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Some New Tests of Conformity with Benford’s Law

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  • Roy Cerqueti

    (Department of Social and Economic Sciences, Sapienza University of Rome, P.le Aldo Moro 5, I-00185 Rome, Italy
    London South Bank University Business School, 103 Borough Road, London SE1 0AA, UK.)

  • Claudio Lupi

    (Department of Economics, University of Molise, Via De Sanctis snc, I-86100 Campobasso, Italy)

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 Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:44-761:d:629818
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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. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Granger, Clive W.J., 1998. "Extracting Information from Mega-Panels and High-Frequency Data," University of California at San Diego, Economics Working Paper Series qt17t2d9n6, Department of Economics, UC San Diego.
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    Cited by:

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

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