Power laws, Pareto distributions and Zipf's law

2004/12/01 by M. E. J. Newman, MEJ Newman · 2 voices · 333 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech #physics.data-an #physics.soc-ph

paper · pdf · doi:10.1080/00107510500052444

published as Contemporary Physics 46, 323-351 (2005) · 28 pages, 16 figures, minor corrections and additions in this version

arxiv created 2006/05/29 · arxiv updated 2019/09/23

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.

Citations

• Computers and the Theory of Statistics: Thinking the Unthinkable
• Log-normal Distributions across the Sciences: Keys and Clues

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Discussions

• Power Laws, Pareto Distributions and Zipf’s Law [hn, 13 points, 1 comments]
• arxiv.org/pdf/cond-mat... [bsky, 1 points, 1 comments]

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