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arXiv:cond-mat/0412004cond-mat.stat-mech

Power laws, Pareto distributions and Zipf's law

M. E. J. Newman

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.

arXiv comments
28 pages, 16 figures, minor corrections and additions in this version
Journal reference
Contemporary Physics 46, 323-351 (2005)
DOI
doi:10.1080/00107510500052444
Subjects
cond-mat.stat-mechStatistical Mechanics physics.data-anData Analysis, Statistics and Probability physics.soc-phPhysics and Society

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Mar 2011 to Feb 2016. Found in 1 HN submission from Jan 2016 to Jan 2016. Open submission discussions.

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  1. Why the Assholes Are Winning: Money Trumps All 1 comment

    • > The distribution of income seems so unnatural Actually, what's striking to my mind is how mysteriously consistent the income distribution is with the same family of power law distributions (Zipf-Mandelbrot, Pareto, etc.) that describes such other, disparate, natural phenomena…

      6502nerdfaceView on HNParent context

  2. Pioneer Anomaly Solved By 1970s Computer Graphics Technique 1 comment

    • > Mark wrote a paper about this I'm interested. Is it: Power laws, Pareto distributions and Zipf's law, M. E. J. Newman, Contemporary Physics 46, 323–351 (2005). [link: http://arxiv.org/abs/cond-mat/0412004]

      IsamuView on HNParent context

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