Archimedean copulae and positive dependence

Authors:
Alfred Müller;Marco Scarsini
Affiliations:
Institut für Wirtschafistheorie und Operations Research, Universität Karlsruhe, Geb. 20.21, D-76128 Karlsruhe, Germany;Dipartimento di Statistica e Matematica Applicata, Università di Torino, Piazza Arbarello 8, I-10122 Torino, Italy
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

In this paper, we consider different issues related to Archimedean copulae and positive dependence. In the first part, we characterize Archimedean copulae that possess positive dependence properties such as multivariate total positivity of order 2 (MTP2) and conditionally increasingness in sequence. In the second part, we investigate conditions for exchangeable binary sequences to admit an Archimedean copula, and we show that they depend on the extendibility of the sequence, and therefore on its positive-dependence properties.