Randomness, evenness, and Rényi’s index

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 11, 1982-1990

Abstract: This paper links together the notion of entropy and the notion of inequality indices—the former is applied in Statistical Physics to measure randomness, and the latter is applied in Economics to measure evenness. We explore the profound similarities between these diametric notions, construct a mathematical transformation between them, and show how randomness can be used to measure evenness–and vice versa. In particular, we devise and study Rényi’s index—a randomness-based measure of evenness with special properties. Rényi’s index is established as an effectual gauge of statistical heterogeneity in the context of general probability laws defined on the positive half-line.

Keywords: Randomness; Evenness; Rényi’s entropy; Entropy maximization and minimization; Gini’s index; Pietra’s index; Hoover’s “Robin Hood” index; Theil’s index; Hirschman’s index; Simpson’s index; Atkinson’s index (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:11:p:1982-1990

DOI: 10.1016/j.physa.2010.11.008

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