Benford or Not Benford: A Systematic But Not Always Well-Founded Use of an Elegant Law in Experimental Fields

Abstract

In this paper, we will propose a way to accurately model certain naturally occurring collections of data. Through this proposed model, the proportion of d as leading digit, $d\in \llbracket 1,9\rrbracket $, in data is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford’s Law, as one might have expected. These probability distributions fluctuate nevertheless around Benford’s values. These peculiar fluctuations have often been observed in the literature in such data sets (where the physical, biological or economical quantities considered are upper bounded). Knowing beforehand the value of this upper bound enables to find, through the developed model, a better adjusted law than Benford’s one.

Keywords

Benford’s Law / Leading digit / Experimental data

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