A characterization of the Riesz distribution

Abdelhamid Hassairi (1) , Sallouha Lajmi (1) , Raoudha Zine (1)

1 Laboratory of Probability and Statistics

Bobecka and Wesolowski (2002) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (See Casalis and Letac (1996)), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the Wishart distribution. In the present work, we show that, when we use the division algorithm defined by the Cholesky decomposition, we get a characterization of the Riesz distribution.

Mots clés: Symmetric cone; division algorithm; Wishart distribution; Riesz distribution; Beta-Riesz distribution; functional equation

Domaines: Probabilités [math.PR]

Abdelhamid Hassairi, Sallouha Lajmi, Raoudha Zine. A characterization of the Riesz distribution. 2006. ⟨hal-00151753⟩