Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form
Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a comm...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Modelling |
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| Online Access: | https://www.mdpi.com/2673-3951/4/2/8 |
| _version_ | 1827736291790290944 |
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| author | Christophe Chesneau |
| author_facet | Christophe Chesneau |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
| description | Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper. |
| first_indexed | 2024-03-11T02:07:42Z |
| format | Article |
| id | doaj.art-c9d34984791a4cae9089b2dbc21cd9cf |
| institution | Directory Open Access Journal |
| issn | 2673-3951 |
| language | English |
| last_indexed | 2024-03-11T02:07:42Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Modelling |
| spelling | doaj.art-c9d34984791a4cae9089b2dbc21cd9cf2023-11-18T11:46:22ZengMDPI AGModelling2673-39512023-03-014210213210.3390/modelling4020008Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio FormChristophe Chesneau0Department of Mathematics, University of Caen-Normandie, 14032 Caen, FranceCopulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper.https://www.mdpi.com/2673-3951/4/2/8copulasdependence modeltrigonometric functionsinequalitiescorrelation |
| spellingShingle | Christophe Chesneau Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form Modelling copulas dependence model trigonometric functions inequalities correlation |
| title | Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form |
| title_full | Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form |
| title_fullStr | Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form |
| title_full_unstemmed | Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form |
| title_short | Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form |
| title_sort | theoretical advancements on a few new dependence models based on copulas with an original ratio form |
| topic | copulas dependence model trigonometric functions inequalities correlation |
| url | https://www.mdpi.com/2673-3951/4/2/8 |
| work_keys_str_mv | AT christophechesneau theoreticaladvancementsonafewnewdependencemodelsbasedoncopulaswithanoriginalratioform |