Distributions on symmetric cones I: Riesz distribution

Abstract

The Riesz distribution for real normed division algebras is derived in this work. Then two versions of these distributions are proposed and some of their properties are studied.

P. 5, properties 1., 2. and 5 have been modified. Throughout the article the square root decomposition was replaced by the Cholesky decomposition; and each expression of Riesz type II distribution, $q_{\kappa }(\mathbf{\Sigma })$ must be replaced by $q_{\kappa }^{-1}({\mathbf{\Sigma }}^{-1})$. P. 8. In expression (23) the left side has ben deleted. P. 8. Theorem 2 and its proof have been modified

References in corpus (2)

• Special Functions: Integral properties of Jack polynomials, hypergeometric functions and invariant polynomials
• An identity of Jack polynomials

Cited by in corpus (2)

• Moments of the Riesz distribution
• Relations between generalised Wishart matrices, the Muttalib--Borodin model and matrix spherical functions