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Generalizing Benford's law using power laws: application to integer sequences

2006/07/06 by Werner Hürlimann, Hurlimann, Werner
Mathematics · #11B73 #11B83 #11K31 #62E15 #62E17 #Benford’s Law and Fraud Detection #FOS: Mathematics #Number Theory (math.NT) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0607166

openalex publication_date 2006/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple method to derive parametric analytical extensions of Benford's law for first digits of numerical data is proposed. Two generalized Benford distributions are considered, namely the two-sided power Benford distribution and the new Pareto Benford distribution. The fitting capabilities of these generalized Benford distributions are illustrated and compared at some interesting and important integer sequences.

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