Benford's law states that many data sets have a bias towards lower leading digits (about $30\%$ are 1s). There are 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 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.

Version 1.0, 13 pages, 2 figures. This work was done at the 2010 SMALL REU at Williams College, and a summary of it will appear in Chapter Three of The Theory and Applications of Benford's Law, PUP (to appear, S. J. Miller, editor). Since this work was written many of these results have been independently derived and applied them to internet traffic; see the work of Arshadi and Jahangir [AJ]