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Some New Tests of Conformity with Benford’s Laws

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  • Roy Cerqueti

    (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

  • C Lupi

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.
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Suggested Citation

  • Roy Cerqueti & C Lupi, 2021. "Some New Tests of Conformity with Benford’s Laws," Post-Print hal-03789183, HAL.
    • Handle: RePEc:hal:journl:hal-03789183
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    References listed on IDEAS

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    1. Ausloos, Marcel & Castellano, Rosella & Cerqueti, Roy, 2016. "Regularities and discrepancies of credit default swaps: a data science approach through Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 8-17.
    2. De Ceuster, Marc J. K. & Dhaene, Geert & Schatteman, Tom, 1998. "On the hypothesis of psychological barriers in stock markets and Benford's Law," Journal of Empirical Finance, Elsevier, vol. 5(3), pages 263-279, September.
    3. Shi, Jing & Ausloos, Marcel & Zhu, Tingting, 2018. "Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 878-888.
    4. Mir, T.A., 2012. "The law of the leading digits and the world religions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 792-798.
    5. Clippe, Paulette & Ausloos, Marcel, 2012. "Benford’s law and Theil transform of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6556-6567.
    6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    7. Uwe Hassler & Mehdi Hosseinkouchack, 2019. "Testing the Newcomb-Benford Law: experimental evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 26(21), pages 1762-1769, December.
    8. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.
    9. Riccioni, Jessica & Cerqueti, Roy, 2018. "Regular paths in financial markets: Investigating the Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 186-194.
    10. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. Nye John & Moul Charles, 2007. "The Political Economy of Numbers: On the Application of Benford's Law to International Macroeconomic Statistics," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-14, July.
    12. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    13. Mir, T.A., 2014. "The Benford law behavior of the religious activity data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 1-9.
    14. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    15. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
    16. C. W. J. Granger, 1998. "Extracting information from mega‐panels and high‐frequency data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(3), pages 258-272, November.
    17. Zhang, Lingyun, 2007. "Sample Mean and Sample Variance: Their Covariance and Their (In)Dependence," The American Statistician, American Statistical Association, vol. 61, pages 159-160, May.
    18. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    19. J. A. Wellner & R. T. Smythe, 2002. "Computing the covariance of two Brownian area integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 101-109, February.
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    Cited by:

    1. 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.
    2. 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.
    3. Roeland de Kok & Giulia Rotundo, 2022. "Benford Networks," Stats, MDPI, vol. 5(4), pages 1-14, September.

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