Generalized Family of Copulas: Definition and Properties

Abstract

In this paper, through limiting properties of generalized copula introduced, we propose a new family of copula, which includes some of known copulas. For this family, some general formulas for well-known association measures and concepts of dependence of the proposed model are obtained. This class highlights the usefulness of the asymmetric extended copula for modeling the interested variables whose marginal distribution effect on joint distribution is not the same. We also present a method to simulate from our generalized copula, and validate our method and its accuracy using the simulation results to recover the same dependency structure of the original data.