Characterization of the cubic exponential families by orthogonality of polynomials

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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.
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)

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Probability, 60J15 (Primary) 60E10. (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/72783

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410167
 http://arxiv.org/abs/math/0410167
 Annals of Probability 2004, Vol. 32, No. 3, 2463-2476
 doi:10.1214/009117904000000522

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