Journal of Statistical Research 58(2), pp. 259-277.
ISSN/ISBN: Not available at this time. DOI: 10.3329/jsr.v58i2.80606
Abstract: We show, by means of a numerical simulation, that the asymptotic (n ≥ 100) cumulative distribution function of the Chebyshev distance statistic is well approximated by a log- normal function with parameters μ = −0.6183 and σ = 0.3561 in the null hypothesis that Benford’s law holds. The deviations of the cumulative function observed in Monte Carlo simulations from the empirical one are below 0.5%. This makes the statistical test based on the Chebyshev statistic accurate at a level of 1% when testing Benford’s law for moderately large and large numbers of data points. Test values of the Chebyshev distance as a function of the sample size are also estimated empirically by performing a Monte Carlo simulation in the case of low n (10 ≤ n ≤ 99). The ef cacy and power of the goodness-of- t test based on the Chebyshev estimator are analyzed and compared with those based on the Pearson χ2 and Kolmogorov-Smirnov statistics. Finally, an application of the Chebyshev test to the annual deaths counts by country is discussed.
Bibtex:
@article{,
author = {Leonardo Campanelli},
title = {A test of significance for Benford’s law based on the Chebyshev distance},
year = {2025},
journal = {Journal of Statistical Research},
volume = {58},
number= {2},
pages = {259--277},
doi = {10.3329/jsr.v58i2.80606},
url = {https://www.banglajol.info/index.php/JStR/article/view/80606},
}
Reference Type: Journal Article
Subject Area(s): Statistics