Measuring statistical evenness: A panoramic overview |
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Authors: | Iddo I. Eliazar Igor M. Sokolov |
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Affiliation: | a Department of Technology Management, Holon Institute of Technology, P.O. Box 305, Holon 58102, Israelb Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany |
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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. |
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Keywords: | Statistical heterogeneity Evenness gauges Lorenz curve Gini&rsquo s index Pietra&rsquo s index Hoover&rsquo s &ldquo Robin Hood&rdquo   index Amato&rsquo s index The curvature index Hirschman&rsquo s index Theil&rsquo s index Atkinson&rsquo s indices Ré nyi&rsquo s entropies Ré nyi&rsquo s indices Pareto&rsquo s 20-80 rule Pareto&rsquo s probability law Lorenzian fractality Power-laws Rank distributions |
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