On the Gaussian representation of the Riesz probability distribution on symmetric matrices

AStA Advances in Statistical Analysis - The Riesz probability distribution on symmetric matrices represents an important extension of the Wishart distribution. It is defined by its Laplace...     

Wilks’ factorization of the matrix-variate Dirichlet–Riesz distributions

The Riesz distributions on positive definite symmetric matrices are used to introduce a class of Dirichlet–Riesz distributions. In addition, several distributional properties are stated. Essentially, we show the relationship between the Dirichlet–Riesz distributions of the first kind and the second kind, respectively. We derive Wilks’ factorization of the matrix-variate Dirichlet–Riesz. Further, several results on the product of Riesz and beta–Riesz matrices with a set of Dirichlet–Riesz matrices of the first kind have been derived.     

Riesz inverse Gaussian distributions

The notion of generalized power of a positive definite symmetric matrix and a related notion of generalized Bessel function are used to introduce an extension of the class of matrix generalized inverse Gaussian distributions. The new distributions are shown to arise as conditional distributions of Peirce components of Riesz random matrices. Things are explained in the modern framework of symmetric cones and simple Euclidean Jordan algebra.