Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index

José Manuel Gavilan-Ruiz, África Ruiz-Gándara (), Francisco Javier Ortega-Irizo and Luis Gonzalez-Abril
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José Manuel Gavilan-Ruiz: Department of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, Spain
África Ruiz-Gándara: Department of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, Spain
Francisco Javier Ortega-Irizo: Department of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, Spain
Luis Gonzalez-Abril: Department of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, Spain

Stats, 2024, vol. 7, issue 4, 1-12

Abstract: A new family of inequality indices based on the deviation between the expected maximum and the expected minimum of random samples, called the nth Gini index is presented. These indices generalize the Gini index. At the same time, this family of indices and the S -Gini index are generalized by proposing the u v - Gini index, which turns out to be a convex combination of the S-Gini index and the Lorenz family of inequality measures. This family of Gini indices provides a methodology for achieving perfect equality in a given distribution of incomes. This is achieved through a series of successive and equal increases in the incomes of each individual.

Keywords: inequality measures; mean difference; order statistics; rank-dependent inequality measurement (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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