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Investigating equality: The Rényi spectrum

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2017, vol. 481, issue C, 90-118

Abstract: An equality index is a score quantifying the socioeconomic egalitarianism of the distribution of wealth in human societies; the score takes values in the unit interval, with the unit upper bound characterizing purely communist societies. In this paper we explore the Rényi spectrum, a continuum of equality indices that: (i) is based on the moments of the societies’ distributions of wealth; (ii) unifies various measures of socioeconomic inequality, including the Theil and Atkinson indices; (iii) displays a collection of amicable analytic properties; (iv) admits multiple Rényi-divergence representations; and (v) provides a high-resolution gauging of egalitarianism that is way beyond what can be offered by the common-practice measures of socioeconomic inequality, the Gini and Pietra indices. At large, the Rényi spectrum is applicable in the context of any distribution of non-negative sizes with a positive mean—yielding a high-resolution gauging of the distribution’s inherent statistical heterogeneity.

Keywords: Equality and inequality; Theil and Atkinson indices; Gini and Pietra indices; Lorenz curve; Rényi divergence; Extreme poverty and riches (search for similar items in EconPapers)
Date: 2017
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