2.1.2. Families of Copulas

There exist different types of Copulas that can be classified into three major groups: Fundamental copulas, Implicit and Explicit copulas. Special dependence structures as independence or comonotonicity are represented by so called fundamental copulas. Copulas that are derived from known multivariate distributions but not having an explicit closed-form expressions are known as Implicit copulas. Whereas in contrast, copulas that do posses simple closed-form are Explicit copulas[1].

Fundamental Copulas

The independence copula, as the name suggests, describes independence of random variables and has a form: