Wlodzimierz Wysocki

Classes of generators of archimedean copulas

886

Abstract

We introduce concepts of diagonal generators for Archimedean copulas. Their properties, interrelations, and relations with additive and multiplicative generators are investigated. We show continuous dependence of multiplicative and diagonal generators on additive generators. We also show that almost uniform convergence of some functional sequences defined in terms of superpositions of diagonal copulas allows for building additive generators of Archimedean copulas. A new characterization of two-dimensional Archimedean copulas in terms of corresponding diagonal copulas is presented. We also characterize a class of copulas in relation to sequences of superpositions of diagonal copulas.

Key words: Archimedean copula, diagonal copula, diagonal generator, multiplicative generator