On a new class of continuous indices of inequality

Terence Chan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Gini index is a well-known and long-established measure of inequality for distributions of income and other quantities. However, it has a number of mathematical disadvantages. Firstly, it is discontinuous with respect to all the main modes of convergence of probability measures. Secondly, it relies critically on the finiteness of the mean of the underlying distribution. Finally, even when the underlying distribution has a finite mean, estimation of the Gini index from data can be problematic if the variance of the underlying distribution is infinite. In this paper, we propose a class of inequality indices which are continuous with respect to setwise convergence of probability measures (and hence also with respect to convergence in total variation) and which do not require the underlying distribution to possess any finite moments whatsoever. Moreover, our class of inequality indices can be easily estimated from data and the standard methods of statistical inference can be applied to the estimators.

Original languageEnglish
Pages (from-to)8-23
Number of pages16
JournalMathematical Social Sciences
Volume120
Early online date11 Sep 2022
DOIs
Publication statusE-pub ahead of print - 11 Sep 2022

Keywords

  • Gini index
  • Measures of inequality

ASJC Scopus subject areas

  • Sociology and Political Science
  • Social Sciences(all)
  • Psychology(all)
  • Statistics, Probability and Uncertainty

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