Power laws, Pareto distributions and Zipf's law

TL;DR

This paper reviews the widespread occurrence of power laws, Pareto distributions, and Zipf's law across various scientific disciplines, discussing empirical evidence and theoretical explanations for their origins.

Contribution

It provides a comprehensive review of empirical data and theories explaining the prevalence of power-law distributions in natural and social phenomena.

Findings

Power laws are observed in diverse fields like physics, biology, and economics.

Empirical evidence supports the ubiquity of power-law distributions.

Various theories have been proposed to explain the origin of power-law behavior.

Abstract

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.