DISTRIBUTION OF THE CORRELATION MATRIX FOR A CLASS OF ELLIPTIC MODELS

Let the p-dimensional random vectors X1, X2, ..., X(n) (not necessarily independent) be distributed according to an elliptical model having p.d.f. of the form [GRAPHICS] where K(n, p) is a normalizing constant and theta is a vector of location parameters while LAMBDA is a positive definite symmetric matrix of scale parameters. The exact distribution of the correlation matrix, defined by R = ((r(ik))) where [GRAPHICS] is derived. The case where X1, X2, ..., X(n) is a random sample of size n from N(p)(theta, LAMBDA) is of course a special case of the above model.