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An invariant-sum characterization of Benford's law

Part of: Foundations of probability theory

Published online by Cambridge University Press:  14 July 2016

Pieter C. Allaart
Pieter C. Allaart*
Affiliation:
Vrije Universiteit Amsterdam
*
∗Postal address: Department of Mathematics and Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081HV Amsterdam, The Netherlands.
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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.

Keywords

FIRST SIGNIFICANT DIGITBENFORD'S LAWMANTISSA FUNCTIONSUM-INVARIANCE

MSC classification

Primary: 60A10: Probabilistic measure theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 288 - 291
Copyright
Copyright © Applied Probability Trust 1997 

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References

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