A Brief History of Generative Models for Power Law and Lognormal Distributions

Abstract

Power law distributions are an increasingly common model for computer science applications; for example, they have been used to describe file size distributions and in- and out-degree distributions for the Web and Internet graphs. Recently, the similar lognormal distribution has also been suggested as an appropriate alternative model fro file size distributions. In this paper, we briefly survey some of the history of these distributions, focusing on work in other fields. We find that several recently proposed models have antecedents in work from decades ago. We also find that lognormal and power law distributions connect quite naturally, and hence it is not surprising that lognormal distributions arise as possible alternative to power law distributions.