Limit laws for the maximum of weighted and shifted i.i.d. random variables
type: Item
instance of: scholarly article
title: Limit laws for the maximum of weighted and shifted i.i.d. random variables
zbMATH Open document ID: 0538.60024
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: Let \(X_ 0,X_ 1,X_ 2,..\). be i.i.d. r.v.'s with d.f. F and define a sequence by \(M_ n=\max(X_ 0,...,X_{n-1})\). Classical results by \textit{B. Gnedenko} [Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423-453 (1943)] exhibited the class of possible nondegenerate limit laws that can arise for such sequences and discussed the domain of attraction of this class. This work has later been extended considerably. In the present paper extensions to weighted or translated sequences are studied; special cases are \(\{a^ nX_ n\}\), \(0<a<1\), and \(\{X_ n-nd\}\), \(d>0\). Depending on the weights or translates the limit laws may be both inside and outside Gnedenko's classical class.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 3856098
zbMATH Keywords: extreme value theory
zbMATH Keywords: domain of attraction
zbMATH Keywords: limit laws
author: D. J. Daley
author: Peter Hall
reviewed by: Lars Holst
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993306
OpenAlex ID: W1996440998
DOI: 10.1214/AOP/1176993306
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description: scientific article; zbMATH DE number 3856098