Asymptotic distribution of the normal sample range
type: Item
instance of: scholarly article
title: Asymptotic distribution of the normal sample range
zbMATH Open document ID: 0787.62021
author: Peter C. Mathews
author: Andrew L. Rukhin
published in: The Annals of Applied Probability
publication date: 1993-10-28T00:00:00Z
review text: For a spherically symmetric, multivariate normal random sample \(X_ i\), \(i=1,2,\dots,n\), the asymptotic distribution of \(\max_{1\leq i<j\leq n}| X_ j-X_ i|\) as \(n\to\infty\) is considered. The number of \(| X_ j-X_ i|\) exceeding a high level has a Poisson limit distribution.
reviewed by: Nijolė Kalinauskaitė
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 436549
zbMATH Keywords: normal sample range
zbMATH Keywords: spherically symmetric
zbMATH Keywords: multivariate normal random sample
zbMATH Keywords: Poisson limit distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005433
OpenAlex ID: W2070478189
DOI: 10.1214/AOAP/1177005433
description: scientific article; zbMATH DE number 436549