Measuring statistical heterogeneity: The Pietra index

Iddo I. Eliazar and Igor M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 1, 117-125

Abstract: There are various ways of quantifying the statistical heterogeneity of a given probability law: Statistics uses variance — which measures the law’s dispersion around its mean; Physics and Information Theory use entropy — which measures the law’s randomness; Economics uses the Gini index — which measures the law’s egalitarianism. In this research we explore an alternative to the Gini index–the Pietra index–which is a counterpart of the Kolmogorov–Smirnov statistic. The Pietra index is shown to be a natural and elemental measure of statistical heterogeneity, which is especially useful in the case of asymmetric and skewed probability laws, and in the case of asymptotically Paretian laws with finite mean and infinite variance. Moreover, the Pietra index is shown to have immediate and fundamental interpretations within the following applications: renewal processes and continuous time random walks; infinite-server queueing systems and shot noise processes; financial derivatives. The interpretation of the Pietra index within the context of financial derivatives implies that derivative markets, in effect, use the Pietra index as their benchmark measure of statistical heterogeneity.

Keywords: Statistical heterogeneity; Entropy; Gini index; Pietra index; Kolmogorov–Smirnov statistic; Variance–mean ratio; Entropy maximization; Renewal processes; Continuous Time Random Walks (CTRWs); The M/G/∞ queueing system; Shot noise processes; Call options (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:1:p:117-125

DOI: 10.1016/j.physa.2009.08.006

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