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

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

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 n...

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Bibliographic Details
Main Author: Ressel Paul
Format: Article
Language:English
Published: De Gruyter 2018-12-01
Series:Dependence Modeling
Subjects:
williamson’s theorem
multivariate survival function
archimedean copula
higher order monotonicity
monotone composition theorem
60e05
62h05,26a48
26b40
Online Access:https://doi.org/10.1515/demo-2018-0020
Description
Summary: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.
ISSN:2300-2298

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