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The Weibull
distribution and Benford's law
Victoria Cuff, Allison Lewis and Steven J. Miller
Vol. 8 (2015), No. 5, 859–874
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Abstract |
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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. |
Keywords
Benford's law, Weibull distribution, digit bias, Poisson
summation
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Mathematical Subject Classification 2010
Primary: 60F05, 11K06
Secondary: 60E10, 42A16, 62E15, 62P99
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Milestones
Received: 31 July 2014
Revised: 19 October 2014
Accepted: 1 December 2014
Published: 28 September 2015
Communicated by John C. Wierman
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Authors |
| Victoria Cuff | |
| Department of Mathematics Clemson University Clemson, SC 29634 United States |
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| Allison Lewis | |
| Department of Mathematics North Carolina State University Raleigh, NC 27695 United States |
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| Steven J. Miller | |
| Department of Mathematics and
Statistics Williams College Williamstown, MA 01267 United States |
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