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In this paper, we focus on multivariate doubly truncated first two moments ofgeneralized skew-elliptical (GSE) distributions and derive explicit expressionsfor them.  It includes many useful distributions, for examples, generalized skew-normal(GSN), generalized skew-Laplace (GSLa), generalized skew-logistic (GSLo) andgeneralized skew student-$t$ (GSSt) distributions, all as special cases. Wealso give formulas of multivariate doubly truncated expectation and covariancefor GSE distributions. As applications, we show the results of multivariatetail conditional expectation (MTCE) and multivariate tail covariance (MTCov)for GSE distributions.

Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures