SOME DISTRIBUTIONS RELATED TO A NONCENTRAL WISHART DISTRIBUTION

In this paper, we consider the distribution of the elements of the random matrix, lower triangular with positive diagonal elements. This matrix T arises in the Bartlett's decomposition of random matrix W = TT', whose distribution is a noncentral Wishart. We shall consider the particular case in which the p-normal population has a mean of the form mu = (mu1, 0,...,0)' and the identity matrix, I(p), as its covariance matrix. In section 4, we derive the distribution of det S, where S = SIGMA(alpha=1)N X(alpha)X(alpha)', and X(alpha) approximately N(p)[(mu1, mu2,...,mu(p))',SIGMA]; together with the distribution of trS when SIGMA = I(p).