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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
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215195
Page Count: 4
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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.
Journal of Applied Probability © 1997 Applied Probability Trust