Discussion on Benford's Law and its Application

TL;DR

This paper discusses Benford's Law, illustrating its theoretical basis and real-world applications across various fields, and evaluates dataset conformity using statistical tests to demonstrate its practical utility.

Contribution

The paper provides new ideas and generalizations of Benford's Law, along with detailed illustrations and a comprehensive evaluation framework.

Findings

Benford's Law accurately models many real-world datasets

Statistical tests effectively assess dataset conformity to Benford's distribution

Applications demonstrate the law's power in various scientific and social contexts

Abstract

The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations of Benford's Law from both theoretical and real-life sources on both science and social science areas are shown in detail with some novel ideas and generalizations developed solely by the authors of this paper. Three tests, Chi-Square test, total variation distance, and maximum deviations are adopted to examine the fitness of the datasets to Benford's distribution. Finally, applications of Benford's Law are summarized and explored to reveal the power of this mathematical principle.