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.
Primary Subjects: 60J15
Secondary Subjects: 60E10
Keywords: Exponential family; variance function; Sheffer polynomials; orthogonal polynomials
Full-text: Access granted (open access)
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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