Bivariate distributions with nonmonotone dependence structure

Marco Scarsini (1, 2) , A. Venetoulias

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

A new ordering for nonmonotone dependence is proposed, and a method is presented for describing parametric families of bivariate distributions with fixed marginals and specified dependence structures. The method is easy to use and allows for arbitrary marginals and arbitrary dependence structures (e.g., structures of nonmonotone dependence). Any parametric family of bivariate distributions is ordered by the nonmonotone dependence ordering constructed from the desirable dependence structure. The construction is based on a generalization of the copula of distribution functions to a copula of probability measures on product spaces. Examples are shown for various bivariate distribution

Keywords: Distribution function; Bivariate distribution; Marginal distribution; Ordering; Parametric family; Monotone dependence

Domains: Economy and decision science

Marco Scarsini, A. Venetoulias. Bivariate distributions with nonmonotone dependence structure. Journal of the American Statistical Association, 1993, Vol. 88, N°421, pp. 338-344. ⟨hal-00541945⟩