Advances in Statistical Analysis 109(1), pp. 197–216.
ISSN/ISBN: Not available at this time. DOI: 10.1007/s10182-024-00505-2
Abstract: Benford’s law is a particular discrete probability distribution that is often satis ed by the signi cant digits of a dataset. The nonconformity with Benford’s law suggests the possible presence of data manipulation. This paper introduces two novel gener- alized versions of Benford’s law that are less restrictive than the original Benford’s law—hence, leading to more probable conformity of a given dataset. Such gener- alizations are grounded on the existing mathematical relations between Benford’s law probability distribution elements. Moreover, one of them leads to a set of prob- ability distributions that is a proper subset of that of the other one. We show that the considered versions of Benford’s law have a geometric representation on the three- dimensional Euclidean space. Through suitable optimization models, we show that all the probability distributions satisfying the more restrictive generalization exhibit at least acceptable conformity with Benford’s law, according to the most popular distance measures. We also present some examples to highlight the practical useful- ness of the introduced devices.
Bibtex:
@article{,
author = {Roy Cerqueti and Mario Maggi},
title = {Classes of probability measures built on the properties of Benford’s law},
year = {2025},
journal = {Advances in Statistical Analysis},
volume = {109},
number = {1},
pages = {19--216},
doi = {10.1007/s10182-024-00505-2},
url = {https://link.springer.com/article/10.1007/s10182-024-00505-2},
}
Reference Type: Journal Article
Subject Area(s): Statistics