title: Rank distributions: a panoramic macroscopic outlook.
abstract: 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.
authors.affiliation: School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Iddo I
authors.initials: II
authors.lastname: Eliazar
authors.affiliation: Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA and Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Morrel H
authors.initials: MH
authors.lastname: Cohen
mesh_terms: D000465:Algorithms; D018803:Models, Economic; D015233:Models, Statistical; D011157:Population Dynamics; D016008:Statistical Distributions