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