From Multivariate Skewed Distributions to Copulas

In this paper, a methodology is presented for constructing skewed multivariate copulas to model data with possibly different marginal distributions. Multivariate skew elliptical distributions are transformed into corresponding copulas in the similar way as the Gaussian copula and the multivariate t-copula are constructed. Three-parameter skew elliptical distributions are under consideration. For parameter estimation of the skewed distributions, the method of moments is used. To transform mixed third-order moments into a parameter vector, the star product of matrices is used; for star product and its applications, see, for example, Kollo (J. Multivar. Anal. 99:2328–2338, 2008) or Visk (Commun. Stat. 38:461–470, 2009). Results of the first applications are shortly described and referred to.