Measuring statistical evenness: A panoramic overview

Iddo I. Eliazar and Igor M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 4, 1323-1353

Abstract: Motivated by the question “how equal is the distribution of wealth within a given human population?” economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the Lorenz curve and the following indices: Gini, Pietra, Hoover, Amato, Hirschman, Theil and Atkinson. These quantitative measures–considered in the broader context of general data-sets with positive values–are, in effect, general gauges of statistical evenness. While the application of Gini’s index grew beyond economics and reached diverse fields of science, the aforementioned “evenness toolbox” has largely remained within the confines of the social sciences. The aim of this Paper is to expose this “evenness toolbox” to the physics community by presenting a comprehensive evenness-based approach to a fundamental problem in science—the measurement of statistical heterogeneity.

Keywords: Statistical heterogeneity; Evenness gauges; Lorenz curve; Gini’s index; Pietra’s index; Hoover’s “Robin Hood” index; Amato’s index; The curvature index; Hirschman’s index; Theil’s index; Atkinson’s indices; Rényi’s entropies; Rényi’s indices; Pareto’s 20–80 rule; Pareto’s probability law; Lorenzian fractality; Power-laws; Rank distributions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:4:p:1323-1353

DOI: 10.1016/j.physa.2011.09.007

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