Analogies and Relations between Non-Additive Entropy Formulas and Gintropy
We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/26/3/185 |
| _version_ | 1797241210527547392 |
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| author | Tamás S. Biró András Telcs Antal Jakovác |
| author_facet | Tamás S. Biró András Telcs Antal Jakovác |
| author_sort | Tamás S. Biró |
| collection | DOAJ |
| description | We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis’ <i>q</i>-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented. |
| first_indexed | 2024-04-24T18:19:42Z |
| format | Article |
| id | doaj.art-f5baaa715cfd426490e02a7f43650eec |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-24T18:19:42Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f5baaa715cfd426490e02a7f43650eec2024-03-27T13:36:47ZengMDPI AGEntropy1099-43002024-02-0126318510.3390/e26030185Analogies and Relations between Non-Additive Entropy Formulas and GintropyTamás S. Biró0András Telcs1Antal Jakovác2HUN-REN Wigner Research Centre for Physics, 1121 Budapest, HungaryHUN-REN Wigner Research Centre for Physics, 1121 Budapest, HungaryHUN-REN Wigner Research Centre for Physics, 1121 Budapest, HungaryWe explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis’ <i>q</i>-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented.https://www.mdpi.com/1099-4300/26/3/185entropyGini indexLorenz curvenon-extensive |
| spellingShingle | Tamás S. Biró András Telcs Antal Jakovác Analogies and Relations between Non-Additive Entropy Formulas and Gintropy Entropy entropy Gini index Lorenz curve non-extensive |
| title | Analogies and Relations between Non-Additive Entropy Formulas and Gintropy |
| title_full | Analogies and Relations between Non-Additive Entropy Formulas and Gintropy |
| title_fullStr | Analogies and Relations between Non-Additive Entropy Formulas and Gintropy |
| title_full_unstemmed | Analogies and Relations between Non-Additive Entropy Formulas and Gintropy |
| title_short | Analogies and Relations between Non-Additive Entropy Formulas and Gintropy |
| title_sort | analogies and relations between non additive entropy formulas and gintropy |
| topic | entropy Gini index Lorenz curve non-extensive |
| url | https://www.mdpi.com/1099-4300/26/3/185 |
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