Properties of noncentral Dirichlet distributions

Let X-1,..., Xr+1 be independent random variables, X-i similar to Ga (a(i), theta, delta(i)), i= 1,...,r+1. Define U-i = X-i/Sigma(r+1)(i=1), i = 1,...,r and V-i = X-i/Xr+1, i = 1,...,r. Then, (U-1,...,U-r) and (V-1,...,V-r) follow noncentral Dirichlet Type 1 and Type 2 distributions, respectively. In this article several properties of these distributions and their connections with the uniform, the noncentral multivariate-F and the noncentral multivariate-t distributions are discussed. (c) 2006 Elsevier Ltd. All rights reserved.