Elliptical symmetry and exchangeability with characterizations
type: Item
instance of: scholarly article
title: Elliptical symmetry and exchangeability with characterizations
zbMATH Open document ID: 0732.62048
DOI: 10.1016/0047-259X(90)90002-Y
author: Abdulhamid A. Alzaid
author: Damodar Shanbhag
author: C. R. Rao
published in: Journal of Multivariate Analysis
publication date: 1990-01-01T00:00:00Z
review text: The purpose of this very interesting paper is to give some general results characterizing subclasses of elliptically symmetric distribtions (e.s.d.), such as the spherically symmetric distributions (s.s.d.). After the introduction, section 2 provides two general results on the characterization of the normal distribution in the class of s.s.d., translating well-known characterizations of normality under the assumption of independence of the components of the n-vector random variable \({\mathbb{X}}\), based on properties of linear quadratic statistics, to characterizations of normality in the class of s.s.d. Section 3 of the paper deals with characterizations of probability distributions through regression properties of statistics based on exchangeable random variables yielding, among other things, certain characterizations of members of the family of s.s.d. and other related distributions. As a consequence of the general results it is possible for the authors to obtain results already existing in the literature as special cases and also to derive various other characterizations of well-known distributions such as the mixed gamma, the Poisson, the binomial and the negative binomial distributions.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 4211291
zbMATH Keywords: de Finetti's theorem
zbMATH Keywords: Skitovic-Darmois theorem
zbMATH Keywords: Schoenberg representation
zbMATH Keywords: subclasses of elliptically symmetric distribtions
zbMATH Keywords: spherically symmetric distributions
zbMATH Keywords: normal distribution
zbMATH Keywords: characterizations
zbMATH Keywords: linear quadratic statistics
zbMATH Keywords: regression properties
zbMATH Keywords: exchangeable random variables
zbMATH Keywords: mixed gamma
zbMATH Keywords: Poisson
zbMATH Keywords: binomial
zbMATH Keywords: negative binomial distributions
reviewed by: John Panaretos
MaRDI profile type: Publication
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full work available at URL: 0047-259x(90)90002-y
OpenAlex ID: W1992734306
description: scientific article; zbMATH DE number 4211291