Version 1
: Received: 26 September 2024 / Approved: 1 October 2024 / Online: 2 October 2024 (07:10:37 CEST)
How to cite:
Ruiz, J. M. G.; Ruiz-Gándara, Á.; Irizo, F. J. O.; Abril, L. G. Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index. Preprints2024, 2024100088. https://doi.org/10.20944/preprints202410.0088.v1
Ruiz, J. M. G.; Ruiz-Gándara, Á.; Irizo, F. J. O.; Abril, L. G. Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index. Preprints 2024, 2024100088. https://doi.org/10.20944/preprints202410.0088.v1
Ruiz, J. M. G.; Ruiz-Gándara, Á.; Irizo, F. J. O.; Abril, L. G. Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index. Preprints2024, 2024100088. https://doi.org/10.20944/preprints202410.0088.v1
APA Style
Ruiz, J. M. G., Ruiz-Gándara, Á., Irizo, F. J. O., & Abril, L. G. (2024). Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index. Preprints. https://doi.org/10.20944/preprints202410.0088.v1
Chicago/Turabian Style
Ruiz, J. M. G., Francisco Javier Ortega Irizo and Luis Gonzalez Abril. 2024 "Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index" Preprints. https://doi.org/10.20944/preprints202410.0088.v1
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 generalised by proposing the uv−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
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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