The inverse Riesz probability distribution on symmetric matrices

The Riesz distributions on positive definite symmetric matrices are used to introduce a class of inverse Riesz distributions. Some fundamental properties of these new distributions are established. We prove a property of independence between blocks of an inverse Riesz matrix, and we show that some projections of these distributions are also inverse Riesz. We also show the relationship between these distributions with the Riesz inverse Gaussian distributions introduced by Hassairi et al. (2007) [7].