Multivariate tail covariance for generalized skew-elliptical distributions

TL;DR

This paper introduces the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions, providing theoretical formulas and comparisons for specific cases like skew-normal and skew-t distributions.

Contribution

It develops a new theoretical framework for MTCov in generalized skew-elliptical distributions and derives explicit formulas for special cases.

Findings

MTCov formulas for skewed and non-skewed normal distributions

Comparison of MTCov in skewed vs. non-skewed cases

Explicit formula for generalized skew-elliptical distributions

Abstract

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.