Characterization of the cubic exponential families by orthogonality of polynomials

Hassairi, Abdelhamid; Zarai, Mohammed

Ann. Probab., Tome 32 (2004) no. 1A, p. 2463-2476 / Harvested from Project Euclid

Résumé

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.

Publié le : 2004-07-14
Classification: Exponential family, variance function, Sheffer polynomials, orthogonal polynomials, 60J15, 60E10

@article{1091813620,
     author = {Hassairi, Abdelhamid and Zarai, Mohammed},
     title = {Characterization of the cubic exponential families by orthogonality of polynomials},
     journal = {Ann. Probab.},
     volume = {32},
     number = {1A},
     year = {2004},
     pages = { 2463-2476},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1091813620}
}

Hassairi, Abdelhamid; Zarai, Mohammed. Characterization of the cubic exponential families by orthogonality of polynomials. Ann. Probab., Tome 32 (2004) no. 1A, pp.  2463-2476. http://gdmltest.u-ga.fr/item/1091813620/