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An Invariant-Sum Characterization of Benford's Law

Pieter C. Allaart
Journal of Applied Probability
Vol. 34, No. 1 (Mar., 1997), pp. 288-291
DOI: 10.2307/3215195
Stable URL: http://www.jstor.org/stable/3215195
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
An Invariant-Sum Characterization of Benford's Law
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Abstract

The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit d (d = 1, 2, ⋯, 9) is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits d1, ⋯, dk is constant for every fixed k.

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