|
|
Alawadhi, A, Karpoff, J, Koski, JL and Martin, GD (2023). The prevalence and price distorting effects of undetected financial misrepresentation:
Empirical evidence. Preprint.
|
|
|
|
|
Albers, DJ (1995). Professor of Magic Mathematics. Math Horizons Vol 2(3), February, pp. 11-15.
|
|
|
|
|
Albrecht, CC (2008). Fraud and forensic accounting in a digital environment. White Paper for The Institute for Fraud Prevention, Brigham Young University.
|
|
|
|
|
Albrecht, CC, Albrecht, WS and Dunn, JG (2000). Conducting a Pro-Active Fraud Audit: A Case Study. The Journal of Forensic Accounting II: pp. 203-218. ISSN/ISBN:1524-5586.
|
|
|
|
|
Albrecht, J (2000). Die Eins von Planet Zob. Die Zeit, 28 September.
GER
|
|
|
|
|
Albrecht, WS and Albrecht, CC (2002). Root out financial deception. Journal of Accountancy 193(4), pp. 30-34. ISSN/ISBN:0021-8448.
|
|
|
|
|
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.
|
|
|
|
|
Alekseyev, MA (2016). Primenimost' zakona Benforda dlya opredeleniya dostovernosti finansovoy otchotnosti [The applicability of Benford's law to determine the reliability of financial statements]. Bulletin of the Novosibirsk State. Un. economics and management, No. 4, pp. 114-128.
RUS
|
|
|
|
|
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.
|
|
|
|
|
Ali, A and Haque, S (2022). Application of Benford’s law to COVID-19 cases in selected countries of the Caribbean and globally. Caribbean Medical Journal. ISSN/ISBN:2664-5599.
|
|
|
|
|
Ali, AM, Futaih, RF, Shukur, M and Al-Orfali, AK (2024). Forensic Accounting and Fraud Detection Emerging Trends and Techniques. Journal of Ecohumanism 3(5) pp. 525 – 542. DOI:10.62754/joe.v3i5.3921.
|
|
|
|
|
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.
|
|
|
|
|
Allaart, PC (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability 34(1), pp. 288-291.
|
|
|
|
|
Allbright, JA and Merz, CJ (2019). Data analysis systems and methods for identifying recurring payment programs. Patent US2019/014748A Issued on May 16, 2019.
|
|
|
|
|
Allen, DP (1999). A new approach to the first digit phenomenon. The Toth-Maatian Review 14(3), pp. 6839-6847.
|
|
|
|
|
Alshaikh, L (2022). Benford's Law on Social Media. Young Scientists Journal, posted January 16, 2022, last accessed January 31, 2022.
|
|
|
|
|
Altamirano, C and Robledo, A (2009). Generalized Thermodynamics underlying the laws of Zipf and Benford. In: J. Zhou (ed.), Complex Sciences 2009, Part II, LNICST 5, pp. 2232-2237. ISSN/ISBN:1867-8211. DOI:10.1007/978-3-642-02469-6_100.
|
|
|
|
|
Altamirano, C and Robledo, A (2011). Possible thermodynamic structure underlying the laws of Zipf and Benford. Eur. Phys. J. B 81, pp. 345-351. ISSN/ISBN:1434-6036. DOI:10.1140/epjb/e2011-10968-5.
|
|
|
|
|
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.
|
|
|
|
|
Alves, AM and Lyra, CS (2008). Manchas Solares y la Ley de Newcomb-Benford. . RELEA 6, pp. 21-31. DOI:10.37156/RELEA/2008.06.021.
SPA
|
|
|
|
|
Amanda Bowman, A (2016). Contributions to the Testing of Benford's Law. Masters Thesis, McMaster University, Hamilton, Canada.
|
|
|
|
|
Amerini, I, Becarelli, R, Caldelli, R, Del Mastio, A and (2014). Splicing forgeries localization through the use of first digit features. Proceedings of 2014 IEEE International Workshop on Information Forensics and Security (WIFS), Atlanta, GA, USA, 2014, pp. 143-148 . DOI:10.1109/WIFS.2014.7084318.
|
|
|
|
|
Amershi, AH and Feroz, EH (2000). The occurrence of Fibanocci numbers in time series of financial accounting ratios: Anomalies or indicators of firm survival, bankruptcy and fraud? An exploratory study. Managerial Finance 26(11), pp. 5-20. DOI:10.1108/03074350010766954.
|
|
|
|
|
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) .
|
|
|
|
|
Amruthnath, N (2020). Benford’s Law: Applying to Existing Data. Posted on R-bloggers.com, last accessed August 29, 2020.
|
|
|
|
|
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.
|
|
|
|
|
Anonymous (2007). A Guide to Benford’s Law. A CaseWare IDEA Research Department Document; last accessed December 7, 2019.
|
|
|
|
|
Anonymous (2008). Ley de Benford. Blog posted on Estadistica para todos; last accessed January 4, 2022.
SPA
|
|
|
|
|
Anonymous (2011). Corporate Fraud: Every good boy deserves fudged profits. The Economist, October 13.
|
|
|
|
|
Anonymous (2012). The scam busters. The Economist, Dec 15th, Free Exchange.
|
|
|
|
|
Anonymous (2014). Benford's Law. Online posting last accessed 22 Feb 2016.
|
|
|
|
|
Anonymous (2016). How to: Apply Benford’s Law in Excel to Detect Fraudulent Activity. Posted on oregonaudits.org blog January 5; last accessed October 11, 2019.
|
|
|
|
|
Anonymous (2016). The Diary of Frank Benford. Ebook published by ACL Software, September 28.
|
|
|
|
|
Antonio, GR (2023). Numbers Don’t Lie: Decoding Financial Error and Fraud through Benford’s Law. UTSAHA (Journal of Entrepreneurship) 2(3)
. DOI:10.56943/joe.v2i3.367.
|
|
|
|
|
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.
|
|
|
|
|
Aono, JY and Guan, L (2008). The Impact of Sarbanes-Oxley Act on Cosmetic Earnings Management. Research in Accounting Regulation, Vol. 20, pp. 205–215. ISSN/ISBN:1052-0457. DOI:10.1016/S1052-0457(07)00212-3.
|
|
|
|
|
Archambault, JJ and Archambault, ME (2011). Earnings management among firms during the pre-SEC era: a Benford’s law analysis. The Accounting Historians Journal
Vol. 38, No. 2 (December 2011), pp. 145-170 . ISSN/ISBN:0148-4184.
|
|
|
|
|
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.
|
|
|
|
|
Aris, NA, Othman, R, Arif, SMM, Malek, MAA and Omar, N (2013). Fraud Detection: Benford’s Law vs Beneish Model. 2013 IEEE Symposium on Humanities, Science and Engineering Research (SHUSER).
|
|
|
|
|
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.
|
|
|
|
|
Arita, M (2005). Scale-freeness and biological networks. Journal of Biochemistry, 138 (1): 1-4. ISSN/ISBN:0021-924X. DOI:10.1093/jb/mvi094.
|
|
|
|
|
Arkan, MM (2010). Analisis Penggunaan Benford’s Law Dalam perencanaan Audit Pada Direktorat Jenderal Bea dan Cukai. [Analysis of the use of Benford's Law in planning an audit at the Directorate General of Customs and Excise]. Masters thesis, Universitas Gadjah Mada Yogyakarta, and presentation at Simposium Nasional Akuntansi XIII. Purwokerto, Indonesia.
IND
|
|
|
|
|
Armstrong, JS (2001). Extrapolation for time-series and cross-sectional data. . In: Principles of Forecasting: a Handbook for Researchers and Practitioners, Kluwer Academic Publishers.
|
|
|
|
|
Aron, J (2013). Mathematical crime-fighter helps hunt for alien worlds. New Scientist Online, 28 November 2013.
|
|
|
|
|
Aron, J (2013). Crime-fighting maths law confirms planetary riches. New Scientist, 220(2945), p. 12. ISSN/ISBN:1364-8500. DOI:10.1016/S0262-4079(13)62775-X.
|
|
|
|
|
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.
|
|
|
|
|
Arslan, U, Calıyurt, KT and Kahyaoglu, SB (2024). Financial statement anomaly detection based on Benford law and Beneish model: Case of a public sector hospital. The EDP Audit, Control, and Security Newsletter 69, pp.69-87. DOI:10.1080/07366981.2024.2312018.
|
|
|
|
|
Asadi, AN (2015). An approach for detecting anomalies by assessing the inter-arrival time of UDP packets and flows using Benford's law. 2nd International Conference on Knowledge-Based Engineering and Innovation (KBEI), Tehran, pp. 257-262. DOI:10.1109/KBEI.2015.7436057.
|
|
|
|
|
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
|
|
|
|
|
Ascioglu, A, Gonzalez, J and Zbib, L (2021). Analysis of Sustainability Reports for Top 20 Companies in the S&P 500 Index. The Journal of Impact and ESG Investing 2(2). DOI:10.3905/jesg.2021.1.036.
|
|
|
|
|
Ascioglu, A, Gonzalez, J and Zbib, L (2022). Practical Applications of Analysis of Sustainability Reports for Top 20 Companies in the S&P 500 Index. Practical Applications 9(2). DOI:10.3905/pa.2022.pa516.
|
|
|
|
|
Ashcraft, MH (1992). Cognitive arithmetic: A review of data and theory. Cognition 44 (Aug), pp. 75-106. ISSN/ISBN:0010-0277. DOI:10.1016/0010-0277(92)90051-I.
|
|
|
|
|
Ashcraft, MH and Christy, KS (1995). The Frequency of Arithmetic Facts in Elementary Texts: Addition and Multiplication in Grades 1-6. Journal for Research in Mathematics Education 26(5), pp. 396-421.
|
|
|
|
|
Asllani, A and Naco, M (2014). Using Benford’s Law for Fraud Detection in Accounting Practices. Journal of Social Science Studies 2(1), pp. 129-143. DOI:10.5296/jsss.v2i1.6395.
|
|
|
|
|
Atakan, S and Orman, G (2023). On the usage of Benford’s Law on coronavirus data statistics. Proceedings of 2023 IEEE International Conference on Big Data (BigData), pp. 4848-4853. DOI:10.1109/BigData59044.2023.10386606.
|
|
|
|
|
Auffhammer, M and Carson, RT (2007). Forecasting the Path of China’s CO2 Emissions: Offsetting Kyoto - And Then Some. Department of Agricultural & Resource Economics, UCB CUDARE Working Papers no. 971 (University of California, Berkeley).
|
|
|
|
|
Auffhammer, M and Carson, RT (2008). Forecasting the path of China's CO2 emissions using province-level information. J. Environ. Econ. Manage. 55(3), pp. 229-247. ISSN/ISBN:0095-0696. DOI:10.1016/j.jeem.2007.10.002.
|
|
|
|
|
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.
|
|
|
|
|
Australia, H (2020). Joe Biden’s votes violate Benford’s Law (Mathematics). Posted on GNews.org blog Nov 7, 2020; last accessed November 8, 2020.
|
|
|
|
|
Avcı, O and Demirci, Z (2016). Benford Kanunu’nun Vergi Denetiminde Kullanımı Ve Bir Örnek Uygulama [Use of Benford's Law in Tax Auditing and A Sample Application]
. İnsan ve Toplum Bilimleri Araştırması Dergisi 5(7), pp. 2232-2246. DOI:10.15869/itobiad.260262.
TUR
|
|
|
|
|
Avery, N and Xin, Z (2013). China Export Surge Spurs Data Skepticism at Goldman, UBS. Bloomberg News, January 13, 2013.
|
|
|
|
|
Awad, MM (2022). Evaluation of COVID-19 Reported Statistical Data Using Cooperative Convolutional Neural Network Model (CCNN). COVID 2(5), pp. 674–690. DOI:10.3390/covid2050051.
|
|
|
|
|
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.
|
|
|
|
|
Aydın, S (2017). Muhasebe hilelerinin tespit edilmesinde Benford Yasasının Kullanılması [Using Benford's Law to detect accounting fraud]. Master Thesis, Okan University Institute of Social Sciences, Istanbul.
TUR
|
|
|
|
|
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.
|
|
|
|
|
Azevedo, CdS, Gonçalves, RF, Gava, VL and Spinola, MdM (2021). A Benford’s Law based method for fraud detection using R Library. MethodsX 2021. DOI:10.1016/j.mex.2021.101575.
|
|
|
|
|
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.
|
|
|
|
|
Badkar, M (2013). Benford's Law Raises New Doubts About Chinese Economic Data. Business Insider, Jan 11, 2013; last accessed Jun 13, 2019.
|
|
|
|
|
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.
|
|
|
|
|
Baguzin, Z (2013). Benford law or first digit law. Posted on Warrior's Way Blog (in Russian) Jan 4, 2013; last accessed Mar 23, 2019.
RUS
|
|
|
|
|
Bahmann, P (2015). Eine Analyse von monetären, makroökonomischen Daten der BRD und DDR: Ziffernanalyse auf Grundlage des Benford's Law [An analysis of monetary, macroeconomic data of the FRG and the GDR: numeric analysis on the basis of Benford’s Law. AV Akademikerverlag: Saarbrücken, Germany. ISSN/ISBN:978-3-639-80882-7.
GER
|
|
|
|
|
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.
|
|
|
|
|
Baird, JC (1975). Psychophysical study of numbers: V. Preferred State Theory of Matching Functions. Psychological Research 38 (Jun), pp. 189-207. DOI:10.1007/BF00308524.
|
|
|
|
|
Baird, JC (1975). Psychophysical study of numbers: IV. Generalized Preferred State Theory. Psychological Research 38 (Jun), pp. 175-187. DOI:10.1007/BF00308523.
|
|
|
|
|
Baird, JC and Noma, E (1975). Psychophysical study of numbers: I. Generation of numerical responses. Psychological Research 37 (Dec), pp. 281-297. DOI:10.1007/BF00309723.
|
|
|
|
|
Bak-Coleman, J, Wack, M, Schafer, J, Spiro, E and West, J (2020). Vote Data Patterns used to Delegitimize the Election Results. Posted on EIPartnership.net November 6, 2020; last accessed December 1, 2020. NOTE: Some information in this posting has been disputed. Please see https://arxiv.org/abs/2011.13015 for details.
|
|
|
|
|
Balado, F and Silvestre, GCM (2018). Towards Optimum Counterforensics of Multiple Significant Digits Using Majorisation-Minimisation. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, 2018, pp. 2116-2120. DOI:10.1109/ICASSP.2018.8462378.
|
|
|
|
|
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 (2023). Generalised Benford Law. Classic HTML Society Repository.
|
|
|
|
|
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.
|
|
|
|
|
Balamurugan, A, Harish, A and Gandhi, S (2019). Application of Benford's Law on Stock Turnover. International Journal of Business and Management Invention (IJBMI) 8(01), pp. 63-67. ISSN/ISBN:2319 – 801X.
|
|
|
|
|
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.
|
|
|
|
|
Balanzario, EP and Sánchez-Ortiz, J (2010). Sufficient conditions for Benford’s law. Statistics & Probability Letters 80(23-24), pp. 1713-1719. DOI:10.1016/j.spl.2010.07.014.
|
|
|
|
|
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.
|
|
|
|
|
Balcıoğlu, YS, Merter, AK, Cerez, S and Özer, G (2024). Analysis of Annual Reports of Firms Listed on Borsa Istanbul Using Benford’s Law. In: Ozatac, N., Taspinar, N., Rustamov, B. (eds) Sustainable Development in Banking and Finance. ICBFP 2023. Springer Proceedings in Business and Economics. Springer, Cham.. DOI:10.1007/978-3-031-65533-3_7.
|
|
|
|
|
Ball, J (2012). Russian election: does the data suggest Putin won through fraud?. The Guardian, March 5, 2012.
|
|
|
|
|
Bandeira de Oliveira, A and Jordão da Gama Silva, PV (2024). Governance in public procurement: accounting analysis of public acquisitions in Brazil during the COVID-19 pandemic. International Journal of Procurement Management Vol. 19, No. 3, pp 315-335.
|
|
|
|
|
Banks, DG (1999). Benford’s Law Made Easy. Fraud Magazine, September/October 1999.
|
|
|
|
|
Banks, DG (2000). Get M.A.D. with the Numbers! Moving Benford's Law from Art to Science. Fraud Magazine, September/October 2000.
|
|
|
|
|
Banks, M (2009). Benford’s law and the Iranian election. Institute of Physics website: physicsworld.com blog June 23, 2009.
|
|
|
|
|
Banks, WP and Hill, DK (1974). The Apparent Magnitude of Number Scaled by Random Production. Journal of Experimental Psychology 102 (2), pp. 353-376. ISSN/ISBN:0022-1015. DOI:10.1037/h0035850.
|
|
|
|
|
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 Perotta, D (2021). A combined test of the Benford Hypothesis With Anti-fraud Applications. Proceedings of 13th Scientific Meeting of the Classification and Data Analysis Group, Florence, September 9-11. STAMPA, pp. 256-259. DOI:10.36253/978-88-5518-340-6.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Bareja, K (2022). Benford's Law: Managing Insider Threat Program. LinkedIn blog.
|
|
|
|
|
Barjaktarović, L , Milojević, M and Terzić, I. (2014). Results of Applience of Benford’s Law on Serbian Companies. Proceedings of XIV International Symposium SymOrg, Zlatibor.
|
|
|
|
|
Barlow, JL and Bareiss, EH (1985). On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic. Computing 34(4), pp. 325-347. ISSN/ISBN:0010-485X. DOI:10.1007/BF02251833.
|
|
|
|
|
Barnard, PJ, Scott, SK and May, J (2001). When the central executive lets us down: Schemas, attention, and load in a generative working memory task. Memory, 9 (4-6), pp. 209-221. ISSN/ISBN:0965-8211. DOI:10.1080/09658210143000191.
|
|
|
|
|
Barney, BB and Schulzke, KS (2016). Moderating "Cry Wolf" events with excess MAD in Benford's law research and practice. J. Forensic Account. Res. 1 (1), A66–A90. DOI:10.2308/jfar-51622.
|
|
|
|
|
Barone, G, Conti, L, Narciso, G and Tonello, M (2020). Auditors’ conflict of interest: does random selection work?. Trinity Economics Papers tep0820, Trinity College Dublin, Department of Economics.
|
|
|
|
|
Barrale, T, Hendel, R and Sluys, M (2010). Sequences of the initial digits of Fibonacci numbers. In: Proceedings of the 14th international conference on Fibonacci numbers and their applications, Morelia, Mexico, July 5–9, 2010, pp. 25–42.
|
|
|
|
|
Barrow, JD (2011). Benford's Very Strange Law. Gresham Lecture, February 1, 2011, 1:00pm,
Museum of London.
|
|
|
|
|
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
|
|
|
|
|
Basrak, B and Varga, I (2013). Benford's law. Math.e 23(1), pp. 1-6.
HRV
|
|
|
|
|
Basset, K (2020). I used Benford’s law to analyze COVID-19 in 113 countries. Blog posted on kevinbasset.medium.com November 15, 2020.
|
|
|
|
|
Bastian, H, Frye, E, Gary, C, Houck, D, Schneider, M, Thomason, F and Werner, B (2021). Data Analytics to Enhance Election Transparency. Critique of MITRE Report MP210086, Appendix C.
|
|
|
|
|
Batange, C, Burgett, D, Haws, L and Nelson, SP (2023). The "Benfordness" of Bach Music. Journal of Humanistic Mathematics 13(2) pp. 389-397.
|
|
|
|
|
Battersby, S (2009). Statistics hint at fraud in Iranian election. New Scientist, 24 June, 202(2714), p. 10.
|
|
|
|
|
Batun, M (2009). Benford Yasası ve Vergi Denetiminde KullanılabilirliğI [Benford's Law and Its Availability in Tax Audit]. Yaklaşım Dergisi 204.
TUR
|
|
|
|
|
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
|
|
|
|
|
Baumgartner, T, Guettier, A and Kim, F (2022). Bitcoin Flash Crash on May 19, 2021: What did really happen on Binance?. Invited for presentation at the MIT Golub Center for Finance and Policy (GCFP) 2022 in Cambridge, MA. Also to be presented at the Paris December Finance Meeting 2022.
|
|
|
|
|
Beber, B and Scacco, A (2008). What the Numbers Say: A Digit-Based Test for Election Fraud Using New Data from Nigeria. Presented at the Annual Meeting of the American Political Science Association. Boston, MA August 28– 31.
|
|
|
|
|
Beber, B and Scacco, A (2009). The Devil is in the Digits. Washington Post, 20 June.
|
|
|
|
|
Beber, B and Scacco, A (2012). What the Numbers Say: A Digit-Based Test for Election Fraud. Political Analysis 20 (2), pp. 211-234. DOI:10.1093/pan/mps003.
|
|
|
|
|
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.
|
|
|
|
|
Becker, TJ (2000). Sorry, Wrong Number. Century-old math rule ferrets out modern-day digital deception. Georgia Tech Research Horizons, Fall 2000.
|
|
|
|
|
Beebe, NHF (2012). Newcomb, Benford, Pareto, Heaps, and Zipf Are arbitrary numbers random?. Posted on StudyLib, January 12, 2012.
|
|
|
|
|
Beebe, NHF (2018). A bibliography of publications about Benford's law, Heap's law and Zipf's law. Available online from: ftp://ftp.math.utah.edu/public_html/public_html/
pub/tex/bib/benfords-law.pdf (last accessed July 16, 2021).
|
|
|
|
|
Beeli, G, Esslen, M and Jäncke, L (2007). Frequency Correlates in Grapheme-Color Synaesthesia. Psychological Science, 18(9), pp. 788-792. ISSN/ISBN:0956-7976.
|
|
|
|
|
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.
|
|
|
|
|
Behrends, E (2005). Das Benfordsche Gesetz oder warum die Ziffer 1 häufiger am Anfang steht. Die Welt, April 4, 2005.
GER
|
|
|
|
|
Beiglou, PHB, Gibbs, C, Rivers, L, Adhikari, U and Mitchell, J (2017). Applicability of Benford’s Law to Compliance Assessment of Self-Reported Wastewater Treatment Plant Discharge Data. Journal of Environmental Assessment Policy and Management 19(04). DOI:10.1142/S146433321750017X.
|
|
|
|
|
Bellos, A (2014). Alex Through the Looking Glass. Chapter 2, Bloomsbury Publishing: New York. ISSN/ISBN:9781408845752.
|
|
|
|
|
Belluzzo, T (2019). A framework for Benford's Law conformity assessment. Code repository posted on GitHub.com/TommasoBelluzzo
/BenfordLaw; last accessed Jun 21, 2021.
|
|
|
|
|
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.
|
|
|
|
|
Benford, F (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, Vol. 78, No. 4 (Mar. 31, 1938), pp. 551-572.
|
|
|
|
|
Benford, FA (2016). Construction of Benford Random Variables: Generators and Seed Functions. Preprint arXiv:1609.04852 [math.GM]; last accessed Aug 9, 2017.
|
|
|
|
|
Benford, FA (2017). Base Dependence of Benford Random Variables. Preprint arXiv:1702.01644 [math.GM]; last accessed Aug 9, 2017.
|
|
|
|
|
Benford, FA (2020). Fourier Analysis and Benford Random Variables. Preprint arXiv:arXiv:2006.07136 [stat.OT]; last accessed June 20, 2020.
|
|
|
|
|
Benford, FA (2021). Base Dependence of Benford Random Variables. Stats 4(3), pp. 578-594. DOI:10.3390/stats4030034.
|
|
|
|
|
Benjamin, AT (2019). The Long and the Short of Benford’s Law. Math Horizons 26(4), pp. 8-9. DOI:10.1080/10724117.2019.1568086.
|
|
|
|
|
Bensmail, H and Haoudi, A (2003). Postgenomics: Proteomics and Bioinformatics in Cancer Research. Journal of Biomedicine and Biotechnology 2003(4), pp. 217-230. ISSN/ISBN:1110-7243. DOI:10.1155/S1110724303209207.
|
|
|
|
|
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.
|
|
|
|
|
Bërdufi, D (2013). Statistical Detection of Vote Count Fraud: 2009 Albanian Parliamentary Election and Benford’s Law. Academic Journal of Interdisciplinary Studies 2(8), pp. 379-396. (Also published in Mediterranean Journal of Social Sciences, 5(2) pp. 755– 771). DOI:10.5901/ajis.2013.v2n8p379.
|
|
|
|
|
Berger, A (2001). Chaos and Chance. De Gruyter, Berlin and New York.
|
|
|
|
|
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 (2005). Dynamics and digits: on the ubiquity of Benford’s law. In: F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel (eds): Proceedings of Equadiff 2003. World Scientific, pp. 693-695. DOI:10.1142/9789812702067_0115 .
|
|
|
|
|
Berger, A (2010). Large spread does not imply Benford's Law. Technical Report, Dept. of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada.
|
|
|
|
|
Berger, A (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), pp. 137-159. DOI:10.1080/10236198.2010.549012.
|
|
|
|
|
Berger, A (2015). Most linear flows on ℝ^d are Benford
. Journal of Differential Equations 259(5), pp. 1933–1957. DOI:10.1016/j.jde.2015.03.016.
|
|
|
|
|
Berger, A, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), pp. 197-219. ISSN/ISBN:0002-9947. DOI:10.1090/S0002-9947-04-03455-5.
|
|
|
|
|
Berger, A and Eshun, G (2014). Benford solutions of linear difference equations. Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics Volume 102, pp. 23-60. ISSN/ISBN:978-3-662-44139-8. DOI:10.1007/978-3-662-44140-4_2.
|
|
|
|
|
Berger, A and Eshun, G (2016). A characterization of Benford's law in discrete-time linear systems. Journal of Dynamics and Differential Equations 28(2), pp. 432-469. ISSN/ISBN:1040-7294. DOI:10.1007/s10884-014-9393-y.
|
|
|
|
|
Berger, A and Evans, SN (2013). A Limit Theorem for Occupation Measures of Lévy Processes in Compact Groups. Stochastics and Dynamics 13(1), p. 1250008. DOI:10.1142/S0219493712500086.
|
|
|
|
|
Berger, A and Hill, TP (2006). A characterisation of Newton maps. ANZIAM J. 48, pp. 211-223.
|
|
|
|
|
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 (2015). A Short Introduction to the Mathematical Theory of Benford’s Law. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 23-67.
|
|
|
|
|
Berger, A and Hill, TP (2017). What is…Benford's Law?. Notices of the AMS 64(2), pp. 132-134.
|
|
|
|
|
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 Twelves, I (2018). On the significands of uniform random variables. Journal of Applied Probability 55(2), pp. 353-367. DOI:10.1017/jpr.2018.23.
|
|
|
|
|
Berger, A and Xu, C (2018). Best Finite Approximations of Benford’s Law. Journal of Theoretical Probability. DOI:10.1007/s10959-018-0827-z.
|
|
|
|
|
Berleant, D, Cheong, MP, Chu,C, Guan,Y, Kamal,A, Shedble, G, Ferson,S and Peters, JF (2003). Dependable Handling of Uncertainty. Reliable Computing 9(6), pp. 407-418. ISSN/ISBN:1385-3139. DOI:10.1023/A:1025888503247.
|
|
|
|
|
Bernhardsson, E (2014). Detecting corporate fraud using Benford’s law. Blog posted on erikbern.com, October 7; last accessed Jun 8, 2019.
|
|
|
|
|
Bernik, VI and Kalosha, NI (2007). Benford’s law and the approximation of logarithms of natural numbers by rational numbers. Vestsi Nats. Akad. Navuk Belarusi Ser. Fiz.-Mat. Navuk, no. 3, pp. 68-73. DOI:10.22405/2226-8383-2016-17-4-203-210.
RUS
|
|
|
|
|
Berry, N (2012). Benford's Law. Posted on Datagenetics.com blog, March; last accessed August 19, 2019.
|
|
|
|
|
Berton, L (1995). He’s Got Their Number: Scholar Uses Math to Foil Financial Fraud. The Wall Street Journal, p. B1, July 10.
|
|
|
|
|
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.
|
|
|
|
|
Bharati, R, Crain, SJ and Kaminski, V (2012). Clustering in crude oil prices and the target pricing zone hypothesis. Energy Economics Vol. 34, No. 4, pp. 1115–1123. DOI:10.1016/j.eneco.2011.09.009.
|
|
|
|
|
Bhattacharya, P, Chatterjee, A and Chakrabarti, BK (2005). A common mode of origin of the power law distributions in models of market and earthquake. Physica A Statistical Mechanics and its Applications 381, pp. 377-382. DOI:10.1016/j.physa.2007.02.096.
|
|
|
|
|
Bhattacharya, S (2002). From Kautilya to Benford – Trends in Forensic and Investigative Accounting. Bond Business School Publications. Paper 60.
|
|
|
|
|
Bhattacharya, S and Kumar, K (2008). Forensic Accounting and Benford’s Law. IEEE Signal Processing Magazine, 25(2), p. 152. DOI:10.1109/MSP.2007.914724.
|
|
|
|
|
Bhattacharya, S, Kumar, K and Smarandache, F (2005). Conditional probability of actually detecting a financial fraud – a neutrosophic extension to Benford’s law. International Journal of Applied Mathematics 17(1), pp. 7-14.
|
|
|
|
|
Bhattacharya, S, Xu, D and Kumar, K (2010). An ANN-based auditor decision support system using Benford's Law. Decision support systems, 50 (3), pp. 576-584.
|
|
|
|
|
Bhole, G, Shukla, A and Mahesh, TS (2014). Benford distributions in NMR. Preprint arXiv:1406.7077 [physics.data-an]; last accessed June 7, 2018.
|
|
|
|
|
Bhole, G, Shukla, A and Mahesh, TS (2015). Benford analysis: A useful paradigm for spectroscopic analysis. Chemical Physics Letters 639, pp. 36–40. DOI:10.1016/j.cplett.2015.08.061.
|
|
|
|
|
Bhosale, S (2021). Identifying Bots on Twitter with Benford’s Law. Masters project, Dept. of Computer Science, San Jose State University.
|
|
|
|
|
Bhosale, S and Di Troia, F (2022). Twitter Bots’ Detection with Benford’s Law and Machine Learning. In Proceedings of Silicon Valley Cybersecurity Conference. SVCC 2022. Communications in Computer and Information Science, vol 1683, Bathen, L., Saldamli, G., Sun, X., Austin, T.H., Nelson, A.J. (eds). Springer, Cham. DOI:10.1007/978-3-031-24049-2_3.
|
|
|
|
|
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.
|
|
|
|
|
Bialik, C (2009). Rise and Flaw of Internet's Election-Fraud Hunters. The Wall Street Journal, 1 July.
|
|
|
|
|
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.
|
|
|
|
|
Bijma, F, Jonker, M and van der Vaart, A (2017). An Introduction to Mathematical Statistics. Amsterdam University Press; 2nd edition (Chapter 2.4 Application), pp. 41-44. ISSN/ISBN:978-9462985100.
|
|
|
|
|
Birajdar, GK and Mankar, VH (2013). Digital image forgery detection using passive techniques: A survey. Digital Investigation, Vol. 10, No. 3, pp. 226–245. DOI:10.1016/j.diin.2013.04.007.
|
|
|
|
|
Block, HW and Savits, TH (2010). A General Example for Benford Data. The American Statistician 64(4), pp. 335-339.
|
|
|
|
|
Blondeau Da Silva, S (2018). Benford or not Benford: new results on digits beyond the first. Preprint arXiv:1805.01291v1 [stat.OT]; last accessed July 29, 2018.
|
|
|
|
|
Blondeau Da Silva, S (2019). Benford or Not Benford: A Systematic But Not Always Well-Founded Use of an Elegant Law in Experimental Fields. Communications in Mathematics and Statistics, pp. 1-35. ISSN/ISBN:2194-6701. DOI:10.1007/s40304-018-00172-1.
|
|
|
|
|
Blondeau da Silva, S (2019). BeyondBenford: An R Package to Determine Which of Benford’s or BDS’s Distributions is the Most Relevant. Preprint hal-02310013; also posted on arXiv:1910.06104 [physics.soc-ph]; last accessed October 21, 2019.
|
|
|
|
|
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.
|
|
|
|
|
Blondeau Da Silva, S (2020). BeyondBenford: Compare the Goodness of Fit of Benford's and Blondeau Da Silva's Digit Distributions to a Given Dataset. R package version 1.4.
|
|
|
|
|
Blondeau Da Silva, S (2021). BeyondBenford R Package to compare Benford's and BDS's Distributions. Computer Science Journal of Moldova 29(2), p. 241-256.
|
|
|
|
|
Blondeau Da Silva, S (2022). An Alternative to the Oversimplifying Benford’s Law in Experimental Fields. Sankhya B. DOI:10.1007/s13571-022-00287-0.
|
|
|
|
|
Blum, W (2007). Die Nummer eins im Alltag. Süddeutsche Zeitung, May 23.
GER
|
|
|
|
|
Boffa, J (2023). Forensic Accounting Using the Benford
Formula. Chapter 5 in: AI Assisted Business Analytics. Springer, Cham.. ISSN/ISBN:978-3-031-40820-5. DOI:10.1007/978-3-031-40821-2_5.
|
|
|
|
|
Bogomolny, A (2004). Benford’s Law and Zipf's Law. Posted on Cut The Knot website, last accessed June 7, 2018.
|
|
|
|
|
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.
|
|
|
|
|
Bonettini, N, Bestagini, P, Milani, S and Tubaro, S (2020). On the use of Benford's law to detect GAN-generated images. Preprint arXiv:arXiv:2004.07682 [cs.CV]; last accessed April 21, 2020
(2020 25th International Conference on Pattern Recognition (ICPR), pp. 5495-5502)
.
|
|
|
|
|
Boring, EG (1920). The logic of the normal law of error in mental measurement. American Journal of Psychology 31, pp. 1-33. ISSN/ISBN:0002-9556. DOI:10.2307/1413989.
|
|
|
|
|
Bormashenko, E, Shulzinger, E, Whyman, G and Bormashenko, Y (2016). Benford’s law, its applicability and breakdown in the IR spectra of polymers. Physica A 444, pp. 524–529. DOI:10.1016/j.physa.2015.10.090.
|
|
|
|
|
Boronico, J, Harris, P and Teplitsky, F (2014). Benford's law and applications for the international auditor. Journal of Internal Auditing 29(6), pp. 32-36.
|
|
|
|
|
Bose, I, Piramuthu, S and Shaw, MJ (2011). Quantitative methods for Detection of Financial Fraud. Decision Support Systems, 50(3), pp. 557–558. ISSN/ISBN:1873-5797. DOI:10.1016/j.dss.2010.08.005.
|
|
|
|
|
Bouchetara, M and Nassour, A (2020). Internal Auditing in the Face of Banking Fraud, Application of the Benford Law on Algerian Private Bank. UTMS Journal of Economics 11(2), pp. 108–120.
|
|
|
|
|
Bourke, N and van Peursem, K (2004). Detecting fraudulent financial reporting: teaching the 'watchdog' new tricks. Working paper 79, University of Waikato. ISSN/ISBN:1173-7182.
|
|
|
|
|
Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), pp. 879-886. ISSN/ISBN:0002-9890. DOI:10.2307/2975136.
|
|
|
|
|
Boztepe, E (2013). Benford Kanunu ve Muhasebe Denetiminde Kullanılabilirliği. EUL Journal of Social Sciences IV:I, pp. 73-83.
TUR
|
|
|
|
|
Bradinoff, N and Duits, M (2023). Benford's law and the CβE. Preprint arXiv:2302.02932 [math.PR]; last accessed March 10, 2023. DOI:10.48550/ARXIV.2302.02932.
|
|
|
|
|
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
|
|
|
|
|
Brady, WG (1978). More on Benford’s law. Fibonacci Quarterly 16(1), pp. 51-52.
|
|
|
|
|
Brähler, G, Bensmann, M and Emke, AL (2010). Der Einsatz mathematisch-statistischer Methoden in der
digitalen Betriebsprüfung. Illmenauer Schriften zur Betriebswirtschaftslehre 4/2010.
GER
|
|
|
|
|
Brähler, G, Bensmann, M and Jakobi, HR (2011). Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Prüfung von Fahrtenbüchern. Ilmenauer Schriften zur Betriebswirtschaftslehre 3/2011. ISSN/ISBN:978-3-940882-28-8.
GER
|
|
|
|
|
Brandolini, L and Travaglini, G (2012). La legge di Benford. Posted on: http://pmf.cilea.it/file.php/1/articoli/PMF2012_Benford.pdf; last retrieved June 8, 2018 .
ITA
|
|
|
|
|
Branets, S (2019). Detecting money laundering with Benford’s law and machine learning . Masters Thesis, University of Tartu.
|
|
|
|
|
Brase, CH and Brase, CP (2014). Understandable Statistics. Cengage Learning Publishing, Chapter: Hypothesis Testing, pp. 435-527. ISSN/ISBN:9781305142909.
|
|
|
|
|
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 2. Posted on Datatodisplay.com blog; last accessed April 25, 2019.
|
|
|
|
|
Brock, T (2014). Benford's law and elections - part 1. Posted on Datatodisplay.com blog; last accessed April 25, 2019.
|
|
|
|
|
Brooks, D (2001). War, Politics & Customer Loyalty: Forecasting Using Benford’s Law. Frequencies, The Journal of Size Law Applications, 1(1), Aug. 2001, pp. 1-15.
|
|
|
|
|
Brooks, D (2002). Naked-Eye Quantum Mechanics:
Practical Applications of Benford's Law for Integer Quantities. Frequencies - The Journal of Size Law Applications, Special Paper #1, pp. 1-8.
|
|
|
|
|
Brooks, D (2002). Zipf Ranking, Benford’s Law, and Ratio Analysis. Frequencies - The Journal of Size Law 1(2), pp. 1--9 .
|
|
|
|
|
Brooks, M (2017). Benford's law. New Scientist 235(3140), pp. 38-39.
|
|
|
|
|
Brown, JR and Duncan, RL (1970). Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences. Fibonacci Quarterly 8, pp. 482-486. ISSN/ISBN:0015-0517.
|
|
|
|
|
Brown, K (2000). Benford's Law. Posted on mathpages.com blog; last accessed August 19, 2019.
|
|
|
|
|
Brown, MS (2012). Does the Application of Benford's Law Reliably Identify Fraud on Election Day? . Masters thesis, Georgetown University.
|
|
|
|
|
Brown, P, Chua, A and Mitchell, J (2002). The influence of cultural factors on price clustering: Evidence from Asia–Pacific stock markets. Pacific-Basin Finance Journal 10(3), pp. 307-332. DOI:10.1016/S0927-538X(02)00049-5.
|
|
|
|
|
Brown, P and Mitchell, J (2008). Culture and stock price clustering: evidence from the peoples’ republic of China. Pacific-Basin Finance Journal 16(1), pp. 95-120 . ISSN/ISBN:0927-538X. DOI:10.1016/j.pacfin.2007.04.005.
|
|
|
|
|
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.
|
|
|
|
|
Brown, RJC (2007). The use of Zipf's law in the screening of analytical data: a step beyond Benford. Analyst 132(4), pp. 344-349. ISSN/ISBN:0003-2654. DOI:10.1039/B618255K.
|
|
|
|
|
Browne, MW (1998). Following Benford’s law, or looking out for no. 1. The New York Times, August 4, 1998.
|
|
|
|
|
Brunell, TL and Glazer, A (2001). Rational Response to Irrational Attitudes: The Level of the Gasoline Tax in the United States. Journal of Policy Analysis and Management 20(4), pp. 761-769. ISSN/ISBN:0276-8739.
|
|
|
|
|
Buck, B, Merchant, AC and Perez, SM (1993). An illustration of Benford’s first digit law using alpha decay half lives. European Journal of Physics 14, pp. 59-63.
|
|
|
|
|
Bugarin, MS and da Cunha, FCR (2015). A didactic note on the use of Benford’s Law in public works auditing with an application to the construction of the Brazilian ‘Amazon Arena’ 2014
World Cup soccer stadium. Economia 66(1),pp. 23-55.
|
|
|
|
|
Bugarin, MS and da Cunha, FCR (2017). Lei de Benford aplicada à auditoria da reforma do Aeroporto Internacional de Minas Gerais. Revista Do Serviço Público 68(4), pp. 915-940. DOI:10.21874/rsp.v68i4.1567.
POR
|
|
|
|
|
Bumby, R and Ellentuck, E (1969). Finitely additive measures and the first digit problem. Fundamenta Mathematicae 65, pp. 33-42. ISSN/ISBN:0016-2736.
|
|
|
|
|
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.
|
|
|
|
|
Burke, J and Kincanon, E (1991). Benford's Law and Physical Constants - The Distribution of Initial Digits. American Journal of Physics 59 (10), p. 952. ISSN/ISBN:0002-9505. DOI:10.1119/1.16838.
|
|
|
|
|
Burns, BD (2009). Sensitivity to statistical regularities: People (largely) follow Benford’s law. pp 2872-2877 in: Proceedings of CogSci 2009, Amsterdam, The Netherlands.
|
|
|
|
|
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.
|
|
|
|
|
Burns, BD and Krygier, J (2015). Psychology and Benford’s Law. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 267-275.
|
|
|
|
|
Bushee, B (2019). Benford's Law 3.6. Retrieved from Coursera:
https://www.coursera.org/lecture/accounting-analytics/benfords-law-3-6-oPSSY; last accessed October 12, 2020.
|
|
|
|
|
Busta, B and Sundheim, R (1992). Tax return numbers tend to obey Benford's law. Center for Business Research Working Paper No. W93-106-94, St. Cloud State University, Minnesota.
|
|
|
|
|
Busta, B and Sundheim, R (1992). Detecting manipulated tax returns with the use of Benford's Law. Center for Business Research Working Paper W95-106-94, St. Cloud State University, Minnesota.
|
|
|
|
|
Busta, B and Weinberg, R (1998). Using Benford’s law and neural networks as a review procedure. Managerial Auditing Journal 13(6), pp. 356-366. DOI:10.1108/02686909810222375.
|
|
|
|
|
Bustoz, J, Feldstein, A, Goodman, R and Linnainmaa, S (1979). Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic. Journal of the Association for Computing Machinery 26(4), pp. 716-730. ISSN/ISBN:0004-5411. DOI:10.1145/322154.322162.
|
|
|
|
|
Butgereit, L (2021). Covid-19 New Cases Measurements and Benford's Law with Specific Focus on South Africa. International Conference on Artificial Intelligence, Big Data, Computing and Data Communication Systems (icABCD), Durban, South Africa, pp. 1-5. DOI:10.1109/icABCD51485.2021.9519321.
|
|
|
|
|
Butgereit, L (2021). Focusing Benford’s Law on the Daily Covid-19 Cases Numbers and Daily Covid-19 Deaths Numbers. 2021 IEEE AFRICON, pp. 1-6. DOI:10.1109/AFRICON51333.2021.9570989.
|
|
|
|
|
Butgereit, L (2021). Covid Cases and Covid Deaths as seen through Benford's Law – With a Special View to Africa. 2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), pp. 1-6 . DOI:10.1109/ICECCME52200.2021.9591143.
|
|
|
|
|
Buttorff, G (2008). Detecting fraud in America's gilded age. Working Paper No. 2, University of Iowa, Cal Tech/MIT Voting Technology Project.
|
|
|
|
|
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.
|
|
|
|
|
Bwarleling, TH (2017). Pendeteksian Fraud dengan Hukum Benford [Fraud Detection with Benford's Law]. Jurnal Akuntansi Bisnis 4(2), pp. 56-74.
IND
|
|
|
|
|
Bwarleling, TH (2020). Aplikasi Hukum Benford Dalam Menganalisa Kasus Garuda Indonesia [Benford's Law Application in Analyzing the Garuda Indonesia Case] . Jurnal Akuntansi Bisnis 13(2), pp. 78-99. DOI:10.30813/jab.v13i2.2240.
IND
|
|
|
|
|
Bwarleling, TH and Kinasih, PR (2022). Language Preferences from Accounting and
Linguistic Perspective in Sustainability Report
. Proceedings of 9th International Conference on Opportunities and Challenges In Management,
Economics, and Accounting, Paris, France
. DOI:10.33422/9th.omeaconf.2022.08.100.
|
|
|
|
|
Byalko, AV (1991). Statistics of Coefficients in Physical Formulas. Theoretical and Mathematical Physics 88(1), pp. 782-787. ISSN/ISBN:0040-5779. DOI:10.1007/BF01016350.
|
|
|
|
|
Cabarle, C (2018). Using Benford’s law to predict the risk of financial statement fraud in equity crowd funding offerings. Proceedings of 2018 Engaged management scholarship conference, Philadelphia, PA.. DOI:10.2139/ssrn.3240900.
|
|
|
|
|
Cabarle, C (2019). Predicting the Risk of Fraud in Equity Crowdfunding Offers and Assessing the Wisdom of the Crowd. PhD Thesis, Temple University, ProQuest Dissertations Publishing, 2019. 13863507.
|
|
|
|
|
Cáceres, JLH, García, JLP, Ortiz, CMM and Dominguez, LG (2008). First digit distribution in some biological data sets. Possible explanations for departures from Benford's Law. Electronic J Biomed 1, pp. 27-35.
|
|
|
|
|
Café, RM (2015). O uso da Lei de Benford na auditoria de obras públicas: o caso do VLP. Undergraduate thesis, Universidade de Brasília.
POR
|
|
|
|
|
Café, RM and Bugarin, M (2017). Uma proposta metodológica para a auditoria de obras públicas no Distrito Federal. Brasília: Companhia de Planejamento do Distrito Federal, Texto para Discussão no. 30.
POR
|
|
|
|
|
Caffarini, J, Gjini, K, Sevak, B, Waleffe, R, Kalkach-Aparicio, Poly, M and Struck, AF (2022). Engineering Nonlinear Epileptic Biomarkers Using Deep Learning and Benford’s Law. Scientific Reports 12(2), p. 5397. DOI:10.1038/s41598-022-09429-w.
|
|
|
|
|
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2017). Leading Digits of Mersenne Numbers. Preprint in arXiv:1712.04425 [math.NT]; last accessed October 23, 2018.
|
|
|
|
|
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2019). The Surprising Accuracy of Benford’s Law in Mathematics. Preprint arXiv:1907.08894 [math.PR]; last accessed July 31, 2019.
|
|
|
|
|
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2020). The Surprising Accuracy of Benford’s Law in Mathematics. The American Mathematical Monthly 127(3), pp. 217-237. DOI:10.1080/00029890.2020.1690387.
|
|
|
|
|
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2021). Leading digits of Mersenne numbers. Experimental Mathematics 30(3), pp. 405–421. DOI:10.1080/10586458.2018.1551162.
|
|
|
|
|
Cai, Z, Hildebrand, AJ and Li, J (2018). A local Benford Law for a class of arithmetic sequences. Preprint arXiv:1808.01496 [math.NT]; last accessed October 22, 2018.
|
|
|
|
|
Cai, Z, Hildebrand, AJ and Li, J (2019). A local Benford law for a class of arithmetic sequences. International Journal of Number Theory 15(3), pp.613-638. DOI:10.1142/S1793042119500325.
|
|
|
|
|
Cajueiro, D (2016). Existem formas de detectar fraudes em bases de dados?. Posted on Prorum.com February 5, 2016; last accessed November 17, 2020.
POR
|
|
|
|
|
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.
|
|
|
|
|
Campanario, JM and Coslado, MA (2011). Benford's law and citations, articles and impact factors of scientific journals. Scientometrics 88(2), pp. 421-432. DOI:10.1007/s11192-011-0387-9.
|
|
|
|
|
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). Breaking Benford’s law: A statistical analysis of Covid-19 data using the Euclidean distance statistic. Preprint submitted to Statistics in Transition.
|
|
|
|
|
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.
|
|
|
|
|
Campanelli, L (2023). A test of significance for Benford’s law based on the Chebyshev distance. Preprint on Researchgate.
|
|
|
|
|
Campolieti, M (2022). COVID-19 deaths in the USA: Benford’s law and under-reporting. Journal of Public Health 44(2), pp. e268-e271. DOI:10.1093/pubmed/fdab161.
|
|
|
|
|
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.
|
|
|
|
|
Candeloro, D (1998). Some remarks on the first digit problem. Atti Sem. Mat. Fis. Univ. Modena 46 (1998), suppl., 511-532.
|
|
|
|
|
Canessa, E (2003). Theory of analogous force on number sets. Physica A 328, pp. 44-52. DOI:10.1016/S0378-4371(03)00526-0.
|
|
|
|
|
Cangiotti, N and Sensi, M (2022). Benford’s Law: A Number-Theoretical Perspective . Palestine Journal of Mathematics 11(3), pp. 379–385.
|
|
|
|
|
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 (2024). Proportional appropriation systems and financial statement quality in municipally owned entities: empirical evidence from Italy. Journal of Public Budgeting, Accounting & Financial Management 36(3), pp. 343-362. DOI:10.1108/JPBAFM-01-2023-0015.
|
|
|
|
|
Carmo, CRS, Caneppele, FdL and Nunes, FC (2021). Analysis of Covid-19 Contamination and Deaths Cases in Brazil According to The Newcomb-Benford Law. Revista Brasileira de Biometria 39(4), pp.522-535. DOI:10.28951/rbb.v39i4.535.
|
|
|
|
|
Carmo, CRS, Nunes, FC and Caneppele, FdL (2023). The limits of conformity analysis under the Newcomb-Benford law and the COVID-19 pandemic in Brazil
. Brazilian Journal of Biometrics 41, pp. 234-248 . DOI:10.28951/bjb.v41i3.626.
|
|
|
|
|
Carmo, PAA (2018). Compliance of payment card spending of the Federal Government: A study of forensic accounting based on Law of Newcomb-Benford. Multidisciplinary Core scientific journal of knowledge. 03 year, Ed. 06, vol. 05, pp. 54-78.
|
|
|
|
|
Carr, E (2000). Fraudsters' Days are Numbered. Financial Times, Thursday, August 17, 2000.
|
|
|
|
|
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.
|
|
|
|
|
Carrera, C (2015). Tracking exchange rate management in Latin America. Review of Financial Economics, Available online 13 March 2015 . ISSN/ISBN:1058-3300. DOI:10.1016/j.rfe.2015.02.004.
|
|
|
|
|
Carslaw, CAPN (1988). Anomalies in Income Numbers: Evidence of Goal Oriented Behavior. The Accounting Review 63(2), pp. 321-327.
|
|
|
|
|
Cartlidge,E (2010). In nature, number one dominates
. Institute of Physics, Enviornmental Research Letters Oct 25, 2010.
|
|
|
|
|
Cascão Júnior, CA, Portugal, AC, Soares, M and da Cunha, FC (2018). Aplicação da Lei de Benford Na Detecção de Jogo de Planilha: O Caso do Estádio Nacional de Brasília. Economics and Politics Working Paper 92/2018 December 4th, 2018, University of Brasilia, Economics and Politics Research Group–EPRG (also published as Trabalho apresentado no XVIII Simpósio Nacional de Auditoria de Obras Públicas – João Pessoa, PB).
POR
|
|
|
|
|
Casey, MC (2004). Integrated Learning in Multi-net Systems. University of Surrey Ph.D. Thesis submitted Feb 2004.
|
|
|
|
|
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
|
|
|
|
|
Caster, P, Mittag, B and Scherga, C (2003). Application of Digital Analysis To Assess the Quality and Usability of the ATA Database. Journal of Forensic Accounting 4, pp. 95-104.
|
|
|
|
|
Ceccato, F and Bugarin, M (2017). Lei de Benford Aplicada À Auditoria da Reforma do Aeroporto Internacional de Minas Gerais [Benford's Law Applied to the Audit of the Renovation of the Minas Gerais International Airport]. Revista do Serviço Público.
POR
|
|
|
|
|
Cella, RS and Rech, IJ (2017). Petrobas Case: Could Benford's Law Detect a Fraud?. Revista de Gestão, Finanças e Contabilidade, UNEB, Salvador, v. 7, n. 3, pp. 86-104. ISSN/ISBN:2238-5320.
POR
|
|
|
|
|
Cella, RS and Zanolla, E (2018). Benford’s Law and transparency: an analysis of municipal expenditure. Brazilian Business Review, 15(4), pp. 331-347. DOI:10.15728/bbr.2018.15.4.2.
|
|
|
|
|
Cengi̇z, E (2012). Hile Risklerinin Tespitinde Benford Analizi: Vaka Çalışması [Benford Analysis in Detection of Fraud Risks: Case Study]. Muhasebe Bilim Dünyası Dergisi 3, pp. 111-129.
TUR
|
|
|
|
|
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.
|
|
|
|
|
Cerioli, A, Barabesi, L, Cerasa, A and Perrotta, D (2022). Who is afraid of the probability-savvy fraudster?. Conference presentation at MBC2 2022 Models and Learning for Clustering and Classification 6th International Workshop, Catania.
|
|
|
|
|
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.
|
|
|
|
|
Cerqueti, R and Provenzano, D (2023). Benford's Law for economic data reliability: The case of tourism flows in Sicily. Chaos, Solitons & Fractals 173, p. 113635. DOI:10.1016/j.chaos.2023.113635.
|
|
|
|
|
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.
|
|
|
|
|
Chaitin-Chatelin, F (1994). Le calcul sur ordinateur a precision finie. Theorie et etat de l’art. CERFACS REPORT TR/PA/94/05.
FRE
|
|
|
|
|
Chaitin-Chatelin, F (1995). Le calcul qualitatif. Comment donner un sens a des resultats faux?. CERFACS REPORT TR/PA/95/10.
FRE
|
|
|
|
|
Chaitin-Chatelin, F (1996). Is finite precision arithmetic useful for physics?. Journal of Universal Computer Science 2(5), pp. 380-395.
|
|
|
|
|
Chaitin-Chatelin, F and Frayssé, V (1996). Lectures on Finite Precision Computations. SIAM.
|
|
|
|
|
Chakrabarthy, B, Moulton, PC, Pugachev, L and Wang, X (2019). Catch Me If You Can: Improving the Scope and Accuracy of Fraud Prediction. E-print available at SSRN: https://ssrn.com/abstract=3352667, March 13, 2019. DOI:10.2139/ssrn.3352667.
|
|
|
|
|
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.
|
|
|
|
|
Chandee, V, Li, X, Pollack, P and Roy, AS (2022). On Benford's Law for Multiplicative Functions. Preprint arXiv:2203.13117v2 [math.NT]; last accessed May 30, 2022.
|
|
|
|
|
Chang, JC (2017). A Study of Benford's Law, With Applications to the Analysis of Corporate Financial Statements. Masters Thesis, The Graduate School Eberly College of Science, The Pennsylvania State University.
|
|
|
|
|
Chang, M (2012). Paradoxes in scientific inference . CRC Press: Boca Raton (Chapter 1.2.1), pp. 12-13. ISSN/ISBN:978-1466509863.
|
|
|
|
|
Chang, S and Miller, SJ (2023). Benford’s Law under Zeckendorf expansion. Preprint arXiv:2309.00090 [math.NT]; last accessed September 12, 2023.
|
|
|
|
|
Chang, SA and Chang, C (2023). Identification of Behavioral Signature: Benford’s Law in Online Auctions. International Journal of Business & Management Studies 4(9). DOI:10.56734/ijbms.v4n9a1.
|
|
|
|
|
Charoenwong, B and Reddy, P (2022). Using forensic analytics and machine learning to detect bribe payments in regime-switching environments: Evidence from the India demonetization. PLoS ONE 17(6): e0268965. DOI:10.1371/journal.pone.0268965.
|
|
|
|
|
Chatterjee, S, Sarkar, A, Karmakar, M, Chatterjee, S and Paul, R (2020). EIRD model to study the asymptomatic growth during COVID-19 pandemic in India. Indian Journal of Physics. DOI:10.1007/s12648-020-01928-8.
|
|
|
|
|
Chatziapostolou, E (2019). Fraud detection using Benford’s Law (Python Code). Published in Towards Data Science, August 12.
|
|
|
|
|
cheesinglee (2015). Detecting numeric irregularities with Benford’s Law. Blog posted on bigML.com, last accessed October 9, 2023.
|
|
|
|
|
Chen, C-W, Yu, S-Y and Chen, H-Y (2021). Investigation of Benford’s Law with YouTube Social
Media Statistics. Journal of Student Research (High School Edition) 10(3). ISSN/ISBN:2167-1907. DOI:10.47611/jsrhs.v10i3.1677.
|
|
|
|
|
Chen, E, Park, PS and Swaminathan, AA (2016). On logarithmically Benford Sequences. Proc. Amer. Math. Soc. 144, pp. 4599-4608. DOI:10.1090/proc/13112 .
|
|
|
|
|
Chen, T and Tsourakakis, CE (2022). AntiBenford Subgraphs: Unsupervised Anomaly Detection in Financial Networks. Preprint arXiv:2205.13426 [cs.; last accessed June 9, 2022.
|
|
|
|
|
Chen, W and Shi, YQ (2009). Detection of Double MPEG Compression Based on First Digit Statistics. In H. J. Kim, S. Katzenbeisser, & A.T.S. Ho (Eds.), Digital watermarking: Seventh International Workshop (IWDW ’08) (pp. 16-30). Berlin: Springer-Verlag. DOI:10.1007/978-3-642-04438-0_2.
|
|
|
|
|
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.
|
|
|
|
|
Chenavier, N and Schneider, D (2018). On the discrepancy of powers of random variables. Statistics & Probability Letters 134, pp. 5-14. DOI:10.1016/j.spl.2017.10.006.
|
|
|
|
|
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.
|
|
|
|
|
Chi, D (2024). The Influence of Statistical Information on Number Estimation Under Uncertainty: Why Do People Present Benford Bias?. PhD Thesis, School of Psychology, Faculty of Science, University of Sydney.
|
|
|
|
|
Chi, D and Burns, BD (2022). Why do People fit to Benford’s Law? – A Test of the Recognition Hypothesis. In: Proceedings of the 44th Annual Conference of the Cognitive Science Society, J. Culbertson, A. Perfors, H. Rabagliati & V. Ramenzoni (Eds.), pp. 3648-3654.
|
|
|
|
|
Chinchon, AS (2014). Mixing Benford, GoogleVis And On-Line Encyclopedia of Integer Sequences. "Ripples, very small waves in R", Blog, Dec 23rd, 2014, last accessed June 14, 2018.
|
|
|
|
|
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.
|
|
|
|
|
Chiverton, J and Wells, K (2015). PV Modeling of Medical Imaging Systems. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 319-337.
|
|
|
|
|
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.
|
|
|
|
|
Choi, C-H and Park, J-H (2017). Detection possibility of sport game manipulation: Benford's laws appearing in sports data. The Korean Journal of Measurement and Evaluation in Physical Education and Sports Science 19(1), pp. 69-89.
KOR
|
|
|
|
|
Chou, MC, Kong, Q, Teo, C-P and Zheng, H (2015). Managing Risk in Numbers Games. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 276-289.
|
|
|
|
|
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.
|
|
|
|
|
Christensen, JA and Byington, JR (2003). The computer: an essential fraud detection tool. Journal of Corporate Accounting & Finance 14(5), pp. 23-27. DOI:10.1002/jcaf.10179 .
|
|
|
|
|
Christian, CW and Gupta, S (1993). New evidence on "Secondary Evasion". The Journal of the American Taxation Association 15(1), pp. 72-93.
|
|
|
|
|
Ciaponi, F and Mandanici, F (2014). Using Digital Frequencies To Detect Anomalies in Receivables and Payables: An Analysis of the Italian Universities. Journal of Economic and Social Development 2(1), pp. 86-108.
|
|
|
|
|
Cigler, J (1964). Methods of summability and uniform distribution mod 1. Compositio Mathematica 16, pp. 44-51.
|
|
|
|
|
Cigler, J and Helmberg, G (1961). Neuere Entwicklungen der Theorie der Gleichverteilung. Jahresbericht der Deutschen Mathematiker Vereinigung 64, pp. 1-50.
GER
|
|
|
|
|
Cinelli, C (2014). Indício de fraude nas eleições? Usando a Lei de Benford. Blog posted on Análise Real, November 2, 2014. Last accessed September 21, 2022.
POR
|
|
|
|
|
Cinelli, C (2017). Benford analysis for data validation and Forensic analytics. Online software R package benford.analysis V. 0.1.4.1.
|
|
|
|
|
Cinelli, C, Lins, R, Stachelek, J and Gorecki, J (2020). The Benford Analysis (benford.analysis) package . Posted on GitHub Repository; last accessed November 17, 2020.
|
|
|
|
|
Cinko, M (2014). Testing distribution of BIST-100 returns by Benford law. Journal of Economics, Finance and Accounting – (JEFA) 1(3), pp.184–191.
TUR
|
|
|
|
|
Ciofalo, M (2009). Entropy, Benford’s first digit law, and the distribution of everything. Unpublished manuscript.
|
|
|
|
|
Cleary, R and Thibodeau, J (2015). Benford’s Law as a bridge between statistics and accounting. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 177-190. DOI:10.1515/9781400866595-010.
|
|
|
|
|
Cleary, R and Thibodeau, JC (2005). Applying Digital Analysis Using Benford‘s Law to Detect Fraud: The Dangers of Type I Errors. Auditing - A Journal of Practice & Theory 24(1), pp. 77-81. ISSN/ISBN:0278-0380. DOI:10.2308/aud.2005.24.1.77.
|
|
|
|
|
Clenshaw, CV, Olver, FWJ and Turner, PR (1989). Level-Index Arithmetic - An Introductory Survey. Lecture Notes in Mathematics 1397, pp. 95-168. ISSN/ISBN:0075-8434. DOI:10.1007/BFb0085718.
|
|
|
|
|
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.
|
|
|
|
|
Cockshott, WP, McGregor, D and Wilson, J (1998). High-Performance Operations Using a Compressed Database Architecture. The Computer Journal 41(5), pp. 283-296. ISSN/ISBN:0010-4620. DOI:10.1093/comjnl/41.5.283.
|
|
|
|
|
Coderre, D (2000). Computer assisted fraud detection. Internal Auditor 57(4) pp. 25-27.
|
|
|
|
|
Coderre, D. (1999). Fraud Detection: Using Data Analysis Techniques to Detect Fraud. Global Audit Publications, ACL, Vancouver, Canada.
|
|
|
|
|
Coeurjolly, J-F (2020). Digit analysis for Covid-19 reported data . Preprint arXiv:2005.05009 [stat.AP]; last accessed May 17, 2020.
|
|
|
|
|
Cohen, DIA (1976). An Explanation of the First Digit Phenomenon. Journal of Combinatorial Theory Series A 20(3), pp. 367-370. ISSN/ISBN:0097-3165.
|
|
|
|
|
Cohen, DIA and Katz, TM (1984). Prime Numbers and the First Digit Phenomenon. Journal of Number Theory 18(3), pp. 261-268. ISSN/ISBN:0022-314X. DOI:10.1016/0022-314X(84)90061-1.
|
|
|
|
|
Cole, MA, Maddison, DJ and Zhang, L (2020). Testing the emission reduction claims of CDM projects using the Benford's Law. Climatic Change 160 (3), pp. 407–426. DOI:10.1007/s10584-019-02593-5.
|
|
|
|
|
Coleman, D (2014). Benford’s Law and Financial Statements. Blog posted on auditAnalytics.com October 20; last accessed Jun 16, 2019.
|
|
|
|
|
Collins, JC (2017). Using Excel and Benford’s Law to detect fraud. Journal of Accountancy Feature/Technology Workshop, April 1.
|
|
|
|
|
Coman, D, Horga, M, Danila, A and Coman, M (2018). Using Benford’s Law in the Analysis of Socio-Economic Data. Journal of Science & Arts 42(1), pp. 167-174. ISSN/ISBN:1844 – 9581.
|
|
|
|
|
Condeço, PIH (2014). Aplicação da lei de Benford e a importância do controlo interno. Master's Thesis, Instituto politécnico de Lisboa,
Instituto superior de contabilidade e administração de Lisboa.
POR
|
|
|
|
|
Cong, LW, Li, X, Tang, K and Yang, Y (2021). Crypto Wash Trading. Management Science 69(11), pp. 6427-6454. DOI:10.1287/mnsc.2021.02709.
|
|
|
|
|
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.
|
|
|
|
|
Conway,D (2010). Benford’s Law Tests for Wikileaks Data
. Zero Intelligence Agents blog posting August 1, 2010.
|
|
|
|
|
Cook, JD (2017). Search Results for: Benford's law (multiple topics). John D. Cook blog - https://www.johndcook.com/blog/?s=Benford%27s+law.
|
|
|
|
|
Coracioni, A (2013). Cercetare privind aplicarea modelului Benford în detectarea riscului de frauda [Research Regarding the Usage of the Benford's Model for the Fraud Detection]. Audit Financiar 11(8), pp. 23-27.
RON
|
|
|
|
|
Coracioni, A-T and Dănescu, T (2020). Testing of Published Information on Greenhouse Gas Emissions. Conformity Analysis with the Benford’s Law Method. Audit Financiar XVIII(4) pp. 821-830,. DOI:10.20869/AUDITF/2020/160/029.
|
|
|
|
|
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 (2012). Desenvolvimento de metodologias contabilométricas aplicadas a auditoria contábil digital: uma proposta de análise da lei de Newcomb-Benford para os Tribunais de Contas. Thesis, Universidade Federal de Pernambuco, Recife, Brasil.
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 and dos Santos, J (2013). Application of Newcomb-Benford Law in accounting audit: A bibliometric analysis in the period from 1988 to 2011. 10th International Conference on Information Systems and Technology Management - CONTECSI
June, 12 to 14, 2013 - São Paulo, Brazil, pp. 16-30.
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
|
|
|
|
|
Costas, E, López-Rodas, V, Toro, FJ and Flores-Moya, A (2008). The number of cells in colonies of the cyanobacterium Microcystis aeruginosa satisfies Benford's law. Aquatic Botany 89(3), pp. 341-343. DOI:10.1016/j.aquabot.2008.03.011.
|
|
|
|
|
Coufalová, L, Mikula, S and Žídek, L (2022). Misreporting in financial statements in a centrally planned economy: The case of Czechoslovak state-owned enterprises in late socialism. Accounting History. DOI:10.1177/10323732221109652.
|
|
|
|
|
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.
|
|
|
|
|
Courtland, R (2010). Curious mathematical law is rife in nature. Issue 2782, New Scientist, 14 October.
|
|
|
|
|
Cox, RAK, Cheng, Q and Cos, GRA (2024). The Anomalous Behavior of Stock Prices on the Canadian Securities Exchange. International Journal of Financial Research 15(4). DOI:10.5430/ijfr.v15n4p1.
|
|
|
|
|
Craig, TR (1992). Round-off bias in earnings-per-share calculations. Journal of Applied Business Research 8 (4), pp. 106-113. DOI:10.19030/jabr.v8i4.6131.
|
|
|
|
|
Crato, N (2010). Mr. Benford. In: Figuring It Out: Entertaining Encounters with Everyday Math, Springer-Verlag: Berlin, pp. 173-177. ISSN/ISBN:978-3-642-04833-3. DOI:10.1007/978-3-642-04833-3_41.
|
|
|
|
|
Crisan, D and Gota, DI (2023). The First-Digit Law application in digital forensics in crystal forgery research. Proceedings of 3rd International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), Tenerife, Canary Islands, Spain, pp. 1-7. DOI:10.1109/ICECCME57830.2023.10253354.
|
|
|
|
|
Crişan, D, Irimia, A, Gota, D, Miclea, L, Puscasiu, A, Ovidiu, S and Valean, H (2021). Analyzing Benford’s Law’s Powerful Applications in Image Forensics . Appl. Sci. 11(23), p. 11482. DOI:10.3390/app112311482 .
|
|
|
|
|
Cristelli, M, Batty, M and Pietronero, L (2012). There is more than a power law in Zipf. Scientific Reports 2:812. DOI:10.1038/srep00812.
|
|
|
|
|
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.
|
|
|
|
|
Çubukcu, S (2009). Muhasebe Hilelerini Ortaya Çikarmada Benford Modeli'nin İlk İki Basamak Yaklaşimi İle Kullanilmasi [Using Benford Model in First Two Step Approach to Reveal Accounting Cheats]. World of Accounting Science 11(3), pp. 113-142.
TUR
|
|
|
|
|
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
|
|
|
|
|
Çakır, S (2004). Muhasebe Hilelerinin Tespitinde İstatistiksel Yöntemler (Benford Yöntemi'nin İrdelenmesi) [Statistical Methods for Detection of Accounting Fraud (Examination of the Benford Method)]. Master Thesis. Dokuz Eylul University Institute of Social Sciences, Department of Business Administration. Izmir.
|
|
|
|
|
D'Alessandro, A (2020). Benford's law and metabolomics: A tale of numbers and blood. Transfusion and Apheresis Science 59(6), pp. 103019. DOI:10.1016/j.transci.2020.103019.
|
|
|
|
|
da Cruz Filho, EC, Nunes, DMS and Santana, CM (2021). LEI DE BENFORD: uma análise de sua aplicabilidade na detecção de fraudes nas prestações de contas de senadores da República. Revista Brasileira de Ciências Policiais 12(6). DOI:10.31412%2Frbcp.v12i6.830.
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 Cunha, FCR and Bugarin, MS (2014). Lei de Benford e Auditoria de Obras Públicas: uma análise de sobrepreço na reforma do Maracanã [Benford’s Law and Public Works Audit: an analysis of overpricing in the maracanã remodeling]. Revista do TCU 131, pp. 46-53.
|
|
|
|
|
da Cunha, FCR and Bugarin, MS (2015). Benford's law for audit of public works: an analysis of overpricing in Maracanã soccer arena's renovation. Economics Bulletin 35(2), pp. 1168-1176.
|
|
|
|
|
da Cunha, FCR and Bugarin, MS (2015). Lei de Benford para a auditoria de obras públicas: análise de sobrepreço na construção da Arena da Amazônia. Bole m de Licitações e Contratos (BLC/NDJ) 28(8), pp. 841-857.
POR
|
|
|
|
|
da Cunha, FCR, Bugarin, MS and Portugal, AC (2016). Seleção de amostra de auditoria de obras públicas pela Lei de Benford. Sao Paulo: Instituto Brasileiro de Auditoria de Obras Públicas (IBRAOP). ISSN/ISBN:978-85-93840-00-5.
POR
|
|
|
|
|
da Silva, ÂHL (2009). O Uso da Lei Newcomb-Benford na contabilidade e auditoria. Revista do TCU 38(115), pp. 17-23.
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 .
|
|
|
|
|
Dacey, J (2020). Benford’s law and the 2020 US presidential election: nothing out of the ordinary. PhysicsWorld Everyday Science Blog posted 19 Nov 2020; last accessed 15 Dec 2021.
|
|
|
|
|
Dahlstrom, KL and Clegg, CP (2013). The Organized Universe. Outskirts Press, Inc.. ISSN/ISBN:978-1-4787-0121-7.
|
|
|
|
|
Dahlstrom, KL and Clegg, CP (2015). The DNA of Scripture. Westbow Press: Bloomington, IN. ISSN/ISBN:978-1-4908-7600-9.
|
|
|
|
|
Dalal, C (2000). Fraud Detection using Benford's Law. Bombay Chartered Accountant's Society (bcasonline.org) - Last retrieved 10 September 2014.
|
|
|
|
|
Dang, CT (2019). Donors and recipients: charities, NGOs and aid. PhD thesis, University of Nottingham.
|
|
|
|
|
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.
|
|
|
|
|
Dang, CT and Owens, T (2019). Does transparency come at the cost of charitable services? Evidence from investigating British charities. CREDIT Research Paper 19/02; published (2020) in Journal of Economic Behavior & Organization 172, pp. 314–343.
|
|
|
|
|
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.
|
|
|
|
|
Darhasani and Usman, F (2021). Benford's Law Test Method in Tax Audit Planning. European Journal of Business and Management Research 6(6), pp. 240-246. DOI:10.24018/ejbmr.2021.6.6.1195.
|
|
|
|
|
Das, RC (2022). Earnings Management Detection Using Digital Analysis: A Concept in Benford’s Law. Research Developments in Arts and Social Studies 1, pp. 7–21. DOI:10.9734/bpi/rdass/v1/3183E.
|
|
|
|
|
Das, RC, Mishra, CS and Rajib, P (2017). Detection of Anomalies in Accounting Data Using Benford’s Law: Evidence from India. Journal of Social Science Studies 4(1), pp. 123-139. DOI:10.5296/jsss.v4i1.9873.
|
|
|
|
|
Das, S and Zhang, H (2001). The stock market’s under-reaction to rounding-up in EPS. Preprint.
|
|
|
|
|
Das, S and Zhang, H (2003). Rounding-up in reported EPS, behavioral thresholds, and earnings management. Journal of Accounting & Economics 35(1), pp. 31-50. ISSN/ISBN:0165-4101. DOI:10.1016/S0165-4101(02)00096-4.
|
|
|
|
|
Datta, D and Banks, D (2021). Was There Any Widespread Fraud in 2020 Presidential Election? What does Benford's Law say?. Journal of Student Research (High School Edition) 10(3), pp. . ISSN/ISBN:2167-1907. DOI:10.47611/jsrhs.v10i3.1848.
|
|
|
|
|
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.
|
|
|
|
|
Davies, B (2022). Arbitral Analytics: How Moneyball Based Litigation/Judicial Analytics Can Be Used to Predict Arbitration Claims and Outcomes. Pepperdine Dispute Resolution Law Journal 22(2), pp. 321-376.
|
|
|
|
|
Davis, B (1976). Some Remarks on Initial Digits. Fibonacci Quarterly 14(1), pp. 13-14. ISSN/ISBN:0015-0517.
|
|
|
|
|
Davis, BS and Davis, TA (1989). Fibonacci numbers and the golden mean in nature. The Mathematical Scientist 14(2), pp. 89-100.
|
|
|
|
|
Davis, JG and Garcıa-Cestona, M (2021). CEO age, financial statement irregularities, and earnings management. Unpublished manuscript.
|
|
|
|
|
Davis, JG and Garcia-Cestona, M (2023). CEO age, financial reporting quality, and the role of clawback provisions. Journal of Financial Reporting and Accounting. DOI:10.1108/JFRA-04-2023-0176.
|
|
|
|
|
Davydov, D and Swidler, S (2016). Auditing Bank Financial Statements in Emerging Market Countries: The Use of the Benford Distribution. In: Risk Management in Emerging Markets, Emerald Group Publishing Limited, Boubaker, S., Buchanan, B. and Nguyen, D. (Eds.), pp. 187-200. DOI:10.1108/978-1-78635-452-520161018.
|
|
|
|
|
Davydov, D and Swidler, S (2016). Reading Russian Tea Leaves: Assessing the Quality of Bank Financial Statements with the Benford Distribution. Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pp. 1-20. DOI:10.1142/S0219091516500211.
|
|
|
|
|
de Bruijne, J, de Jong, J and De Ridder, J (2019). Benfords' Law: Gaia parallaxes and distances. Poster presented at 53rd ESLAB Symposium: The Gaia Universe, held 8-12 April in at ESTEC/ESA, Noordwijk, The Netherlands. DOI:10.5281/zenodo.2643075.
|
|
|
|
|
De Ceuster, MJK, Dhaene, G and Schatteman, T (1998). On the hypothesis of psychological barriers in stock markets and Benford’s law. Journal of Empirical Finance 5(3), pp. 263-279. DOI:10.1016/S0927-5398(97)00024-8.
|
|
|
|
|
de Jong, J (2018). De wet van Benford-Bizar en nog onverklaarbaar. Posted on scientias.nl website.
DUT
|
|
|
|
|
de Jong, J (2019). De Wet van Benford. Posted on website Natuur en Wetenschap vzw.
DUT
|
|
|
|
|
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 Kok, R and Rotundo, G (2022). Benford Networks. Stats 5(4), pp. 934-947. DOI:10.3390/stats5040054.
|
|
|
|
|
de Macedo, IAS and de Figueiredo, JJS (2018). Using Benford’s law on the seismic reflectivity analysis. Interpretation 6(3), pp. T689-T697. DOI:10.1190/int-2017-0201.1.
|
|
|
|
|
de Macedo, IAX (2019). On the well-to-seismic-tie analysis: effects of the borehole geometry and assumptions on wavelet estimation . Ph.d Thesis, Federal University of Pará Institute of Geosciences Geophysics Graduate Program.
|
|
|
|
|
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.
|
|
|
|
|
De Vries, P and Murk, AJ (2013). Compliance of LC50 and NOEC data with Benford's Law: An indication of reliability?. Ecotoxicology and Environmental Safety 98, pp. 171–178. DOI:10.1016/j.ecoenv.2013.09.002.
|
|
|
|
|
Deakin, MAB (1993). Another derivation of Benford’s law. Australian Mathematical Society Gazette 20, pp. 162-163.
|
|
|
|
|
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.
|
|
|
|
|
Deckert, J, Myagkov, M and Ordeshook, PC (2010). The Irrelevance of Benford's Law for Detecting Fraud in Elections. CALTECH working paper 9.
|
|
|
|
|
Deckert, J, Myagkov, M and Ordeshook, PC (2011). Benford's Law and the Detection of Election Fraud. Political Analysis 19(3), pp. 245-268. DOI:10.1093/pan/mpr014.
|
|
|
|
|
DeHaan, M (2011). The surprising “Benford’s law” of leading digits. Posted on Decoding Science website; last updated November 12, 2019; last accessed December 9, 2019.
|
|
|
|
|
Dehaene, S and Mehler, J (1992). Cross-Linguistic Regularities in the Frequency of Number Words. Cognition 43(1), pp. 1-29. ISSN/ISBN:0010-0277. DOI:10.1016/0010-0277(92)90030-L.
|
|
|
|
|
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.
|
|
|
|
|
Deligny, H and Jolissaint, P (2012). Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]. Elemente der Mathematik, 68(1), pp. 9-21. DOI:10.4171/EM/213.
FRE
|
|
|
|
|
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 (2018). Forensics, Elasticities and Benford's Law. CEPR Discussion Papers 12798, C.E.P.R. Discussion Papers.
|
|
|
|
|
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.
|
|
|
|
|
Demir, M (2014). Benford yasası ve hile denetiminde kullanılması [Benford's use of law and fraud]. Masters Thesis, Istanbul Commerce University.
TUR
|
|
|
|
|
Demirci, Z and Avci, O (2016). Vergi Denetiminde Alternatif Bir Yol: Benford Kanunu [An Alternative Way to Tax Auditing: Benford's Law]. Vergi Sorunları Dergisi 329, pp. 100-111.
TUR
|
|
|
|
|
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
|
|
|
|
|
den Heijer, E and Eiben, AE (2014). Investigating aesthetic measures for unsupervised evolutionary art. Swarm and Evolutionary Computation, Vol. 16, pp. 52–68. DOI:10.1016/j.swevo.2014.01.002.
|
|
|
|
|
den Hollander, F and Kalle, C (2021). De oorsprong van ergodentheorie [The origin of ergodic theory]. Nieuw Arch. Wiskd. (5), 22(1), pp. 9-13.
DUT
|
|
|
|
|
Depken, CA (2008). Benford, Zipf and the blogosphere. Applied Economics Letters, 15(9), pp. 689–692. ISSN/ISBN:1350-4851. DOI:10.1080/13504850600735270.
|
|
|
|
|
Derks, K, de Swart, J, Wagenmakers, E-J and Wetzels, R (2021). The Bayesian Approach to Audit Evidence: Quantifying Statistical Evidence using the Bayes Factor. Preprint PsyArXiv; last accessed July 29, 2021. DOI:10.31234/osf.io/kzqp5.
|
|
|
|
|
Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), pp. 72-81. ISSN/ISBN:0091-1798.
|
|
|
|
|
Diaconis, P (1977). Examples of the theory of infinite iteration of summability methods. Canadian Journal of Mathematics 29(3), pp. 489-497. DOI:10.4153/CJM-1977-053-1.
|
|
|
|
|
Diaconis, P (2002). G.H. Hardy and Probability ???. Bulletin of the London Mathematical Society 34(4), pp. 385-402. DOI:10.1112/S002460930200111X.
|
|
|
|
|
Diaconis, P and Freedman, D (1979). On Rounding Percentages. Journal of the American Statistical Association 74(366), pp. 359-364. ISSN/ISBN:0162-1459.
|
|
|
|
|
Diaz, J, Gallart, J and Ruiz, M (2014). On the Ability of the Benford’s Law to Detect Earthquakes and Discriminate Seismic Signals. Seismological Research Letters 86(1), pp. 192-201. DOI:10.1785/0220140131.
|
|
|
|
|
Dickinson, JR (2002). A universal mathematical law criterion for algorithmic validity. Developments in Business Simulation and Experiential Learning 29, pp. 26-33.
|
|
|
|
|
Diekmann, A (2002). Diagnose von Fehlerquellen und methodische Qualität in der sozialwissen- schaftlichen Forschung [Sources of bias and quality of data in social science research]. Institute of Technology Assessment (ITA) Working Paper No. ITA-02-04. DOI:10.2139/ssrn.518402.
GER
|
|
|
|
|
Diekmann, A (2007). Not the First Digit! Using Benford's Law to Detect Fraudulent Scientific Data. Journal of Applied Statistics 34(3), pp. 321-329. ISSN/ISBN:0266-4763. DOI:10.1080/02664760601004940.
|
|
|
|
|
Diekmann, A (2012). Making Use of ‘‘Benford’s Law’’ for the Randomized Response Technique. Sociological Methods and Research 41(2), pp. 325-334. DOI:10.1177/0049124112452525.
|
|
|
|
|
Diekmann, A and Jann, B (2010). Benford’s Law and Fraud Detection: Facts and Legends. German Economic Review 11(3), pp. 397–401. DOI:10.1111/j.1468-0475.2010.00510.x.
|
|
|
|
|
Diepenmaat, H (2018). The Path of Humanity. Social Innovation for the World of Tomorrow. Parthenon Publishing House: Almere, The Netherlands, Section 8.3. ISSN/ISBN:9789079578900.
|
|
|
|
|
Dimm, WC (2015). Detecting Fraud Using Benford's Law. Criminal Justice, Summer2015, Vol. 30 Issue 2, pp. 67-68.
|
|
|
|
|
Diniz, JA, Corrar, LJ and Slomski, V (2010). Análise digital: uma abordagem cognitiva na detecção de não conformidade em prestações de contas municipais. Anais do Congresso Controladoria e Contabilidade USP, São Paulo, SP, Brasil.
POR
|
|
|
|
|
Diniz, JA, dos Santos, J, Dieng, M and Diniz, MAA (2006). Comprovação de Eficácia da Aplicação de Modelos Contabilométricos no Campo daAuditoria Digital das Contas Públicas Municipais: caso de um Tribunal de Contas de um estado brasileiro. Proceedings of 6th Congresso USP de Controladoria e Contabilidade.
POR
|
|
|
|
|
Dissanayake, CK and Daniel, J (2021). Do Pandemic Related Datasets with High Artificial Control Still Follow the Benford’s Law?. Proceedings of the 4th European International Conference on Industrial Engineering and Operations Management, Rome, Italy, August 2-5.
|
|
|
|
|
Dlugosz, S (2004). Digitalanalyse als Ansatz zur Betrugserkennung in Finanzdaten. Diploma thesis, Westfälische Wilhelms-Universität Münster, Germany.
GER
|
|
|
|
|
Dlugosz, S and Müller-Funk, U (2009). The value of the last digit: statistical fraud detection with digit analysis. Advances in Data Analysis and Classification 3, pp. 281-290. DOI:10.1007/s11634-009-0048-5.
|
|
|
|
|
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
.
|
|
|
|
|
Doi, J (2016). Benford’s Law data examples - US Census Data I – Population Estimates. Cal Poly Statistics Dept. Shiny Series; last accessed December 7, 2019.
|
|
|
|
|
Doi, JA (2019). Lecture Examples using Simulation-Based Inference and Active Learning. Journal of Japan Society of Mathematical Education 101(3), pp. 28-39.
|
|
|
|
|
Dominguez, MP and Burguillo, JDA (1999). El primer digito significativo. Revista Epsilon de la S.A.E.M. "Thales", 45 (15/3), pp. 339-352.
SPA
|
|
|
|
|
Domínguez- Bustos, AR, Cabrera-Castro, R, Ramos, ML, Abaunza, P and Báez, JC (2024). Using Benford's Law to Detect Possible Biases in Reported Catches of Tropical Tuna From the Indian Ocean. Fisheries Management and Ecology, p. e12749. DOI:10.1111/fme.12749.
|
|
|
|
|
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.
|
|
|
|
|
Dorneich, A (2014). Benfords Gesetz und seine Anwendung in der Betrugsaufdeckung. Unpublished manuscript.
GER
|
|
|
|
|
Dorogovtsev, SN, Mendes, JFF and Oliveira, JG (2006). Frequency of occurrence of numbers in the World Wide Web. Physica A: Statistical Mechanics and its Applications 360(2), pp. 548-556. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2005.06.064.
|
|
|
|
|
Dorrell, DD and Gadawski, GA (2012). Financial Forensics Body of Knowledge. Wiley Finance: Hoboken, NJ. ISSN/ISBN:978-0-470-88085-2.
|
|
|
|
|
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 Corrar, LJ (2009). A Lei de Newcomb-Benford. In: Corrar, L. J.; Paulo, E.; Dias Filho, J. M. Análise multivariada: para os cursos de administração, ciências contábeis e economia, São Paulo: Atlas, pp. 506-540. ISSN/ISBN:9788522447077.
POR
|
|
|
|
|
dos Santos, J, Diniz, JA and Ribeiro Filho, JF (2003). A Lei de Newcomb- Benford: uma aplicação para determinar o DNA-equivalente das despesas no setor público. Proceedings of 3rd Congresso usp de controladoria e contrabilidade congresso, Brazil.
POR
|
|
|
|
|
dos Santos, J, Filho, JFR, Lagioia, U, Filho, BFA and Araújo, IJCD (2009). Applications of the Newcomb-Benford law in the tax audit of the service tax (ISS). Revista Contabilidade & Finanças 20(49), pp. 63-78. DOI:10.1590/S1519-70772009000100006.
POR
|
|
|
|
|
Doucouliagos, C (2004). Number preference in Australian stocks. Applied Financial Economics 14(1), pp. 43-54. DOI:10.1080/0960310042000164211.
|
|
|
|
|
Doucouliagos, C (2005). Price exhaustion and number preference: time and price confluence in Australian stock prices. The European Journal of Finance 11(3), pp. 207-222. DOI:10.1080/1351847042000254194.
|
|
|
|
|
Drake, PD and Nigrini, MJ (2000). Computer assisted analytical procedures using Benford’s law. Journal of Accounting Education 18, pp. 127-146. DOI:10.1016/S0748-5751(00)00008-7.
|
|
|
|
|
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.
|
|
|
|
|
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651.
|
|
|
|
|
Druica, E, Oancea, B and Valsan, C (2018). Benford's law and the limits of digit analysis. International Journal of Accounting Information Systems 31, pp. 75–82. DOI:10.1016/j.accinf.2018.09.004.
|
|
|
|
|
Duan, H, Yue, W and Li, W (2024). Reliability Assessment of PM2.5 Concentration Monitoring Data: A Case Study of China. Atmosphere 15(11) pg. 1303. ISSN/ISBN:2073-4433. DOI:10.3390/atmos15111303.
|
|
|
|
|
Ducharme, RG, Kaci, S and Vovor-Dassu ,C (2020). Smooths Tests of Goodness-of-fit for the Newcomb-Benford distribution. Preprint: arXiv:2003.00520v1 [math.ST]. Published in Mathématiques appliquées et stochastiques, 3(1).
FRE
|
|
|
|
|
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.
|
|
|
|
|
Dümbgen, L and Leuenberger, C (2015). Explicit Error Bounds via Total Variation. In: S.J. Miller (ed.) Benford's Law: Theory and Applications, Princeton University Press: Princeton, NJ, pp. 119-134.
|
|
|
|
|
Dumičić, K and Cunjak Mataković, I (2019). Challenges of Benford’s Law goodness-of-fit testing in discovering the distribution of first digits: comparison of two industries. In Proceedings of 15th International Symposium on Operational Research SOR'19, Zadnik Stirn, L., Kljajić Borštnar, M., Žerovnik, J., Drobne, S., Povh, J. (Eds.), Slovenian Society Informatika, Section for Operational Research, Ljubljana, pp. 290-295.
|
|
|
|
|
Duncan, RL (1967). An application of uniform distributions to the Fibonacci numbers. Fibonacci Quarterly 5, pp. 137-140.
|
|
|
|
|
Duncan, RL (1969). Note on the initial digit problem. Fibonacci Quarterly 7(5), pp. 474-475.
|
|
|
|
|
Dündar, U (2014). Kamu Mali Denetiminde İstatistiksel Bir Yaklaşım: Benford Yasası [An Analytical Test for Public Auditing: Benford’s Law] . Proceedings of 29. Türkiye Maliye Sempozyumu- Sakarya Üniversitesi İİBF Maliye Bölümü, 16-20 Mayıs 2014 – Antalya, pp. 133-144.
TUR
|
|
|
|
|
Duran, JP (1974). Almost convergence, summability and ergodicity. Canadian Journal of Mathematics 26(2), pp. 372-387. DOI:10.4153/CJM-1974-039-6.
|
|
|
|
|
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.
|
|
|
|
|
Durrett, R (1996). Probability: Theory and Examples (2nd ed). Duxbury Press (p 301); [Benford refs on different pages in newer editions.].
|
|
|
|
|
Durst, RF, Huynh, C, Lott, A, Miller, SJ, Palsson, EA, Touw, W and Vreind, G (2016). The Inverse Gamma Distribution and Benford's Law. Preprint in arXiv:1609.04106 [math.PR]; last accessed October 23, 2018.
|
|
|
|
|
Durst, RF and Miller, SJ (2017). Benford's Law Beyond Independence: Tracking Benford Behavior in Copula Models. Preprint in arXiv:1801.00212 [math.PR]; last accessed October 23, 2018.
|
|
|
|
|
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.
|
|
|
|
|
Dworschak, M (1998). Weiter Weg zur Zwei. Der Spiegel 47, 16 November, pp. 228-229.
|
|
|
|
|
Dworsky, LN (2019). Probably Not: Future Prediction Using Probability and Statistical Inference. Wiley: Hoboken (Chapter 14). ISSN/ISBN:0470184019.
|
|
|
|
|
Eckhartt, GM and Ruxton, GD (2023). Investigating and preventing scientific misconduct using Benford’s Law. Research Integrity and Peer Review 8(1). DOI:10.1186/s41073-022-00126-w.
|
|
|
|
|
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.
|
|
|
|
|
Egghe, L (2011). Benford’s law is a simple consequence of Zipf’s law. ISSI Newsletter 7(3), pp. 55–56.
|
|
|
|
|
Egghe, L (2013). The functional relation between the impact factor and the uncitedness factor revisited. Journal of Informetrics 7(1), pp. 183–189. DOI:10.1016/j.joi.2012.10.007.
|
|
|
|
|
Egghe, L and Guns, R (2012). Applications of the generalized law of Benford to informetric data. Journal of the American Society for Information Science and Technology 63(8), pp. 1662-1665. ISSN/ISBN:1532-2882. DOI:10.1002/asi.22690.
|
|
|
|
|
Eirado, CRdR, da Silva, GP and Cordeiro, GM (2020). Análise da lei de benford de 2o dígito: Eleições Gerais para Presidente no Brasil e a Votação em Urnas Eletrônicas – 2002 a 2018 [Analysis of the 2nd digit benford law: General Elections for President in Brazil and Voting in Electronic Ballot Boxes – 2002. Revista Brasileira de Estatística 78(243), pp. 7-34.
POR
|
|
|
|
|
Eisenberg, P (2018). Investigating Complex Financial Crime - A Case Study Inspired by the Polly Peck PLC Fraud. Journal of Harmonized Research in Management 4(4), pp. 124-135. DOI:10.30876/JOHR.4.4.2018.124-135.
|
|
|
|
|
El Mouaaouy, F and Riepe, J (2018). Benford and the Internal Capital Market: A Useful Indicator of Managerial Engagement. German Economic Review 19, pp. 309-329. DOI:10.1111/geer.12129.
|
|
|
|
|
El Sehity, T, Hoelzl, E and Kirchler, E (2005). Price developments after a nominal shock: Benford's Law and psychological pricing after the euro introduction. International Journal of Research in Marketing 22(4), pp. 471-480. ISSN/ISBN:0167-8116. DOI:10.1016/j.ijresmar.2005.09.002.
|
|
|
|
|
Elba, F (2020). Dati Covid 2019 e legge di Benford. Preprint arXiv:2008.05884 [physics.soc-ph]; last accessed August 29, 2020.
ITA
|
|
|
|
|
Eliahou, S, Massé, B and Schneider, D (2013). On the mantissa distribution of powers of natural and prime numbers. Acta Mathematica Hungarica, 139(1), pp. 49-63. ISSN/ISBN:0236-5294. DOI:10.1007/s10474-012-0244-1.
|
|
|
|
|
Eliazar, II (2013). Benford's Law: A Poisson Perspective. Physica A 392(16) pp. 3360–3373. DOI:10.1016/j.physa.2013.03.057.
|
|
|
|
|
Eliazar, II (2017). Harmonic statistics. Annals of Physics, Volume 380, pp. 168-187. DOI:10.1016/j.aop.2017.03.016.
|
|
|
|
|
Eliazar, II (2020). First Digits. In: Power Laws. Understanding Complex Systems. Springer, Cham, pp. 153-157. DOI:10.1007/978-3-030-33235-8_14.
|
|
|
|
|
Elitaş, C (2002). Muhasebe Denetimi'nde Benford Kanunu [Benford's Law in Auditing]. Vergi Sorunları Dergisi 170, pp.142-152.
|
|
|
|
|
Ellenberg, J and Sober, E (2011). Objective Probabilities in Number Theory. Philosophia Mathematica 19 (3), pp. 308-322. ISSN/ISBN:0031-8019. DOI:10.1093/phimat/nkr022.
|
|
|
|
|
Emerging Technology from the Arxiv (2015). How Benford’s Law Reveals Suspicious Activity on Twitter. Posted on the MIT Technology Review April 21; last accessed November 17, 2020.
|
|
|
|
|
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
|
|
|
|
|
Erdoğan, M, Erkan, M, Elitaş, C and Aydemir, O (2014). Muhasebe Hilelerinin Denetiminde Benford Yasası [Benford's Law on Audit of Accounting Cheats]. Ankara: Gazi Kitabevi. ISSN/ISBN:6053441212.
TUR
|
|
|
|
|
Erfani, A, Zhang, K and Cui, Q (2021). TAB Bid Irregularity: Data-Driven Model and Its Application. Journal of Management in Engineering 37(5), p. 04021055. DOI:10.1061/(ASCE)ME.1943-5479.0000958.
|
|
|
|
|
Erfani, A, Zhang, K and Cui, Q (2021). TAB (Test of Abnormal Bid) model. Data files posted on GitHub; last accessed July 20, 2021.
|
|
|
|
|
Ergin, E and Erturan, IE (2020). Is Benford’s Law Effective in Fraud Detection for Expense Cycle? . Marmara Üniversitesi İktisadi ve İdari Bilimler Dergisi 42(2), pp. 316–326. DOI:10.14780.muiibd.854444.
|
|
|
|
|
Erkan M, Elitaş, C, Aydemir, O and Elitaş, BL (2009). Hile Tespitinde Benford Kanunu: Afyonkarahisar İli Vergi Beyanları Üzerinde Ampirik Bir Uygulama [Benford's Law in Detection of Fraud: An Empirical Application on Afyonkarahisar Province Tax Declarations]. Proceedings of 1. Ulusal Kurumsal Yönetim, Yolsuzluk, Etik ve Sosyal Sorumluluk Konferansı, Trakya Üniversitesi İktisadi ve İdari Bilimler Fakültesi, Edirne.
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
|
|
|
|
|
Esnaashari, H, Bandari, S, Hossein, M and Hossein, R (2022). Cosmetic earnings (losses) and debt management with emphasis on corporate governance role. Journal of Accounting Advances 12(2), pp. 1-26. DOI:10.22099/jaa.2020.35676.1959.
|
|
|
|
|
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.
|
|
|
|
|
Evsutin, O, Melman, A and Meshcheryakov, R (2020). Algorithm of error-free information embedding into the DCT domain of digital images based on the QIM method using adaptive masking of distortions. Signal Processing. DOI:10.1016/j.sigpro.2020.107811.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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
|
|
|
|
|
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.
|
|
|
|
|
Fallico, D (2023). Searching Applications of Benford’s Law to Investigate Beam Jitter. Presentation for Teacher Research Associate
(TRAC) Program at Fermilab.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Farkas, J and Gyürky, G (2010). The significance of using the Newcomb-Benford law as a test of nuclear half-life calculations. Acta Physica Polonica B 41(6), pp. 1213-1221. ISSN/ISBN:PL 0587-4254.
|
|
|
|
|
Farnsworth, DF, Horan, KK and Galgon, RM (2007). A guide to Benford's law. Mathematics and Computer Education 41(3), pp. 230-243. ISSN/ISBN:0730-8639.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Favaretto, F (2007). Verificacao da qualidade de dados atraves da lei de Benford. Proceedings of XXVII Brazilian National Conference on Engineering, October 2007.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Feller, W (1971). An Introduction to Probability Theory and Its Applications. 2nd ed., J. Wiley (see p 63, vol 2).
|
|
|
|
|
Fellman, J (2014). The Benford paradox. Journal of statistical and econometric methods 3(4), pp. 1-20. ISSN/ISBN:2241-0384 .
|
|
|
|
|
Fellman, J (2016). En statistisk paradox. Quintensen No.2, pp. 15-17.
SWE
|
|
|
|
|
Fellman, J (2017). Benfordparadoxen. Arkhimedes 2017(4), pp. 26-33.
SWE
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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, 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.
|
|
|
|
|
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.
|
|
|
|
|
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
|
|
|
|
|
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 .
|
|
|
|
|
Fewster, RM (2009). A Simple Explanation of Benford's Law. American Statistician 63(1), pp. 26-32. DOI:10.1198/tast.2009.0005.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
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.
|
|
|
|
|
Filipponi, P (1994). Fn and Ln cannot have the same initial digit. Pi Mu Epsilon Journal 10.1, pp. 5-6.
|
|
|
|
|
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.
|
|
|
|
|
Finch, S (2011). Newcomb-Benford Law. Online publication - last accessed July 16, 2018.
|
|
|
|
|
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
.
|
|
|
|
|
Fisher, D (2014). The Simple Mathematical Law That Financial Fraudsters Can't Beat. Forbes.com, May 30.
|
|
|
|
|
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.
|
|
|
|
|
Flam, F (2000). Math formula could help spot tax cheats. The Pittsburg Post-Gazette, 19 April.
|
|
|
|
|
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
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Florack, LMJ (1999). Visual representations embodying spacetime structure. Technical Report, University Utrecht, UU-CS-1999-07.
|
|
|
|
|
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.
|
|
|
|
|
Ford, C (2016). Earthquake data and Benford’s Law. Posted on blog "Statistics you can probably trust" .
|
|
|
|
|
Forgan, D (2013). Benford’s Law – Can you detect fraud by the first digit?. Research the HeadLines website; last accessed Dec 6, 2019.
|
|
|
|
|
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
|
|
|
|
|
Franel, J (1917). A propos des tables de logarithmes. Festschrift der Naturforschenden Gesellschaft in Zürich, Vierteljahrsschrift 62, pp. 286-295.
|
|
|
|
|
Frank, A (2006). Benford's law. Reason-and-Rhyme Blog.
|
|
|
|
|
Freeman, RB (2018). Benford's Law. Lecture 17 notes for Economics 1818 course, Harvard University.
|
|
|
|
|
Freidank, C-C and Kusch, A (2008). Das Benfordsche Gesetz als Instrument zur Aufdeckung von Unregelmäßigkeiten im Rahmen der Jahresabschlussprüfung. Wirtschaftswissenschaftliches Studium, Vol. 37, No. 2, pp. 100-102. ISSN/ISBN:0340-1650.
GER
|
|
|
|
|
Frey, B (2006). Spot Faked Data. Hack #64 in: Statistic Hacks, pp 251-262
O'Reilley Media, Sebastopol, CA. ISSN/ISBN:978-0-596-10164-0.
|
|
|
|
|
Friar, JL, Goldman, T and Pérez-Mercader, J (2016). Ubiquity of Benford’s law and emergence of the reciprocal distribution. Physics Letters A 380(22), pp. 1895–1899. ISSN/ISBN:0375-9601. DOI:10.1016/j.physleta.2016.03.045.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Friedberg, SH (1984). The Distribution of First Digits. College Mathematics Journal 15(2), pp. 120-125. ISSN/ISBN:0049-4925. DOI:10.2307/2686516.
|
|
|
|
|
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.
|
|
|
|
|
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.
|
|
|
|
|
Frost, J (2023). Benford’s Law Explained with Examples. Posted on Statistics by Jim blog; last accessed June 28, 2023.
|
|
|
|
|
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, Fang, Z, Villas-Boas, SB and Judge, G (2014). An Investigation of the Quality of Air Data in Beijing. Unpublished manuscript.
|
|
|
|
|
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.
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
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.
|
|
|
|
|
Gabhane, P, Rahangdale, P, Raipure, P, Sinde, S and Rathod, S.C. (2023). Analyzing the Effectiveness of Benford's Law in Detecting Image Forgery: A Systematic Review. International Research Journal of Modernization in Engineering Technology and Science 5(5). DOI:0.56726/IRJMETS38131.
|
|
|
|
|
Gadetska, S, Dubnitskiy, V, Lukin, V and Khodyrev, A (2019). Application of Benford’s law (first-digit law, anomalous numbers law) in financial audit. Ivan Kozhedub Kharkiv National Air Force University (Knafu)
Scientific Publications. DOI:10.30748/soi.2019.157.03.
RUS
|
|
|
|
|
Gajdosikova, D, Nagy, M and Valaskova, K (2022). Earnings Management Detection: Practical Application of Benford's Law in Business Practice. Journal of Management and Business: Research and Practice 14(1). ISSN/ISBN:1339-9381. DOI:10.54933/jmbrp-2022-14-1-1.
|
|
|
|
|
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.
|
|
|
|
|
Galati, L (2023). The political role of local government corporate ownership: An interdisciplinary outlook based on Benford’s law. In Proceedings of the International Online Conference on Corporate Governance: An Interdisciplinary Outlook, E. Karger & A. Kostyuk (Eds.), pp. 108–114. DOI:10.22495/cgaiop21.
|
|
|
|
|
Galvêas, D, Barros, F and Fuzo, CA (2021). A forensic analysis of SARS-CoV-2 cases and COVID-19 mortality misreporting in the Brazilian population. Public Health. DOI:10.1016/j.puhe.2021.05.010.
|
|
|
|
|
Gambarara, F and Nagy, O (2004). Benford Distribution in Science. ETH Zürich website; last accessed July 18, 2018.
|
|
|
|
|
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
|
|
|
|
|
Gan, R, Wang, L, Xue, L and Lin, X (2024). Exposing Stealthy Wash Trading on Automated Market Maker Exchanges. ACM Transactions on Internet Technology 24(4), pp. 1-30. DOI:10.1145/3689631.
|
|
|
|
|
Gao, J, Zhao, Y and Cui, R (2020). Research on the Applicability of Benford’s Law in Chinese Texts. Proceedings of 2nd International Conference on Artificial Intelligence and Advanced Manufacture (AIAM), Manchester, United Kingdom, pp. 13-17. DOI:10.1109/AIAM50918.2020.00009.
|
|
|
|
|
García, PMC (2019). Aplicación de la ley de Benford en la detección de fraudes. Universidad y Sociedad 11(5), pp. 421-427.
SPA
|
|
|
|
|
Garcia, PMC (2021). Aplicabilidad de la Ley de Benford a la detección de fraudes [Applicability of Benford's law to fraud detection]. Universidad y Sociedad 13(4), pp.461-467.
SPA
|
|
|
|
|
Garcia-Berthou, E and Alcaraz, C (2004). Incongruence between test statistics and P values in medical papers. BMC Medical Research Methodology 4(13). DOI:10.1186/1471-2288-4-13.
|
|
|
|
|
García-Sosa, AT (2019). Benford's law in medicinal chemistry: Implications for drug design. Future Medicinal Chemistry 11(17), pp. 2247-2253. DOI:10.4155/fmc-2019-0006.
|
|
|
|
|
García-Sosa, AT (2023). Benford’s Law and distributions for better drug design. Expert Opinion on Drug Discovery, pp. 1-7
. DOI:10.1080/17460441.2023.2277342.
|
|
|
|
|
Garlick, R, Orkin, K and Quinn, S (2019). Call Me Maybe: Experimental Evidence on Frequency and Medium Effects in Microenterprise Surveys. World Bank Economic Review, forthcoming.
|
|
|
|
|
Gauvrit, N (2013). A propos du bias d'équiprobabilité [About the 'equiprobability bias']. Recherches en Didactique des Mathématiques 33, pp. 163-182.
FRE
|
|
|
|
|
Gauvrit, N and Delahaye, J-P (2008). Pourquoi la loi de Benford n’est pas mystérieuse - A new general explanation of Benford’s law. Mathematiques et sciences humaines/ Mathematics and social sciences, 182(2), pp. 7-15. ISSN/ISBN:0987-6936. DOI:10.4000/msh.10363.
FRE
|
|
|
|
|
Gauvrit, N and Delahaye, J-P (2009). Scatter and regularity imply Benford's Law ... and more. Preprint arXiv: 0910.1359 [math.PR]; last accessed July 18, 2018
.
|
|
|
|
|
Gauvrit, N and Delahaye, J-P (2009). Loi de Benford générale (General Benford Law). Mathématiques et sciences humaines/ Mathematics and Social Sciences 186, pp. 5–15.
FRE
|
|
|
|
|
Gauvrit, N and Delahaye, J-P (2011). Scatter and Regularity Implies Benford's Law... and More. in H. Zenil (Ed.) Randomness Through Complexity, Singapore, World Scientific, 53-69. ISSN/ISBN:13978-981-4327-74-9.
|
|
|
|
|
Gauvrit, N, Houillon, J-C and Delahaye, J-P (2017). Generalized Benford’s Law as a Lie Detector. Advances in Cognitive Psychology 13(2), pp. 121-127. DOI:10.5709/acp-0212-x.
|
|
|
|
|
Gava, AM and Vitiello, L (2014). Inflation, Quarterly Balance Sheets and the Possibility of Fraud: Benford's Law and the Brazilian case. Journal of Accounting, Business & Management Vol. 21 Issue 1, pp. 43-52. ISSN/ISBN:0216-423X.
|
|
|
|
|
Gava, AM and Vitiello, LRdS (2007). Inflation, Quarterly Financial Statements and Fraud: Benford’s Law and the Brazilian Case. XXXI Encontro da ANPAD, Rio de Janeiro, Sep 22-26, 2007.
|
|
|
|
|
Geiringer, H (1948). Review of L.V. Furlan’s book. Journal of the American Statistical Association 43, pp. 325-328. DOI:10.2307/2280379.
|
|
|
|
|
Gelman, A (2006). Benford’s Law and election outcomes. Posted on Statistical Modeling, Causal Inference, and Social Science blog July 28; last accessed April 26, 2019.
|
|
|
|
|
Gelman, A (2009). Unconvincing (to me) Use of Benford’s Law to Demonstrate Election Fraud in Iran. Posted on Fivethirtyeight.com blog; last accessed April 25, 2019.
|
|
|
|
|
Gelman, A and Nolan, D (2002). Teaching Statistics: a bag of tricks. Oxford University Press. ISSN/ISBN:9780198572244.
|
|
|
|
|
Gelman, A and Nolan, D (2002). Some Statistical Sampling and Data Collection Activities. Mathematics Teacher 95(9), pp. 688-693.
|
|
|
|
|
Genest, V and Genest, C (2011). La loi de Newcomb-Benford ou la loi du premier chiffre significatif. Bulletin Association Mathématique du Québec, Vol. LI, no 2, pp. 22-39.
FRE
|
|
|
|
|
Genolini, C and Driss, T (2010). Eveiller l'intérêt pour la statistique par l'exemple. Statistique et Enseignement 1(2), pp. 49-57.
FRE
|
|
|
|
|
Gent, I and Walsh, T (2001). Benford’s Law. Preprint. APES Research Report, 2001.
|
|
|
|
|
Gepp, A, Kumar, K and Bhattacharya, S (2023). Taking the hunch out of the crunch: A framework to
improve variable selection in models to detect financial statement fraud. Accounting & Finance 2023, pp.1–20.. DOI:10.1111/acfi.13192 .
|
|
|
|
|
Geyer, A and Martì, J (2012). Applying Benford’s law to volcanology. Geology 40(4), pp. 327-330. DOI:10.1130/G32787.1
.
|
|
|
|
|
Geyer, CL and Williamson, PP (2004). Detecting Fraud in Data Sets Using Benford's Law. Communications in Statistics: Simulation and Computation 33(1), pp. 229-246. ISSN/ISBN:0361-0918. DOI:10.1081/SAC-120028442.
|
|
|
|
|
Geyer, D (2010). Detecting fraud in financial data sets. Journal of Business and Economics Research 8 (7), pp.75-83.
|
|
|
|
|
Geyer, D (2010). Cheating behavior and the Benford’s Law. Preprint.
|
|
|
|
|
Geyer, D and Drechsler, C (2014). Detecting Cosmetic Debt Management Using Benford's Law
. The Journal of Applied Business Research 30 (5), pp.1485-1492.
|
|
|
|
|
Gheorghe, GC, Manrique-Hernández, EF and Idrovo, AJ (2022). Injuries and fatalities in Colombian mining emergencies (2005-2018): a retrospective ecological study. Revista Brasileira de Medicina do Trabalho 20(4), pp. 591-598. DOI:10.47626/1679-4435-2022-799.
|
|
|
|
|
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.
|
|
|
|
|
Giggacher, J (2011). Rule of One. Science Alert website; last accessed July 19, 2018.
|
|
|
|
|
Giles, DE (2006). The Exact Asymptotic Distribution Function of Watson's UN2 for Testing Goodness-of-Fit with Circular Discrete Data. University of Victoria, Econometrics Working Paper EWP0607. ISSN/ISBN:1485-6441.
|
|
|
|
|
Giles, DE (2007). Benford's law and naturally occurring prices in certain eBay auctions. Applied Economics Letters 14(3), pp. 157-161. ISSN/ISBN:1350-4851. DOI:10.1080/13504850500425667.
|
|
|
|
|
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.
|
|
|
|
|
Gilio, A (1986). Un'applicazione del concetto di pseudodensita al problema della prima cifra significativa dei dati statistici [An application of the pseudodensity concept to the first digit problem significant for statistical data]. Rendiconti di Matematica e delle sue Applicazioni VII. Ser. 6 (1-2), pp. 215-224.
ITA
|
|
|
|
|
Gill, J (2019). What Is Benford's Law and Why Do Fraud Examiners Use It?. Blog on AcfeInsights.com, posted May 16; last accessed May 1, 2021.
|
|
|
|
|
Gini, C (1957). Sulla frequenza delle cifre iniziali dei numeri osservati. Bull. Inst. Internat. Stat., 29th session, 35(2), pp. 57-76.
ITA
|
|
|
|
|
Giuliano, R (2011). Weak convergence of sequences from fractional parts of random variables and applications. Theory of Probability and Mathematical Statistics 83, pp. 59-69. DOI:10.1090/S0094-9000-2012-00841-7 .
|
|
|
|
|
Giuliano, R and Janvresse, E (2010). A unifying probabilistic interpretation of Benford's Law. Uniform Distribution Theory 5(2), pp. 169-182. ISSN/ISBN:1336-913X.
|
|
|
|
|
Giuliano-Antonini, R (1991). On the notion of uniform distribution mod 1. Fibonacci Quarterly 29(3), pp. 230-234.
|
|
|
|
|
Giuliano-Antonini, R and Grekos, G (2005). Regular sets and conditional density: an extension of Benford's law. Colloquium Mathematicum, 103(2), pp. 173–192. DOI:10.4064/cm103-2-3.
|
|
|
|
|
Glen, S (2016). Benford’s Law (The First Digit Law): Simple Definition, Examples. From StatisticsHowTo.com: Elementary Statistics for the rest of us! Last accessed June 12, 2020.
|
|
|
|
|
Glen, S (2020). Fraudulent Covid-19 Data and Benford's Law. Blog posted on December 31; last accessed February 15, 2021.
|
|
|
|
|
Glen, S (2024). Benford’s Law (The First Digit Law): Simple Definition, Examples. statisticshowto.com; last accessed 23 February 2024.
|
|
|
|
|
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.
|
|
|
|
|
Glück, M (2007). Die Benford-Verteilung - Anwendung auf reale Daten der Marktforschung. Diploma thesis, Dresden Technical University (Fachrichtung Mathematik - Institut für Mathematische Stochastik), published as e-book by Grin Verlag. ISSN/ISBN:9783640098415.
GER
|
|
|
|
|
Glück, M (2008). Benfords Gesetz. Benford's Gesetz website, last accessed July 24, 2018.
GER
|
|
|
|
|
Glunz, H (2022). Significant Digits of Primes in Subsets. Preprint arXiv:2207.07204 [math.NT]; last accessed August 8, 2022. DOI:10.48550/ARXIV.2207.07204.
|
|
|
|
|
Glunz, H (2023). Significant Digits of Primes in Subsets. INTEGERS 23. DOI:10.5281/zenodo.8099781.
|
|
|
|
|
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.
|
|
|
|
|
Goh, C (2020). Applying visual analytics to fraud detection using Benford's law. Journal of Corporate Accounting & Finance, pp. 1-7. DOI:10.1002/jcaf.22440.
|
|
|
|
|
Golafshan, M and Mitrofanov, I (2024). Complexity function of the most significant digits of 2ND. Preprint arXiv: 2402.16210[math.DS]; last accessed May 13, 2024.
|
|
|
|
|
Golan, A and Stefanou, S (2024). Potential Value of Data and Free Access to Data. Working Paper 2024-008, Human Capital and Economic Opportunity Working Group, University of Chicago.
|
|
|
|
|
Golbeck, J (2015). Benford’s Law Applies to Online Social Networks. PLoS ONE 10(8): e0135169. DOI:10.1371/journal.pone.0135169.
|
|
|
|
|
Golbeck, J (2019). Benford’s Law can detect malicious social bots. First Monday 24(8). DOI:10.5210/fm.v24i8.10163.
|
|
|
|
|
Golbeck, J (2020). Benford’s Law Does Not Prove Fraud in the 2020 US Presidential Election. Blog posted Nov 10, 2020; last accessed December 15, 2021. NOTE: Some information in this posting has been disputed. Please see https://arxiv.org/abs/2011.13015 for details.
|
|
|
|
|
Golbeck, J (2020). Op/ed: Breaking the (Benford’s) Law? . Maryland Today, November 12.
|
|
|
|
|
Golbeck, J (2023). Benford’s Law applies to word frequency rank in English, German, French, Spanish, and Italian. PLoS ONE 18(9), pp. e0291337. DOI:10.1371/journal.pone.0291337.
|
|
|
|
|
Goldacre, B (2011). Benford’s Law: using stats to bust an entire nation for naughtiness. The Guardian, Saturday 17 September 2011. Published on Bad Science website. Last accessed Jan 4, 2018.
|
|
|
|
|
Goldacre, G (2012). Is there statistical evidence of fraud in the Russian election data?. Posted on Badscience.net; last accessed Apr 25, 2019.
|
|
|
|
|
Golden, J (2021). Local Crime Environment and Corporate Financial Misconduct Using Benford’s Law. Journal of Forensic Accounting Research. DOI:10.2308/JFAR-2021-003.
|
|
|
|
|
Goldoni, E, Savazzi, P and Gamba, P (2012). A novel source coding technique for wireless sensor networks based on Benford's law . 2012 IEEE Workshop on Environmental Energy and Structural Monitoring Systems (EESMS), 26-28 Sept. 2012, pp 32-34
. ISSN/ISBN:978-1-4673-2739-8 .
|
|
|
|
|
Gómez-Camponovo M, Moreno, J, Idrovo, ÁJ, Páez, M and Achkar, M (2016). Monitoring the Paraguayan epidemiological dengue surveillance system (2009-2011) using Benford's law. Biomédica 36, pp. 583-92. DOI:10.7705/biomedica.v36i4.2731.
|
|
|
|
|
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
|
|
|
|
|
Gonsalves, RA (2020). Benford’s Law — A Simple Explanation. Posted on towardsdatascience.com blog October 1; last accessed October 10, 2020.
|
|
|
|
|
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.
|
|
|
|
|
González, RG, González, RN and Valenzuela, RIG (2023). La Supremacía del Número Uno. EPISTEMUS 17(34). DOI:10.36790/epistemus.v17i34.275.
SPA
|
|
|
|
|
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.
|
|
|
|
|
Good, IJ (1965). Letter to the Editor. The American Statistician 19(3), p. 43.
|
|
|
|
|
Good, IJ (1986). Some statistical applications of Poisson’s work. Statistical Science 1(2), pp. 157-170.
|
|
|
|
|
Goodman, RH, Feldstein, A and Bustoz, J (1985). Relative Error in Floating-Point Multiplication. Computing 35, pp. 127-139. ISSN/ISBN:1436-5057. DOI:10.1007/BF02260500.
|
|
|
|
|
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.
|
|
|
|
|
Goodman, WM (2023). Applying and Testing Benford's Law Are Not the Same. Spanish Journal of Statistics 5(1), pp. 43-53. DOI:10.37830/SJS.2023.1.03.
|
|
|
|
|
Gorenc, M (2017). Detection of theft and frauds from financial statements. Poslovna forenzika : zbornik 1. konference, september 2017 - Letn. 10, št. 3/4 (sep. 2017), str. 256-278.
SLV
|
|
|
|
|
Gorenc, M (2018). Benford's law as a useful tool for auditors and forenzic accountants. Poslovodno računovodstvo - Letn. 11, št. 1 (apr. 2018), str. 5-21. ISSN/ISBN:ISSN 1855-4032.
SLV
|
|
|
|