On characterization of multivariate stable distributions via random linear statistics
type: Item
instance of: scholarly article
title: On characterization of multivariate stable distributions via random linear statistics
zbMATH Open document ID: 0815.62031
DOI: 10.1007/BF02213449
author: Wei-Bing Zeng
published in: Journal of Theoretical Probability
publication date: 1995-02-26T00:00:00Z
review text: A random linear statistic \(U\) is a linear combination of \(n\) nondegenerate, independent and identically distributed \(d\times 1\) random vectors \(X_ i\), \(i=1,\dots, n\), when the coefficients form an \(n\times 1\) random vector \(Y\) independent of the \(X_ i\)'s. Multivariate strictly stable distributions of \(X_ 1\) are characterized through independence of \(U\) and \(Y\), when \(Y\) satisfies certain conditions. Some choices of \(Y\) satisfying the stated conditions are given. Characterizations through identical distributions of \(U\) and \(X_ 1\) are also discussed. Specific examples are given for the case \(n=2\).
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 727270
zbMATH Keywords: Marcinkiewicz theorem
zbMATH Keywords: characteristic function
zbMATH Keywords: characterizations
zbMATH Keywords: random linear statistic
zbMATH Keywords: strictly stable distributions
zbMATH Keywords: independence
zbMATH Keywords: examples
reviewed by: S. N. U. A. Kirmani
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 727270