Characterization of the cubic exponential families by orthogonality of polynomials.

DOI10.1214/009117904000000522zbMath1056.62015arXivmath/0410167OpenAlexW3099109863MaRDI QIDQ1889788

Mohammed Zarai, Abdelhamid Hassairi

Publication date: 10 December 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410167

zbMATH Keywords

orthogonal polynomialssequence of polynomialsnatural exponential familySheffer polynomialsexponential generating function2-orthogonality of polynomialscubic variance function

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05) Characterization and structure theory of statistical distributions (62E10) Analysis of variance and covariance (ANOVA) (62J10) Hypergeometric functions (33C99)

Related Items (13)

Bayesian approach to cubic natural exponential families ⋮ Multivariate normal \(\alpha\)-stable exponential families ⋮ Characterization of quadratic Cauchy-Stieltjes kernel families based on the orthogonality of polynomials ⋮ Some properties of 2-orthogonal polynomials associated with inverse Gaussian distribution ⋮ Approximating the first passage time density from data using generalized Laguerre polynomials ⋮ Cauchy–Stieltjes families with polynomial variance functions and generalized orthogonality ⋮ Gibbs sampling, exponential families and orthogonal polynomials ⋮ Characterization of the simple cubic multivariate exponential families ⋮ Bhattacharyya matrices and cubic exponential families ⋮ Orthogonal polynomial expansions to evaluate stop-loss premiums ⋮ Characterization of the Riesz exponential family on homogeneous cones ⋮ Characterizations of some polynomial variance functions by \(d\)-pseudo-orthogonality ⋮ A characterization of multivariate normal stable Tweedie models and their associated polynomials

Cites Work

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• Natural real exponential families with cubic variance functions
• Natural exponential families with quadratic variance functions
• Orthogonal polynomials and natural exponential families
• Some properties of polynomial sets of type zero
• Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
• Some Classes of Orthogonal Polynomials Associated with Martingales
• Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion

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