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An Alternative to the Oversimplifying Benford’s Law in Experimental Fields

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  • Stéphane Blondeau Da Silva

    (Rectorat de Limoges)

Abstract

A way to model the distribution of first digits in some naturally occurring collections of data is here highlighted. The proportion of d as leading digit, d ∈⟦1,9⟧, in data is sometimes more likely to follow a specific law whose probability distribution is determined by a lower and an upper bound, rather than Benford’s Law, as one might have expected. These peculiar probability distributions fluctuate around Benford’s values, such fluctuations having often been observed in the literature in experimental data sets (where the physical, biological or economical quantities considered are lower and upper bounded). Knowing beforehand the values of these bounds enables to find, through the developed model, a better adjusted law than Benford’s one.

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  • Stéphane Blondeau Da Silva, 2022. "An Alternative to the Oversimplifying Benford’s Law in Experimental Fields," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 778-808, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00287-0
    DOI: 10.1007/s13571-022-00287-0
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