Rank distributions: A panoramic macroscopic outlook

Iddo I. Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper presents a panoramic macroscopic outlook of rank distributions. We establish a general framework for the analysis of rank distributions, which classifies them into five macroscopic "socioeconomic" states: monarchy, oligarchy-feudalism, criticality, socialism-capitalism, and communism. Oligarchy-feudalism is shown to be characterized by discrete macroscopic rank distributions, and socialism-capitalism is shown to be characterized by continuous macroscopic size distributions. Criticality is a transition state between oligarchy-feudalism and socialism-capitalism, which can manifest allometric scaling with multifractal spectra. Monarchy and communism are extreme forms of oligarchy-feudalism and socialism-capitalism, respectively, in which the intrinsic randomness vanishes. The general framework is applied to three different models of rank distributions - top-down, bottom-up, and global - and unveils each model's macroscopic universality and versatility. The global model yields a macroscopic classification of the generalized Zipf law, an omnipresent form of rank distributions observed across the sciences. An amalgamation of the three models establishes a universal rank-distribution explanation for the macroscopic emergence of a prevalent class of continuous size distributions, ones governed by unimodal densities with both Pareto and inverse-Pareto power-law tails.

Original languageEnglish (US)
Article number012111
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - Jan 9 2014

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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