A characterization of multivariate \(l_ 1\)-norm symmetric distributions
type: Item
instance of: scholarly article
title: A characterization of multivariate \(l_ 1\)-norm symmetric distributions
zbMATH Open document ID: 0667.62034
DOI: 10.1016/0167-7152(89)90109-0
published in: Statistics \& Probability Letters
publication date: 1989-01-01T00:00:00Z
review text: Let z be an \(n\times 1\) interchangeable random vector and \(z_{(1)}\leq...\leq z_{(n)}\) be its order statistics. Let \[ u_ i=(n- i+1)(z_{(i)}-z_{(i-1)}),\quad i=1,...,n,\quad with\quad z_{(0)}=0 \] and \(u=(u_ 1,...,u_ n)'\). The main result is that \(z=^{d}u\) iff z is a multivariate \(\ell_ 1\)-norm symmetric distribution.
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4092578
zbMATH Keywords: multivariate \(\ell 1\)-norm symmetric distribution
zbMATH Keywords: normalized spacing
zbMATH Keywords: survival function
zbMATH Keywords: interchangeable random vector
zbMATH Keywords: order statistics
author: Bi Qi Fang
author: Kai-Tai Fang
MaRDI profile type: Publication
full work available at URL: 0167-7152(89)90109-0
OpenAlex ID: W2007335926
cites work: Q3026041
cites work: Multivariate Liouville distributions
cites work: Some families of multivariate symmetric distributions related to exponential distribution
description: scientific article; zbMATH DE number 4092578