Power laws, Pareto distributions and Zipf's law

by: MEJ Newman

(1 December 2004)

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arXiv (abstract), arXiv (PDF)

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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, forest fires, solar flares, moon craters 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.

@misc{citeulike:70828, 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, forest fires, solar flares, moon craters 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.}, author = {Newman, M. E. J. }, citeulike-article-id = {70828}, eprint = {cond-mat/0412004}, keywords = {powerlaw}, month = {December}, posted-at = {2007-08-08 17:05:16}, priority = {2}, title = {Power laws, Pareto distributions and Zipf's law}, url = {http://arxiv.org/abs/cond-mat/0412004}, year = {2004} }

RIS record

TY - ELEC ID - citeulike:70828 L3 - citeulike-article-id:70828 TI - Power laws, Pareto distributions and Zipf's law N2 - 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, forest fires, solar flares, moon craters 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. KW - powerlaw AU - Newman, MEJ PY - 2004/12/01/ UR - http://arxiv.org/abs/cond-mat/0412004 ER -

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