If the space of quadratic forms in is splitted in a direct sum and if and are independent random variables of , assume that there exist a real number such that and real distinct numbers such that for any in We prove that this happens only when , when can be structured in a Euclidean Jordan algebra and when and have Wishart distributions corresponding to this structure.
In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with...
This paper concerns generalized quadratic forms for the multivariate case. These forms are used to test linear hypotheses of parameters for the multivariate Gauss-Markoff model with singular covariance matrix. Distributions and independence of these forms are proved.