Methods of Constructing Copulas

Abstract

If we have a collection of copulas then, as a consequence of Sklar’s theorem, we automatically have a collection of bivariate or multivariate distributions with whatever marginal distributions we desire. Clearly this can be useful in modeling and simulation. Furthermore, by virtue of Theorem 2.4.3, the nonparametric nature of the dependence between two random variables, is expressed by the copula. Thus the study of concepts and measures of nonparametric dependence is a study of properties of copulas—a topic we will pursue in Chapter 5. For this study, it is advantageous to have a variety of copulas at our disposal.