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July 2004 Characterization of the cubic exponential families by orthogonality of polynomials
Abdelhamid Hassairi, Mohammed Zarai
Ann. Probab. 32(3B): 2463-2476 (July 2004). DOI: 10.1214/009117904000000522

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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Abdelhamid Hassairi. Mohammed Zarai. "Characterization of the cubic exponential families by orthogonality of polynomials." Ann. Probab. 32 (3B) 2463 - 2476, July 2004. https://doi.org/10.1214/009117904000000522

Information

Published: July 2004
First available in Project Euclid: 6 August 2004

zbMATH: 1056.62015
MathSciNet: MR2078547
Digital Object Identifier: 10.1214/009117904000000522

Subjects:
Primary: 60J15
Secondary: 60E10

Keywords: exponential family , orthogonal polynomials , Sheffer polynomials , variance function

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 3B • July 2004
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