Power-divergence copulas: A new class of Archimedean copulas, with an insurance application
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916994936209408 |
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| author | Pearse, Alan R. Bondell, Howard |
| author_facet | Pearse, Alan R. Bondell, Howard |
| contents | This paper demonstrates that, under a particular convention, the convex functions that characterise the phi divergences also generate Archimedean copulas in at least two dimensions. As a special case, we develop the family of Archimedean copulas associated with the important family of power divergences, which we call the power-divergence copulas. The properties of the family are extensively studied, including the subfamilies that are absolutely continuous or have a singular component, the ordering of the family, limiting cases (i.e., the Frechet-Hoeffding lower bound and Frechet-Hoeffding upper bound), the Kendall's tau and tail-dependence coefficients, and cases that extend to three or more dimensions. In an illustrative application, the power-divergence copulas are used to model a Danish fire insurance dataset. It is shown that the power-divergence copulas provide an adequate fit to the bivariate distribution of two kinds of fire-related losses claimed by businesses, while several benchmarks (a suite of well known Archimedean, extreme-value, and elliptical copulas) do not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power-divergence copulas: A new class of Archimedean copulas, with an insurance application Pearse, Alan R. Bondell, Howard Methodology Information Theory Statistics Theory 62H05 This paper demonstrates that, under a particular convention, the convex functions that characterise the phi divergences also generate Archimedean copulas in at least two dimensions. As a special case, we develop the family of Archimedean copulas associated with the important family of power divergences, which we call the power-divergence copulas. The properties of the family are extensively studied, including the subfamilies that are absolutely continuous or have a singular component, the ordering of the family, limiting cases (i.e., the Frechet-Hoeffding lower bound and Frechet-Hoeffding upper bound), the Kendall's tau and tail-dependence coefficients, and cases that extend to three or more dimensions. In an illustrative application, the power-divergence copulas are used to model a Danish fire insurance dataset. It is shown that the power-divergence copulas provide an adequate fit to the bivariate distribution of two kinds of fire-related losses claimed by businesses, while several benchmarks (a suite of well known Archimedean, extreme-value, and elliptical copulas) do not. |
| title | Power-divergence copulas: A new class of Archimedean copulas, with an insurance application |
| topic | Methodology Information Theory Statistics Theory 62H05 |
| url | https://arxiv.org/abs/2510.06177 |