Kybernetika 45 no. 6, 1003-1011, 2009

Componentwise Concave Copulas and Their Asymmetry

Fabrizio Durante and Pier Luigi Papini


The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the $L^{\infty}$-measure of non-exchangeability for copulas belonging to this class.


copulas, exchangeability, positive regression dependence


60E05, 62H20