Concordance, symmetrization and non-exchangeability for bivariate copulas
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914535555727360 |
|---|---|
| author | Rodríguez-García, Ávaro Úbeda-Flores, Manuel |
| author_facet | Rodríguez-García, Ávaro Úbeda-Flores, Manuel |
| contents | We study the relationship between measures of non-exchangeability $μ_p$ ($p\in[1,+\infty]$), in the sense of Durante et al. (2010), and classical dependence functionals for bivariate copulas. We show that the symmetrization $C\mapsto(C+C^t)/2$ preserves Spearman's $ρ$ while annihilating $μ_p$, and that Blomqvist's $β$ carries no information about the degree of non-exchangeability. We also establish the sharp lower bound $σ(C)\ge 6\,μ_1(C)$, where $σ$ is the Schweizer-Wolff dependence measure, showing that asymmetry implies dependence. Closed-form expressions for $τ$, $ρ$, and the tail-dependence coefficients of the maximally non-exchangeable family $\{M_θ\}$ are derived as illustrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concordance, symmetrization and non-exchangeability for bivariate copulas Rodríguez-García, Ávaro Úbeda-Flores, Manuel Statistics Theory We study the relationship between measures of non-exchangeability $μ_p$ ($p\in[1,+\infty]$), in the sense of Durante et al. (2010), and classical dependence functionals for bivariate copulas. We show that the symmetrization $C\mapsto(C+C^t)/2$ preserves Spearman's $ρ$ while annihilating $μ_p$, and that Blomqvist's $β$ carries no information about the degree of non-exchangeability. We also establish the sharp lower bound $σ(C)\ge 6\,μ_1(C)$, where $σ$ is the Schweizer-Wolff dependence measure, showing that asymmetry implies dependence. Closed-form expressions for $τ$, $ρ$, and the tail-dependence coefficients of the maximally non-exchangeable family $\{M_θ\}$ are derived as illustrations. |
| title | Concordance, symmetrization and non-exchangeability for bivariate copulas |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2605.05173 |