The Weibull distribution and Benford’s law

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, quantify-ing 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.