Orthogonal polynomials and natural exponential families

DOI10.1007/BF02562683zbMath0960.62517OpenAlexW2069037953MaRDI QIDQ1919721

Denys Pommeret

Publication date: 17 May 2001

Published in: Test (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02562683

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (15)

Characterization of the cubic exponential families by orthogonality of polynomials. ⋮ Multidimensional Bhattacharyya matrices and exponential families ⋮ A construction of the UMVU estimator for simple quadratic natural exponential families ⋮ Unbiased estimation in the multivariate natural exponential family with simple quadratic variance function ⋮ Two-dimensional Meixner random vectors of class \({\mathcal{M}}_{L}\) ⋮ Orthogonal polynomials with a resolvent-type generating function ⋮ Orthogonality of the Sheffer system associated to a Lévy process ⋮ An infinite dimensional umbral calculus ⋮ Free Meixner states ⋮ Orthogonal and pseudo-orthogonal multi-dimensional Appell polynomials. ⋮ Polynomial expansions of density of power mixtures ⋮ \(K\) terms recurrence relations and polynomial variance functions of the \(K\)th degree ⋮ Characterizations of some polynomial variance functions by \(d\)-pseudo-orthogonality ⋮ A characterization of simple quadratic natural exponential families with a reverse martingale property ⋮ A characterization of multivariate normal stable Tweedie models and their associated polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Natural exponential families with quadratic variance functions
• On the foundations of combinatorial theory. VIII: Finite operator calculus
• On a problem connected with quadratic regression
• Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
• Some Classes of Orthogonal Polynomials Associated with Martingales
• Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion
• On Multivariate Orthogonal Polynomials

This page was built for publication: Orthogonal polynomials and natural exponential families