Characterization of the cubic exponential families by orthogonality of polynomials
Probability
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0410167,
title = {Characterization of the cubic exponential families by orthogonality of polynomials},
author = {Abdelhamid Hassairi and Mohammed Zarai},
journal= {arXiv preprint arXiv:math/0410167},
year = {2007}
}
Comments
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)