Kybernetika 43 no. 2, 235-244, 2007

Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante, Erich Peter Klement, José Quesada-Molina and Peter Sarkoci


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 $\ast$-product and the $\star$-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.