A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model

We consider the elliptical distribution of n p-dimensional random vectors X1, ..., Xn having p.d.f. of the form k(n, p) [Lambda]-n/2 g([Sigma]j=1n(Xj-[theta])' [Lambda]-1(Xj-[theta])) as a generalization of the multivariate normal distribution. Let A denote the Wishart matrix defined by , where the vector is given by . In this paper we derive the distribution of A when X1, ..., Xn is assumed to have an elliptical distribution. This result is specialized to the case where X1, ..., Xn is assumed to have a multivariate t distribution, a subclass of the elliptical class of distributions. Furthermore, the first two moments of A for this subclass is computed.