Multivariate Doubly Truncated Moments for a Class of Multivariate Location-Scale Mixture of Elliptical Distributions

In this paper, we investigate multivariate doubly truncated moments for a class of multivariate location-scale mixture of elliptical (LSME) distributions. This rich family includes some well-known distributions, such as location-scale mixture of normal, location-scale mixture of Student-t, location-scale mixture of logistic and location-scale mixture of Laplace distributions, as special cases. We first present general formulae for computing the first two moments of the LSME distributions under the double truncation. We then consider a special case for cross moment. As an application, we present the results of multivariate tail conditional expectation (MTCE) for generalized hyperbolic (MGH) distribution.