Convergence of distributions of extremal independent random variables
type: Item
instance of: scholarly article
title: Convergence of distributions of extremal independent random variables
zbMATH Open document ID: 0715.60025
DOI: 10.1007/BF00970835
author: D. Kharzeev
published in: Lithuanian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The results of two previous papers of the author [Litov. Mat. Sb. 27, No.2, 219-223 (1987; Zbl 0636.62009), ibid. 28, No.2, 211-214 (1988; Zbl 0647.62031)] are extended here to the case of triangular arrays of independent random variables \(\{X_{nj},\quad 1\leq j\leq k_ n,\quad n\geq 1\}.\) Namely, the author finds nonuniform estimations of the speed of convergence of distribution functions of the maxima \(Z(n)=\max \{X_{nj}:\;1\leq j\leq k_ n\}\) and \(Z(N_ n)=\quad \max \{X_{nj}:\;1\leq j\leq N_ n\},\) where \(\{N_ n\}\) is a sequence of random indices independent of \(\{X_{nj}\}\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 4178223
zbMATH Keywords: extreme value
zbMATH Keywords: triangular arrays of independent random variables
zbMATH Keywords: speed of convergence
reviewed by: T. Inglot
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00970835
OpenAlex ID: W2060513203
description: scientific article; zbMATH DE number 4178223