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Benford's Law, families of distributions and a test basis

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  • Morrow, John

Abstract

Benford's Law is used to test for data irregularities. While novel, there are two weaknesses in the current methodology. First, test values used in practice are too conservative and the test values of this paper are more powerful and hold for fairly small samples. Second, testing requires Benford's Law to hold, which it often does not. I present a simple method to transform distributions to satisfy the Law with arbitrary precision and induce scale invariance, freeing tests from the choice of units. I additionally derive a rate of convergence to Benford's Law. Finally, the results are applied to common distributions.

Suggested Citation

  • Morrow, John, 2014. "Benford's Law, families of distributions and a test basis," LSE Research Online Documents on Economics 60364, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:60364
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    File URL: http://eprints.lse.ac.uk/60364/
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    References listed on IDEAS

    as
    1. Tam Cho, Wendy K. & Gaines, Brian J., 2007. "Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance," The American Statistician, American Statistical Association, vol. 61, pages 218-223, August.
    2. Grendar, Marian & Judge, George & Schechter, Laura, 2007. "An empirical non-parametric likelihood family of data-based Benford-like distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 429-438.
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    Cited by:

    1. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, August.
    2. Ronelle Burger & Canh Thien Dang & Trudy Owens, 2017. "Better performing NGOs do report more accurately: Evidence from investigating Ugandan NGO financial accounts," Discussion Papers 2017-10, University of Nottingham, CREDIT.
    3. Holz, Carsten A., 2014. "The quality of China's GDP statistics," China Economic Review, Elsevier, vol. 30(C), pages 309-338.
    4. Hürlimann, Werner, 2015. "On the uniform random upper bound family of first significant digit distributions," Journal of Informetrics, Elsevier, vol. 9(2), pages 349-358.
    5. Thomas Stoerk, 2015. "Statistical corruption in Beijing’s air quality data has likely ended in 2012," GRI Working Papers 194, Grantham Research Institute on Climate Change and the Environment.
    6. Kalaichelvan, Mohandass & Lim Kai Jie, Shawn, 2012. "A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law," MPRA Paper 40960, University Library of Munich, Germany.
    7. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).

    More about this item

    Keywords

    Benford's Law; data quality; fraud detection;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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