Properties of Noncentral Dirichlet Distributions

Let X1,…, Xr+1 be independent random variables, Xi∼Ga (ai, θ, δi), i = 1,…, r + 1. Define and Vi = Xi/Xr+1, i = 1,…, r. Then, (U1,…, Ur) and (V1,…, Vr) 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.