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August 1996 The $2d+4$ simple quadratic natural exponential families on ${\bf R}\sp d$
M. Casalis
Ann. Statist. 24(4): 1828-1854 (August 1996). DOI: 10.1214/aos/1032298298

Abstract

The present paper describes all the natural exponential families on $\mathbb{R}^d$ whose variance function is of the form $V(m) = am \otimes m + B(m) + C$, with $m \otimes m(\theta) = \langle \theta, m \rangle m$ and B linear in m. There are $2d + 4$ types of such families, which are built from particular mixtures of families of Normal, Poisson, gamma, hyperbolic on $\mathbb{R}^d$ and negative-multinomial distributions. The proof of this result relies mainly on techniques used in the elementary theory of Lie algebras.

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M. Casalis. "The $2d+4$ simple quadratic natural exponential families on ${\bf R}\sp d$." Ann. Statist. 24 (4) 1828 - 1854, August 1996. https://doi.org/10.1214/aos/1032298298

Information

Published: August 1996
First available in Project Euclid: 17 September 2002

zbMATH: 0867.62042
MathSciNet: MR1416663
Digital Object Identifier: 10.1214/aos/1032298298

Subjects:
Primary: 60E10, 62E10

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • August 1996
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