413
Views
5
CrossRef citations to date
0
Altmetric
Articles

Testing the Newcomb-Benford Law: experimental evidence

&

References

  • Anderson, T. W., and D. A. Darling. 1952. “Asymptotic Theory of Certain “Goodness of Fit” Criteria Based on Stochastic Processes.” The Annals of Mathematical Statistics 23: 193–212. doi:10.1214/aoms/1177729437.
  • Benford, F. 1938. “The Law of Anomalous Numbers.” Proceedings of the American Philosophical Society 78: 551–572.
  • Berger, A., and T. P. Hill. 2011a. “A Basic Theory of Benford’s Law.” Probability Surveys 8: 1–126. doi:10.1214/11-PS175.
  • Berger, A., and T. P. Hill. 2011b. “Benford’s Law Strikes Back: No Simple Explanations in Sight for Mathematical Gem.” Mathematical Intelligencer 33: 85–91. doi:10.1007/s00283-010-9182-3.
  • Berger, A., and T. P. Hill. 2015. “A Short Introduction to the Mathematical Theory of Benford’s Law.” In Benford’s Law: Theory and Applications, edited by S. J. Miller, 23–67, Princeton University Press: Princeton.
  • Berger, A., T. P. Hill, and E. Rogers (2009). “Benford Online Bibliography.” accessed 21 January 2019. http://www.benfordonline.net
  • Carslaw, C. A. P. N. 1988. “Anomalies in Income Numbers: Evidence of Goal Oriented Behavior.” The Accounting Review 63: 321–327.
  • Diekmann, A. 2007. “Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data.” Journal of Applied Statistics 34: 321–329. doi:10.1080/02664760601004940.
  • Diekmann, A., and B. Jann. 2010. “Benford’s Law and Fraud Detection: Facts and Legends.” German Economic Review 11: 397–401. doi:10.1111/(ISSN)1468-0475.
  • Durtschi, C., W. Hillison, and C. Pacini. 2004. “The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data.” Journal of Forensic Accounting 5: 17–34.
  • Fewster, R. M. 2009. “A Simple Explanation of Benford’s Law.” The American Statistician 63: 26–32. doi:10.1198/tast.2009.0005.
  • Giles, D. E. 2007. “Benford’s Law and Naturally Occurring Prices in Certain eBay Auctions.” Applied Economics Letters 14: 157–161. doi:10.1080/13504850500425667.
  • Günnel, S., and K.-H. Tödter. 2009. “Does Benford’s Law Hold in Economic Research and Forecasting?” Empirica 36: 273–292. doi:10.1007/s10663-008-9084-1.
  • Hassler, U. 2016. Stochastic Processes and Calculus: An Elementary Introduction with Applications. Springer: Heidelberg.
  • Hassler, U., and M. Hosseinkouchack. 2018. “Ratio Tests under Limiting Normality.” Econometric Reviews 1–21. doi:10.1080/07474938.2018.142729.
  • Hill, T. P. 1995. “A Statistical Derivation of the Significant-Digit Law.” Statistical Science 10: 354–363. doi:10.1214/ss/1177009869.
  • Judge, G., and L. Schechter. 2009. “Detecting Problems in Survey Data Using Benford’s Law.” Journal of Human Resources 44: 1–24. doi:10.1353/jhr.2009.0010.
  • Kuiper, N. H. 1960. “Tests Concerning Random Points on a Circle.” Indagationes Mathematicae (Proceedings) 63: 38–47. doi:10.1016/S1385-7258(60)50006-0.
  • Ley, E. 1996. “On the Peculiar Distribution of the U.S. Stock Indexes’ Digits.” The American Statistician 50: 311–313.
  • Miller, S. J. 2015a. Benford’s Law: Theory and Applications. Princeton University Press:Princeton.
  • Miller, S. J. 2015b. “Fourier Analysis and Benford’s Law.” In Benford’s Law: Theory and Applications, edited by S. J. Miller, 68–105, Princeton University Press:Princeton.
  • Miller, S. J. 2015c. “A Quick Introduction to Benford’s Law.” In Benford’s Law: Theory and Applications, edited by S. J. Miller, 3–22, Princeton University Press: Princeton.
  • Newcomb, S. 1881. “Note on the Frequency of Use of the Different Digits in Natural Numbers.” American Journal of Mathematics 4: 39–40. doi:10.2307/2369148.
  • Nigrini, M. J. 1996. “Taxpayers Compliance Application of Benford’s Law.” Journal of the American Taxation Association 18: 72–91.
  • Nigrini, M. J., and L. J. Mittermaier. 1997. “The Use of Benford’s Law as an Aid in Analytical Procedures.” Auditing: A Journal of Practice andTheory 16: 52–67.
  • Raimi, R. A. 1976. “The First Digit Problem.” The American Mathematical Monthly 83: 521–538. doi:10.1080/00029890.1976.11994162.
  • Rauch, B., M. Göttsche, G. Brähler, and S. Engel. 2011. “Fact and Fiction in EU-governmental Economic Data.” German Economic Review 12: 243–255. doi:10.1111/geer.2011.12.issue-3.
  • Rodriguez, R. J. 2004a. “First Significant Digit Patterns from Mixtures of Uniform Distributions.” The American Statistician 58: 64–71. doi:10.1198/0003130042782.
  • Rodriguez, R. J. 2004b. “Reducing False Alarms in the Detection of Human Influence on Data.” Journal of Accounting, Auditing & Finance 19: 141–158. doi:10.1177/0148558X0401900202.
  • Schündeln, M. 2018. “Multiple Visits and Data Quality in Household Surveys.” Oxford Bulletin of Economics and Statistics 80: 380–405. doi:10.1111/obes.2018.80.issue-2.
  • Stephens, M. A. 1970. “Use of the Kolmogorov-Smirnov, Cramér-Von Mises and Related Statistics without Extensive Tables.” Journal of the Royal Statistical Society. Series B (Methodological) 32: 115–122. doi:10.1111/rssb.1970.32.issue-1.
  • Tam Cho, W. K., and B. J. Gaines. 2007. “Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance.” The American Statistician 61: 218–223. doi:10.1198/000313007X223496.
  • Thomas, J. K. 1989. “Unusual Patterns in Reported Earnings.” The Accounting Review 64: 773–787.
  • Tödter, K.-H. 2009. “Benford’s Law as an Indicator of Fraud in Economics.” German Economic Review 10: 339–351. doi:10.1111/geer.2009.10.issue-3.
  • Tödter, K.-H. 2015. “Benford’s Law and Fraud in Economic Research.” In Benford’s Law: Theory and Applications, edited by S. J. Miller, 244–256, Princeton University Press: Princeton.
  • Varian, H. R. 1970. “Benford’s Law.” The American Statistician 26, 65–66.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.