Characterization of the cubic exponential families by orthogonality of polynomials

Characterization of the cubic exponential families by orthogonality of polynomials

Abdelhamid Hassairi and Mohammed Zarai

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

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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Primary Subjects: 60J15

Secondary Subjects: 60E10

Keywords: Exponential family; variance function; Sheffer polynomials; orthogonal polynomials

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1091813620
Digital Object Identifier: doi:10.1214/009117904000000522
Mathematical Reviews number (MathSciNet): MR2078547
Zentralblatt MATH identifier: 02121703

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References

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Mathematical Reviews (MathSciNet): MR1182991

Zentralblatt MATH: 0983.62501

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Mathematical Reviews (MathSciNet): MR1041384

JSTOR: links.jstor.org

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Digital Object Identifier: doi:10.1215/S0012-7094-39-00549-1

Project Euclid: euclid.dmj/1077491414

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Digital Object Identifier: doi:10.1063/1.528507

Zentralblatt MATH: 0696.33010

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