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Multivariate tail covariance for generalized skew-elliptical distributions

In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized skew-logistic and generalized skew-Laplace distributions, are also considered. In order to test the theoretical feasibility of our results, the MTCov for skewed and non skewed normal distributions are computed and compared. Finally, we give a special formula of the MTCov for generalized skew-elliptical distributions.