Elliptical symmetry and exchangeability with characterizations
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.
subclasses of elliptically symmetric distribtions
scientific article; zbMATH DE number 4211291
scientific article