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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference7 articles.
1. Benford's law;Varian;Amer. Statistician,1972
2. The First Digit Problem
3. Base-invariance implies Benford's law;Hill;Proc. Amer. Math. Soc.,1994
4. On the Distribution of Numbers
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