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Waaldijk, F (2005). On the foundations of constructive mathematics - Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10(3), 249-324. DOI:10.1007/s10699-004-3065-z. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wagon, S (2009). Benford's Law and Data Spread. Wolfram Online Demonstrations Projects. View Complete Reference Online information Works that this work references Works that reference this work
Walker, S (2021). Machine Learning and Corporate Fraud Detection. PhD Dissertation, UC Berkeley. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Walker, S (2022). Compared to What? Does Benford’s Law Really Detect Corporate Fraud?. Econ Journal Watch 19(1), pp. 30-46. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wallace, WA (2002). Assessing the quality of data used for benchmarking and decision-making. The Journal of Government Financial Management 51(3), pp. 16-22. View Complete Reference Online information Works that this work references Works that reference this work
Wallis, WA and Roberts, HV (1956). First digits of statistical tables. Example 331, pp 331-332 in: Statistics: A New Approach, The Free Press of Glencoe, Illinois, USA. View Complete Reference Online information No Bibliography works referenced by this work. No Bibliography works reference this work
Walthoe, J (2005). En Busca del Numero Uno. Matematicalia 1(2) . SPA View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Walthoe, J, Hunt, R and Pearson, M (1999). Looking out for number one. +plus magazine, September 1999. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Wang, D, Chen, F, Mao, J, Liu, N and Rong, F (2022). Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries . Energy Economics, p. 106310. DOI:10.1016/j.eneco.2022.106310. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wang, H, Liu, T, Zhang, Y, Wu, Y, Sun, Y, Dong, J and Huang, W (2023). Last Digit Tendency: Lucky Numbers and Psychological Rounding in Mobile Transactions. Fundamental Research. DOI:10.1016/j.fmre.2023.11.011. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wang, J, Cha, B-H, Cho, S-H and Kuo, C-CJ (2009). Understanding Benford’s Law and its Vulnerability in Image Forensics. IEEE International Conference on Multimedia and Expo, ICME 2009, pp. 1568 - 1571. ISSN/ISBN:1945-7871. DOI:10.1109/ICME.2009.5202811. View Complete Reference Online information Works that this work references Works that reference this work
Wang, J and He, D (2022). Financial Fraud Risk Governance Effect of Actively Shorting Chinese Concept Stocks——A Case Study Based on Benford's Law Compliance Test. The Chinese Certified Public Accountant pp. 42-46. CHI View Complete Reference No online information available No Bibliography works referenced by this work. Works that reference this work
Wang, L and Ma, B-Q (2023). A concise proof of Benford’s law. Fundamental Research . DOI:10.1016/j.fmre.2023.01.002. View Complete Reference Online information Works that this work references Works that reference this work
Wang, Q, Zhang, R and Qing, K (2015). Passive Detection of Tampered JPEG Image Based on First Digit Statistics. Proceedings of 2015 International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP), Adelaide, SA, Australia, pp. 401-404 . DOI:10.1109/IIH-MSP.2015.42. View Complete Reference Online information Works that this work references Works that reference this work
Wang, S (2009). Statistical evidence for Iranian election fraud?. Posted on election.princeton.edu blog June 18; last accessed August 19, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Wang, Y and Pedlow, S (2005). Detecting Falsified Cases in SCF 2004 Using Benford’s Law. Proceedings of the American Statistical Association, Survey Research Methods Section, pp. 3562-3657. View Complete Reference Online information Works that this work references Works that reference this work
Warshavsky, MS (2010). Applying Benford's Law in financial forensic investigations. National Litigation Consultants Review 10(2), pp. 1-4. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Wase, V (2020). Benford’s law in the Beale ciphers. Cryptologia 45(3), pp. 282-286. DOI:10.1080/01611194.2020.1821409. View Complete Reference Online information Works that this work references Works that reference this work
Washington, LC (1981). Benford’s law for Fibonacci and Lucas numbers. Fibonacci Quarterly 19, 175-177. View Complete Reference No online information available Works that this work references Works that reference this work
Watrin, C and Struffert, R (2006). Benford’s Law und Chi-Quadrat-Test – Chancen und Risiken des Einsatzes bei steuerlichen Prüfungen . Der Betrieb, Vol. 59, No. 33, pp. 1748-1750. GER View Complete Reference Online information Works that this work references Works that reference this work
Watrin, C, Struffert, R and Ullmann, R (2008). Benford’s Law: an instrument for selecting tax audit targets?. Review of Managerial Science 2(3), 219-237. DOI:10.1007/s11846-008-0019-9. View Complete Reference Online information Works that this work references Works that reference this work
Weaver, W (1963). The distribution of first significant digits. pp 270-277 in: Lady Luck: The Theory of Probability, Doubleday Anchor Series, New York. Republished by Dover, 1982. ISSN/ISBN:978-0486243429. View Complete Reference Online information Works that this work references Works that reference this work
Webb, C (2019). Benford’s Law in Python. Blog posted on CodeRome June 7, 2019; last accessed January 12, 2022. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Webb, W (1975). Distribution of the first digits of Fibonacci numbers. Fibonacci Quarterly 13, pp. 334-336. View Complete Reference No online information available Works that this work references Works that reference this work
Wei, A and Vellwock, AE (2020). Is COVID-19 data reliable? A statistical analysis with Benford's Law. Preprint, posted September. DOI:10.13140/RG.2.2.31321.75365/1. View Complete Reference Online information Works that this work references Works that reference this work
Wei, L, Sundararajan, A, Sarwat, AI, Biswas, S and Ibrahim, E (2017). A distributed intelligent framework for electricity theft detection using benford's law and stackelberg game. IEEE Proceedings of 2017 Resilience Week (RWS), pp. 5-11. DOI:10.1109/RWEEK.2017.8088640. View Complete Reference Online information Works that this work references Works that reference this work
Weissmann, SM, Hollingsworth, SR and Baird, JC (1975). Psychophysical studies of numbers: III. Methodological applications. Psychological Research 38(1), 97-115. DOI:10.1007/BF00308941. View Complete Reference Online information Works that this work references Works that reference this work
Weisstein, EW (2003). Benford's Law. pp 181-182 in: CRC concise encyclopedia of mathematics, Chapman & Hall. View Complete Reference Online information Works that this work references Works that reference this work
Weisstein, EW (2009). Benford's Law. MathWorld (A Wolfram Web Resource). View Complete Reference Online information Works that this work references Works that reference this work
Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2005). The Partial Volume Effect in PET/SPECT and Benford's Law. Nuclear Science Symposium Conference Record, 2005 IEEE, Vol. 3, pp. 1804--1808. ISSN/ISBN:0-7803-9221-3. DOI:10.1109/NSSMIC.2005.1596671. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2007). Quantifying the Partial Volume Effect in PET Using Benford's Law. IEEE Transactions on Nuclear Science 54(5), pp. 1616-1625 Part 1. ISSN/ISBN:0018-9499. DOI:10.1109/TNS.2007.903182. View Complete Reference Online information Works that this work references Works that reference this work
Weng, C-K (2012). An Application of Benford's Law in Trading Volume and Accounting Numbers: A Comparison between the U.S. and Taiwan Stock Markets. PhD Thesis, Golden Gate University. ISSN/ISBN:9781267865069. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Weyl, H (1916). Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen 77, 313-352. ISSN/ISBN:0025-5831. DOI:10.1007/BF01475864. GER View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
White, GL (2023). Teaching Case: Election Security and Technology Education. Journal of The Colloquium for Information Systems Security Education 10(1). DOI:10.53735/cisse.v10i1.171. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Whitney, RE (1972). Initial digits for the sequence of primes. American Mathematical Monthly 79(2), pp. 150-152. ISSN/ISBN:0002-9890. View Complete Reference Online information Works that this work references Works that reference this work
Whittaker, JV (1983). On scale-invariant distributions. SIAM Journal on Applied Mathematics 43(2), pp. 257-267. DOI:10.1137/0143017. View Complete Reference Online information Works that this work references Works that reference this work
Whyman, G (2021). Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies. Applied Mathematics 12, pp. 578-586. ISSN/ISBN:2152-7385. DOI:10.4236/am.2021.127041. View Complete Reference Online information Works that this work references Works that reference this work
Whyman, G, Ohtori, N, Shulzinger, E and Bormashenko, E (2016). Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?. Physica A: Statistical Mechanics and its Applications Volume 461, pp. 595-601. DOI:10.1016/j.physa.2016.06.054. View Complete Reference Online information Works that this work references Works that reference this work
Whyman, G, Shulzinger, E and Bormashenko, E (2016). Intuitive considerations clarifying the origin and applicability of the Benford law. Results in Physics Volume 6, pp. 3-6 . DOI:10.1016/j.rinp.2015.11.010. View Complete Reference Online information Works that this work references Works that reference this work
Wikipedia (2018). Benfordsches Gesetz. Posted on German Wikipedia website; last accessed April 30, 2019. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wikipedia (2021). Ley de Benford. Posted on Spanish Wikipedia website. SPA View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Wilkinson, L (2006). Revising the Pareto chart. American Statistician 60(4), 332-334. ISSN/ISBN:0003-1305. DOI:10.1198/000313006X152243. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Williamson, D (2004). Vital Statistics. Accountancy Magazine Vol. 133 Issue 1327, pp. 108-110 . ISSN/ISBN:00014664. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Williamson, J (2000). Random probability functions. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wilms, RJG and Brands, JJAM (1994). On the asymptotically uniform distribution modulo 1 of extreme order statistics. Statistica Neerlandica 48(1), 63-70. DOI:10.1111/j.1467-9574.1994.tb01431.x. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wilson, L (2023). Benford’s Law and its Applications to Accounting. Mathematics Student Projects, Taylor University. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Windsor, DA (2017). Benford’s Law Has its Origin in the Partition of Integers. Posted on bullthistleblogger.blogspot.com blog Sep 4; last accessed March 16, 2021. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Winker, P (2016). Assuring the quality of survey data: Incentives, detection and documentation of deviant behavior. Statistical Journal of the IAOS 32 (3), pp. 295–303. DOI:10.3233/SJI-161012. View Complete Reference Online information Works that this work references Works that reference this work
Winter, C, Schneider, M and Yannikos, Y (2011). Detecting Fraud Using Modified Benford Analysis. Advances in Digital Forensics VII, 7th IFIP WG 11.9 International Conference on Digital Forensics, Orlando, FL, USA, January 31 – February 2, 2011, Revised Selected Papers. Gilbert Peterson and Sujeet Shenoi (Editors). IFIP Advances in Information and Co. ISSN/ISBN:1868-4238. DOI:10.1007/978-3-642-24212-0_10. View Complete Reference Online information Works that this work references Works that reference this work
Winter, C, Schneider, M and Yannikos, Y (2012). Model-Based Digit Analysis for Fraud Detection overcomes Limitations of Benford Analysis. Availability, Reliability and Security (ARES 2012), Seventh International Conference, August 20–24, 2012, Prague, Czech Republic. IEEE CS volume E4775, pages 255–261. IEEE Computer Society. ISSN/ISBN:978-1-4673-2244-7 . DOI:10.1109/ARES.2012.37. View Complete Reference Online information Works that this work references Works that reference this work
Wiriyakraikul, T, Sumetkijakan,S and Santiwipanont,T (2017). Benford’s law for chains of truncated distribution. In: Proceedings of the 22nd Annual Meeting in Mathematics (AMM 2017), Chiang Mai University, Chiang Mai, 2–4 June. View Complete Reference Online information Works that this work references Works that reference this work
Wiryadinata, D, Sugiharto, A and Tarno (2023). The Use of Machine Learning to Detect Financial Transaction Fraud: Multiple Benford Law Model for Auditors. Journal of Information Systems Engineering & Business Intelligence 9(2), pp. 239-252. DOI:10.20473/jisebi.9.2.239-252. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wiseman, S, Cox, AL and Brumby, DB (2013). Designing Devices With the Task in Mind: Which Numbers Are Really Used in Hospitals?. Human Factors 55(1), pp. 61–74. DOI:10.1177/0018720812471988. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wist, H (2019). Assessing The Conformity Of Cryptocurrency Market Data With Benford’s Law. Masters thesis, University of Vaasa, Faculty of Business Studies, Department of Accounting and Finance . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wlodarski, J (1971). Fibonacci and Lucas Numbers tend to obey Benford’s law. Fibonacci Quarterly 9, 87-88. View Complete Reference No online information available Works that this work references Works that reference this work
Wojcik, MR (2013). How fast increasing powers of a continuous random variable converge to Benford’s law. Statistics and Probability Letters 83, pp. 2688–2692. ISSN/ISBN:0167-7152. DOI:10.1016/j.spl.2013.09.003. View Complete Reference Online information Works that this work references Works that reference this work
Wojcik, MR (2013). Notes on scale-invariance and base-invariance for Benford's Law. arXiv:1307.3620 [math.PR]. View Complete Reference Online information Works that this work references Works that reference this work
Wojcik, MR (2014). A characterization of Benford’s law through generalized scale-invariance. Mathematical Social Sciences, Volume 71, September 2014, pp. 1–5. DOI:10.1016/j.mathsocsci.2014.03.006. View Complete Reference Online information Works that this work references Works that reference this work
Wolff, H and Auffhammer, M (2006). Endogenous Choice OF Development Indicators: Are Development Countries Misclassified? Evidence from the HDI. Agricultural and Resource Economics, UC Berkeley, USA. View Complete Reference No online information available Works that this work references Works that reference this work
Wolowik, P (2005). Prawo Benforda – testowanie i wery kacja poprawności danych pomiarowych [Benford's Law - testing and verification of the correctness of measurement data] . Pr- zegląd Telekomunikacyjny – Wiadomości Telekomunikacyjne” 11, pp. 414-418. POL View Complete Reference Online information Works that this work references Works that reference this work
Wong, JT (1969). On the generalization of the distribution of the significant digits under computation. Ph.D. thesis, Department of Mathematics, Oregon State University, Corvallis, OR, USA. View Complete Reference Online information No Bibliography works referenced by this work. No Bibliography works reference this work
Wong, SCY (2010). Testing Benford’s Law with the first two significant digits. Master's Thesis, University of Victoria, Canada. View Complete Reference Online information Works that this work references Works that reference this work
Wong, WK, Juwono, FH, Loh, WN and Ngu, IY (2020). Newcomb-Benford Law Analysis on COVID-19 Daily Infection Cases and Deaths in Indonesia and Malaysia. Research Square preprint. DOI:10.21203/rs.3.rs-131072/v1. View Complete Reference Online information Works that this work references Works that reference this work
Work, KD and Nam, MH (2019). A Study of the Debt Ratio Management Behavior of Local Public Enterprises Using Benford’s Law. Korean Governmental Accounting Review 17(1) pp.99-132. KOR View Complete Reference Online information No Bibliography works referenced by this work. No Bibliography works reference this work
Wouk, A (1961). On digit distributions of random variables. J. Soc. Indust. Appl. Math. 9(4), 597-603. ISSN/ISBN:0368-4245. DOI:10.1137/0109050. View Complete Reference Online information Works that this work references Works that reference this work
Wroński, K (2012). Zastosowanie Rozkładu Benforda do Analizy Plików Dźwiękowych [Benford Distribution Application to the Analysis of Sound File] . Bachelor Thesis, Krakow Academy, Faculty of Economics and Management. POL View Complete Reference Online information Works that this work references No Bibliography works reference this work
Wu, T (2018). Image-Guided Rendering with an Evolutionary Algorithm Based on Cloud Model. Computational Intelligence and Neuroscience Volume 2018, Article ID 4518265. DOI:10.1155/2018/4518265. View Complete Reference Online information Works that this work references No Bibliography works reference this work

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