An Empirical Non-Parametric Likelihood Family of Data-Based Benford-Like Distributions.” Physica A forthcoming

A mathematical expression known as Benford’s law provides an example of an unex-pected relationship among randomly selected sequences of first significant digits (FSD). Newcomb (1881), and later Benford (1938), conjectured that FSD’s would exhibit a weakly monotonic decreasing distribution and proposed a frequency proportional to the logarithmic rule. Unfortunately, the Benford FSD function does not hold for a wide range of scale-invariant multiplicative data. To confront this problem we use information-theoretic methods to develop a data-based family of alternative Benford-like exponential distributions that provide null hypotheses for testing purposes. Two data sets are used to illustrate the performance of generalized Benford-like distribu-tions