A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas

Abstract

Williamson’s integral representation of n-monotone functions on the half-line is generalized to several dimensions. This leads to a characterization of multivariate survival functions with multiply ℓ1- symmetry. We then introduce a new class of generalized Archimedean copulas, where in contrast to nested Archimedean copulas no extra compatibility conditions for their generators are required.

Keywords

• williamson’s theorem
• multivariate survival function
• archimedean copula
• higher order monotonicity
• monotone composition theorem
• 60e05
• 62h05,26a48
• 26b40