Extreme value limit laws in the nonidentically distributed case
type: Item
instance of: scholarly article
title: Extreme value limit laws in the nonidentically distributed case
zbMATH Open document ID: 0624.62026
DOI: 10.1007/BF02769458
author: David Mejzler
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). be independent, not necessarily identically distributed random variables with distribution functions \(F_ 1,F_ 2,... \), and for each integer \(n\geq 1\) let \(X_{1,n}\leq...\leq X_{n,n}\) denote the order statistics based on \(X_ 1,...,X_ n.\) The asymptotic distributional behavior of the intermediate order statistics \(X_{k,n}\), where \(k=k(n)\), k/n\(\to 1\) and n-k\(\to \infty\), is studied. Under appropriate assumptions on the normalizing and centering constants \(a_ n>0\) and \(b_ n\) and the sequences k(n) and \(F_ n\) a characterization of the class of all possible limiting distributions of \((X_{k,n}-b_ n)/a_ n\) is obtained.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4013751
zbMATH Keywords: extreme value theory
zbMATH Keywords: independent, non-identically distributed random variables
zbMATH Keywords: intermediate order statistics
zbMATH Keywords: characterization of the class of all possible limiting distributions
Wikidata QID: Q114852594
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4013751