The Inverse Gamma Distribution and Benford's Law

TL;DR

This paper investigates how the inverse gamma distribution relates to Benford's Law, especially in the context of protein structure data, and analyzes how its parameters influence this relationship.

Contribution

It provides a detailed analysis of the inverse gamma distribution's proximity to Benford's Law as its parameters vary, filling a gap in understanding its digit bias behavior.

Findings

Inverse gamma distribution's closeness to Benford's Law varies with parameters

The distribution can exhibit near-Benford behavior under certain conditions

Applications include analyzing data biases in biological and social datasets

Abstract

According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive sports. There are many common distributions that exhibit such bias, i.e. they are almost Benford. These include the exponential and the Weibull distributions. Motivated by these examples and the fact that the underlying distribution of factors in protein structure follows an inverse gamma distribution, we determine the closeness of this distribution to a Benford distribution as its parameters change.