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

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 <i>S</i>-Gini index are gen...

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Bibliographic Details
Main Authors: José Manuel Gavilan-Ruiz, África Ruiz-Gándara, Francisco Javier Ortega-Irizo, Luis Gonzalez-Abril
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Stats
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Online Access:https://www.mdpi.com/2571-905X/7/4/78
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Summary: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 <i>S</i>-Gini index are generalized by proposing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mi>v</mi><mo>-</mo></mrow></semantics></math></inline-formula>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.
ISSN:2571-905X