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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MDPI AG
2024-11-01
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| author | José Manuel Gavilan-Ruiz África Ruiz-Gándara Francisco Javier Ortega-Irizo Luis Gonzalez-Abril |
| author_facet | José Manuel Gavilan-Ruiz África Ruiz-Gándara Francisco Javier Ortega-Irizo Luis Gonzalez-Abril |
| author_sort | José Manuel Gavilan-Ruiz |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8750166701e4492b806a1a3e29dc8aa2 |
| institution | DOAJ |
| issn | 2571-905X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj-art-8750166701e4492b806a1a3e29dc8aa22025-08-20T02:56:58ZengMDPI AGStats2571-905X2024-11-01741354136510.3390/stats7040078Some Notes on the Gini Index and New Inequality Measures: The nth Gini IndexJosé Manuel Gavilan-Ruiz0África Ruiz-Gándara1Francisco Javier Ortega-Irizo2Luis Gonzalez-Abril3Department of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, SpainDepartment of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, SpainDepartment of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, SpainDepartment of Applied Economics I, Faculty of Economics and Business Studies, University of Seville, Avda. Ramón y Cajal, 1, E-41018 Sevilla, SpainA 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.https://www.mdpi.com/2571-905X/7/4/78inequality measuresmean differenceorder statisticsrank-dependent inequality measurement |
| spellingShingle | José Manuel Gavilan-Ruiz África Ruiz-Gándara Francisco Javier Ortega-Irizo Luis Gonzalez-Abril Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index Stats inequality measures mean difference order statistics rank-dependent inequality measurement |
| title | Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index |
| title_full | Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index |
| title_fullStr | Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index |
| title_full_unstemmed | Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index |
| title_short | Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index |
| title_sort | some notes on the gini index and new inequality measures the nth gini index |
| topic | inequality measures mean difference order statistics rank-dependent inequality measurement |
| url | https://www.mdpi.com/2571-905X/7/4/78 |
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