Benford or not Benford: a systematic but not always well-founded use of an elegant law in experimental fields

TL;DR

This paper challenges the universal applicability of Benford's Law in experimental data, proposing that the leading digit distribution is better modeled by upper-bound-dependent laws, which can improve data analysis accuracy.

Contribution

It introduces a new model for leading digit distribution based on upper bounds, providing a more accurate alternative to Benford's Law for bounded datasets.

Findings

Distributions fluctuate around Benford's Law in bounded data

Knowing the upper bound improves model fit

Proposes a new law better suited for certain datasets

Abstract

In this paper, we will see that the proportion of d as leading digit, d $\in$ 1, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford's Law. These probability distributions fluctuate around Benford's value as can often be observed in the literature in many naturally occurring collections of data (where the physical , biological or economical quantities considered are upper bounded). Knowing beforehand the value of the upper bound can be a way to find a better adjusted law than Benford's one.