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2015 The Weibull distribution and Benford's law
Victoria Cuff, Allison Lewis, Steven J. Miller
Involve 8(5): 859-874 (2015). DOI: 10.2140/involve.2015.8.859

Abstract

Benford’s law states that many data sets have a bias towards lower leading digits (about 30% are 1s). It has numerous applications, from designing efficient computers to detecting tax, voter and image fraud. It’s important to know which common probability distributions are almost Benford. We show that the Weibull distribution, for many values of its parameters, is close to Benford’s law, quantifying the deviations. As the Weibull distribution arises in many problems, especially survival analysis, our results provide additional arguments for the prevalence of Benford behavior. The proof is by Poisson summation, a powerful technique to attack such problems.

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Victoria Cuff. Allison Lewis. Steven J. Miller. "The Weibull distribution and Benford's law." Involve 8 (5) 859 - 874, 2015. https://doi.org/10.2140/involve.2015.8.859

Information

Received: 31 July 2014; Revised: 19 October 2014; Accepted: 1 December 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1329.60086
MathSciNet: MR3404662
Digital Object Identifier: 10.2140/involve.2015.8.859

Subjects:
Primary: 11K06, 60F05
Secondary: 42A16, 60E10, 62E15, 62P99

Rights: Copyright © 2015 Mathematical Sciences Publishers

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