The Meta-elliptical Distributions with Given Marginals

Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method utilized for this procedure is to embed the spherical distribution quantile transformation of each variable into an elliptically contoured distribution. The new class of distributions is then called meta-elliptical distributions. The corresponding analytic forms of the density, conditional distribution functions, and dependence properties are derived. This new class of distributions has the same Kendallʹs rank correlation coefficient as meta-Gaussian distributions. As an extension of elliptically contoured distributions, some new classes of distributions are also obtained.