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Several common probability distributions obey Benford’s law

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  • Fang, Guojun
  • Chen, Qihong

Abstract

Benford’s law states that the frequency of lower first significant digits(FSD) is higher than that of upper FSD in many naturally produced numbers. The law can be applied to many various fields, so it is important to know which common probability distributions obey Benford’s law. We revisit whether the Log-normal probability distribution obeys the law by using the method of Fourier analysis and numerical simulation. Moreover, we use simulation method to judge whether the Weibull distribution and the Inverse Gamma distribution are close to Benford’s law under some conditions. Our work give some reasons to support why Benford’s law is universal in real world.

Suggested Citation

  • Fang, Guojun & Chen, Qihong, 2020. "Several common probability distributions obey Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317649
    DOI: 10.1016/j.physa.2019.123129
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    References listed on IDEAS

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    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. Mebane, Walter R., 2011. "Comment on “Benford's Law and the Detection of Election Fraud”," Political Analysis, Cambridge University Press, vol. 19(3), pages 269-272, July.
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    Cited by:

    1. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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