146 research outputs found
Characterization of the cubic exponential families by orthogonality of polynomials
This paper introduces a notion of 2-orthogonality for a sequence of
polynomials to give extended versions of the Meixner and Feinsilver
characterization results based on orthogonal polynomials. These new versions
subsume the Letac-Mora characterization of the real natural exponential
families having cubic variance function.Comment: Published at http://dx.doi.org/10.1214/009117904000000522 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Singular Riesz measures on symmetric cones
In this paper, we give an explicitdescription of a class of positive measures
on symmetric conesdefined by their Laplace transforms in the framework of the
Rieszintegrals. This work is motivated by the importance of thesemeasures in
probability theory and statistics sincethey represent a generalization of the
measures generating the famous Wishart distributions
On Cauchy-Stieltjes Kernel Families
We explore properties of Cauchy-Stieltjes families that have no counterpart
in exponential families. We relate the variance function of the iterated
Cauchy-Stieltjes family to the pseudo-variance function of the initial
Cauchy-Stieltjes family. We also investigate when the domain of means can be
extended beyond the "natural domain"
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