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Power laws, Pareto distributions and Zipf's law

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arxiv cond-mat/0412004 v3 pith:DOFMV52M submitted 2004-12-01 cond-mat.stat-mech physics.data-anphysics.soc-ph

Power laws, Pareto distributions and Zipf's law

classification cond-mat.stat-mech physics.data-anphysics.soc-ph
keywords powerlawsappeardistributionsfollowparetopower-lawquantity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Formalization of the generalized Pareto principle and structural typicality of the 20/80-rule

    physics.soc-ph 2026-02 unverdicted novelty 7.0

    A formalization of the generalized Pareto principle derives that exponential and normal distributions with 100 to 100,000 samples produce p values near 0.2, close to the 80/20 rule and below prior saturation conjectures.

  2. On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law

    astro-ph.HE 2026-04 unverdicted novelty 5.0

    Power-law distributions arise in colliding hard-sphere systems from Maxwell-Boltzmann when starting far from equilibrium, with scale-free intermediate dynamics and open scale-free boundaries.