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1 Laboratory of Probability and Statistics

Abstract : In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families NEF-s. The first property says that the cumulant function of any basis of the family is a solution of some Monge-Amp\-{e}re equation, the second is that the variance function satisfies a differential equation, and the third is characterized by the equality between two families of prior distributions related to the NEF. These properties represent the extensions to this class of the properties stated by Casalis 1996 and satisfied by the Wishart and the simple quadratic NEF-s. We also show that in the real case, each of these properties provides a new characterization of the Letac-Mora class of real cubic NEF-s.

Keywords : Natural exponential family variance function cumulant function Monge-Amp\-{e}re equation prior distribution

Autor: Maroua Hamza - Abdelhamid Hassairi -



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