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Data validity and statistical conformity with Benford’s Law

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  • Cerqueti, Roy
  • Maggi, Mario

Abstract

Benford’s Law is a statistical regularity of a large number of datasets; assessing the compliance of a large dataset with the Benford’s Law is a theme of remarkable relevance, mainly for its practical consequences. Such a task can be faced by introducing a statistical distance concept between the empirical distribution of the data and the random variable associated with Benford’s Law. This paper deals with the problem of measuring the compliance of a random variable – which can be seen as describing the empirical distribution of a collection of data – with the Benford’s Law. It proposes a statistical methodology for detecting the critical values related to conformity/nonconformity with Benford’s Law in some well-established cases of statistical distance. The followed approach is grounded on the proper selection of a family of parametric random variables – the lognormal distribution, in our case – and of a reference statistical distance concept – mean absolute deviation. A discussion of the obtained results is carried out on the ground of the existing literature. Moreover, some open problems are also presented.

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  • Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100093x
    DOI: 10.1016/j.chaos.2021.110740
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    References listed on IDEAS

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    17. 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.
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    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.
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    Cited by:

    1. Roeland de Kok & Giulia Rotundo, 2022. "Benford Networks," Stats, MDPI, vol. 5(4), pages 1-14, September.
    2. Arezzo, Maria Felice & Cerqueti, Roy, 2023. "A Benford’s Law view of inspections’ reasonability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    3. Adriano Silva & Sergio Floquet & Ricardo Lima, 2023. "Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions," Stats, MDPI, vol. 6(4), pages 1-19, October.
    4. Alex Ely Kossovsky, 2021. "On the Mistaken Use of the Chi-Square Test in Benford’s Law," Stats, MDPI, vol. 4(2), pages 1-35, May.
    5. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    6. Pedro Fernandes & Séamus Ó Ciardhuáin & Mário Antunes, 2024. "Unveiling Malicious Network Flows Using Benford’s Law," Mathematics, MDPI, vol. 12(15), pages 1-37, July.

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