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

TLDR

The debate over whether file size distributions are best modeled by a power law or a lognormal distribution has a long history across many fields, with recent computer science models tracing back to earlier work. The paper surveys the historical development of generative models that produce power law and lognormal distributions. The approach involves reviewing generative mechanisms that generate these distributions. The study finds that lognormal and power law distributions are naturally connected, explaining why lognormals have emerged as alternatives in many domains.

Abstract

Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.