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Article

Some New Tests of Conformity with Benford’s Law

by 1,† and 2,*
1
Department of Social and Economic Sciences, Sapienza University of Rome, P.le Aldo Moro 5, I-00185 Rome, Italy
2
Department of Economics, University of Molise, Via De Sanctis snc, I-86100 Campobasso, Italy
*
Author to whom correspondence should be addressed.
London South Bank University Business School, 103 Borough Road, London SE1 0AA, UK.
Academic Editor: Wei Zhu
Stats 2021, 4(3), 745-761; https://doi.org/10.3390/stats4030044
Received: 19 July 2021 / Revised: 1 September 2021 / Accepted: 2 September 2021 / Published: 6 September 2021
(This article belongs to the Special Issue Benford's Law(s) and Applications)
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. View Full-Text
Keywords: Benford’s law; conformity tests; goodness-of-fit tests; Monte Carlo simulation; size–power graphs Benford’s law; conformity tests; goodness-of-fit tests; Monte Carlo simulation; size–power graphs
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MDPI and ACS Style

Cerqueti, R.; Lupi, C. Some New Tests of Conformity with Benford’s Law. Stats 2021, 4, 745-761. https://doi.org/10.3390/stats4030044

AMA Style

Cerqueti R, Lupi C. Some New Tests of Conformity with Benford’s Law. Stats. 2021; 4(3):745-761. https://doi.org/10.3390/stats4030044

Chicago/Turabian Style

Cerqueti, Roy, and Claudio Lupi. 2021. "Some New Tests of Conformity with Benford’s Law" Stats 4, no. 3: 745-761. https://doi.org/10.3390/stats4030044

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