Tuning up the Kolmogorov–Smirnov test for testing Benford’s law

Leonardo Campanelli

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 3, 739-746

Abstract: For moderately large and large numbers of data points (n≥100), the Kolmogorov-Smirnov test is too conservative for testing Benford’s law. Moreover, the asymptotic cumulative distribution function of the Kolmogorov statistic shows unacceptable large deviations, up to about 35%, from the ones obtained in Monte Carlo simulations. Such deviations can be reduced to a level below 0.5% if an appropriate linear transformation of the argument of the Kolmogorov cumulative function is performed.

Date: 2025
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DOI: 10.1080/03610926.2024.2318608

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