Bivariate Copula Classes, Their Visualization, and Estimation

There are three major construction approaches of copulas. One arising from applying the probability integral transform (see Definition 1.3) to each margin of known multivariate distributions and one to use generator functions. The first approach applied to elliptical distributions yields the class of elliptical copulas. With the second approach, we obtain the class of Archimedean copulas. The well-known examples of this class are the Clayton, Gumbel, Frank, and Joe copula families. The third approach arises from extensions of univariate extreme-value theory to higher dimensions.