The Annals of Probability

Characterization of the cubic exponential families by orthogonality of polynomials

Abdelhamid Hassairi and Mohammed Zarai

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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.

Article information

Ann. Probab., Volume 32, Number 3B (2004), 2463-2476.

First available in Project Euclid: 6 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J15
Secondary: 60E10: Characteristic functions; other transforms

Exponential family variance function Sheffer polynomials orthogonal polynomials


Hassairi, Abdelhamid; Zarai, Mohammed. Characterization of the cubic exponential families by orthogonality of polynomials. Ann. Probab. 32 (2004), no. 3B, 2463--2476. doi:10.1214/009117904000000522.

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