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Some New Tests of Conformity with Benford’s Laws

Author

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  • Roy Cerqueti

    (Sapienza University of Rome - Department of Informatics and System Sciences - UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome])

  • Claudio Lupi

    (UNIMOL - Università degli Studi del Molise = University of Molise)

Abstract

This paper presents new perspectives and methodological instruments for verifying the validity of Benford's law for a large given dataset. To this aim, we first propose new general tests for checking the statistical conformity of a given dataset with a generic target distribution; we also provide the explicit representation of the asymptotic distributions of the relevant test statistics. Then, we discuss the applicability of such novel devices to the case of Benford's law. We implement extensive Monte Carlo simulations to investigate the size and the power of the introduced tests. Finally, we discuss the challenging theme of interpreting, in a statistically reliable way, the conformity between two distributions in the presence of a large number of observations.

Suggested Citation

  • Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Laws," Post-Print hal-03789183, HAL.
    • Handle: RePEc:hal:journl:hal-03789183
    DOI: 10.3390/stats4030044
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    Cited by:

    1. Wolfgang Kössler & Hans-J. Lenz & Xing D. Wang, 2024. "Some new invariant sum tests and MAD tests for the assessment of Benford’s law," Computational Statistics, Springer, vol. 39(7), pages 3779-3800, December.
    2. 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.
    3. Roy Cerqueti & Claudio Lupi, 2023. "Severe testing of Benford’s law," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 677-694, June.
    4. Marcel Ausloos & Probowo Erawan Sastroredjo & Polina Khrennikova, 2025. "Note on pre-taxation reported data by UK FTSE-listed companies. A search for Benford's laws compatibility," Papers 2509.09415, arXiv.org.
    5. Lasse Pröger & Paul Griesberger & Klaus Hackländer & Norbert Brunner & Manfred Kühleitner, 2021. "Benford’s Law for Telemetry Data of Wildlife," Stats, MDPI, vol. 4(4), pages 1-7, November.
    6. Marcel Ausloos & Probowo Erawan Sastroredjo & Polina Khrennikova, 2025. "Note on Pre-Taxation Data Reported by UK FTSE-Listed Companies: Search for Compatibility with Benford’s Laws," Stats, MDPI, vol. 8(1), pages 1-17, February.
    7. Roeland de Kok & Giulia Rotundo, 2022. "Benford Networks," Stats, MDPI, vol. 5(4), pages 1-14, September.

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