×

zbMATH — the first resource for mathematics

Les familles exponentielles à variance quadratique homogène sont des lois de Wishart sur un cône symétrique. (Exponential families with a homogeneous quadratic variance are Wishart distributions on symmetric cones). (French) Zbl 0745.62051
Summary: The aim of this note is to characterize the exponential families on \(\mathbb{R}^ n\) with a variance-function which is quadratic and homogeneous in the mean, i.e. \(V(m_ 1, \dots ,m_ n)= \sum_{i,j=1}^ n A_{ij} m_ i m_ j\), where \(A_{ij}\) are real \((n,n)\) symmetric matrices. They are defined on symmetric cones and thus are products of Wishart families on the five irreducible symmetric cones.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E10 Characterization and structure theory of statistical distributions
60B11 Probability theory on linear topological spaces
PDF BibTeX XML Cite