Characterization of the cubic exponential families by orthogonality of polynomials

2004/10/31 by Abdelhamid Hassairi, Mohammed Zarai
Mathematics · #math.PR #msc:60J15 #msc:60E10.

paper · pdf · doi:10.1214/009117904000000522

published as Annals of Probability 2004, Vol. 32, No. 3, 2463-2476 · 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)

arxiv created 2005/09/01 · arxiv updated 2009/12/01

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.

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