Characterization of the cubic exponential families by orthogonality of polynomials

Details Characterization of the cubic exponential families by orthogonality of polynomials Characterization of the cubic exponential families by orthogonality of polynomials

2004-10-06

arxiv.org/abs/math/0410167v2

Annals of Probability 2004, Vol. 32, No. 3, 2463-2476

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000522 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000522

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.

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