Journal of Theoretical Probability.
ISSN/ISBN: Not available at this time. DOI: 10.1007/s10959-018-0827-z
Abstract: For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Lévy, Kantorovich, and Kolmogorov), given any number of atoms, and allowing for additional constraints regarding weights or positions of atoms. As an application, best (constrained or unconstrained) approximations are identified for Benford’s Law (logarithmic distribution of significands) and other familiar distributions. The results complement and extend known facts in the literature; they also provide new rigorous benchmarks against which to evaluate empirical observations regarding Benford’s law.
Bibtex:
@Article{,
author="Berger, Arno and Xu, Chuang",
title="Best Finite Approximations of Benford's Law",
journal="Journal of Theoretical Probability",
year="2018",
month="Apr",
day="07",
issn="1572-9230",
doi="10.1007/s10959-018-0827-z",
url="https://doi.org/10.1007/s10959-018-0827-z"
}
Reference Type: Journal Article
Subject Area(s): Analysis, Probability Theory