For any multivariate distribution with finite moments we can ask, as in the univariate case, whether or not the distribution is uniquely determined by its moments. In this paper, we summarize, unify and extend some results that are widely scattered in the mathematical and statistical literature....

In this paper, we first show that a k-dimensional Dirichlet random vector has independent components if and only if it is a Kotz Type I Dirichlet random vector. We then consider in detail the class of k-dimensional scale mixtures of Kotz–Dirichlet random vectors, which is a natural extension...

An identity found by Müller (Ann. Inst. Statist. Math. 53 (2001) 567) for normal distributions is generalized to Kotz-type distributions. Some stochastic orders of Kotz-type distributions are discussed by means of this identity.