Stigler’s approach to recovering the distribution of first significant digits in natural data sets

Benford’s Law can be seen as one of the many first significant digit (FSD) distributions in a family of monotonically decreasing distributions. We examine the interrelationship between Benford and other monotonically decreasing distributions such as those arising from Stigler, Zipf, and the power laws. We examine the theoretical basis of the Stigler distribution and extend his reasoning by incorporating FSD first-moment information into information-theoretic methods. We present information-theoretic methods as a way to describe, connect, and unify these related distributions and thereby extend the reach of Benford’s Law and FSD research more generally.