Conditional Tail Independence in Archimedean Copula Models

Abstract

Consider a random vector $U$, whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $U$, conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.

arXiv comment17 pages

References in corpus (1)

• Multivariate Archimedean copulas, $d$-monotone functions and ${\ell }_1$-norm symmetric distributions