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Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante;  Erich Peter Klement;  José Quesada-Molina;  Peter Sarkoci — 2007

Kybernetika

We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

Semicopulas: characterizations and applicability

Fabrizio Durante;  José Quesada-Molina;  Carlo Sempi — 2006

Kybernetika

We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.

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