Use of Moments in Distribution Theory: A Multivariate Case

In recent papers, Johnson and Kotz (Amer. Statist.44, 245-249 (1990); Math. Sci.15, 42-52 (1990)) have explored the utility of moment calculations as a simple way of establishing distributional forms. In particular a characterization theorem for beta distributions has been proved. In this paper these methods are extended to multivariate problems, and a result is established for Dirichlet distributions.