Gini indices as areas and covariances: What is the difference between the two representations?

Edna Schechtman, Ričardas Zitikis

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The Gini (1914) index and its subsequent generalizations have been widely known or interpreted as (weighted) areas between the egalitarian and actual Lorenz curves. When working on stratification and segmentation of populations and, in turn, with a decomposition of the Gini index, Lerman and Yitzhaki (1989), and Yitzhaki (1994) observed and utilized the fact that the Gini index can be expressed as a covariance. It was subsequently noted by several authors that the area- and the covariance-based formulas for the Gini index may or may not coincide, depending on whether the populations are considered as continuous or discrete. Since researchers and practitioners have frequently used the two formulas and, especially, their empirical counterparts interchangeably, it has therefore become of interest to understand and estimate he differences between the numerical values given by the two formulas. The present paper suggests a thorough resolution of this problem.

Original languageEnglish
Pages (from-to)385-397
Number of pages13
JournalMetron
Volume64
Issue number3
StatePublished - 1 Dec 2006

Keywords

  • Covariance
  • Gini index
  • Lorenz curve
  • S-Gini index

ASJC Scopus subject areas

  • Statistics and Probability

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