Gini characterization of extreme-value statistics

Iddo I. Eliazar and Igor M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 21, 4462-4472

Abstract: This paper presents a profound connection between Gini’s index and extreme-value statistics. Gini’s index is a quantitative gauge for the evenness of probability laws defined on the positive half-line, and is the common measure of societal egalitarianism applied in Economics and in the Social Sciences. Extreme-value statistics–namely, the Gumbel, Fréchet and Weibull probability laws–are the only possible asymptotic statistics emerging from the extremes of large ensembles of independent and identically distributed random variables. Extreme-value statistics play a major role–all across Science and Engineering–in the analysis of rare and extreme events. Introducing generalizations of Gini’s index, and exploring an elemental Poissonian structure underlying the extreme-value statistics, we establish in this paper a Gini-based characterization of extreme-value statistics.

Keywords: Gini’s index; Extreme-value statistics; Gumbel law; Fréchet law; Weibull law; Poisson processes; Poissonian populations (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:21:p:4462-4472

DOI: 10.1016/j.physa.2010.07.005

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