Gini characterization of extreme-value statistics

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.