  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.
