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Gini characterization of extreme-value statistics

Author

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  • Eliazar, Iddo I.
  • Sokolov, Igor M.

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.

Suggested Citation

  • Eliazar, Iddo I. & Sokolov, Igor M., 2010. "Gini characterization of extreme-value statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4462-4472.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4462-4472
    DOI: 10.1016/j.physa.2010.07.005
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    Cited by:

    1. José Manuel Gavilan-Ruiz & África Ruiz-Gándara & Francisco Javier Ortega-Irizo & Luis Gonzalez-Abril, 2024. "Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index," Stats, MDPI, vol. 7(4), pages 1-12, November.
    2. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    3. Eliazar, Iddo & Shlesinger, Michael F., 2018. "Universality of accelerating change," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 430-445.
    4. Catana, Luigi-Ionut, 2022. "Stochastic orders of multivariate Jones–Larsen distribution family with empirical applications in physics, economy and social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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