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Statistical models and the Benford hypothesis: a unified framework

Author

Listed:
  • Lucio Barabesi

    (University of Siena)

  • Andrea Cerioli

    (University of Parma)

  • Marco Marzio

    (“G. D’Annunzio” University)

Abstract

The Benford hypothesis is the statement that a random sample is made of realizations of an absolutely continuous random variable distributed according to Benford’s law. Its potential interest spans over many domains such as detection of financial frauds, verification of electoral processes and investigation of scientific measurements. Our aim is to provide a principled framework for the statistical evaluation of this statement. First, we study the probabilistic structure of many classical univariate models when they are framed in the space of the significand and we measure the closeness of each model to the Benford hypothesis. We then obtain two asymptotically equivalent and powerful tests. We show that the proposed test statistics are invariant under scale transformation of the data, a crucial requirement when compliance to the Benford hypothesis is used to corroborate scientific theories. The empirical advantage of the proposed tests is shown through an extensive simulation study. Applications to astrophysical and hydrological data also motivate the methodology.

Suggested Citation

  • Lucio Barabesi & Andrea Cerioli & Marco Marzio, 2023. "Statistical models and the Benford hypothesis: a unified framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1479-1507, December.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:4:d:10.1007_s11749-023-00881-y
    DOI: 10.1007/s11749-023-00881-y
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    References listed on IDEAS

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    9. Lucio Barabesi & Andrea Cerasa & Andrea Cerioli & Domenico Perrotta, 2018. "Goodness-of-Fit Testing for the Newcomb-Benford Law With Application to the Detection of Customs Fraud," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 346-358, April.
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    Cited by:

    1. Manuel Cano-Rodriguez, 2025. "How much is too much? Measuring divergence from Benford's Law with the Equivalent Contamination Proportion (ECP)," Papers 2506.09915, arXiv.org, revised Jun 2025.

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