Strong domain of attraction of extreme generalized order statistics
type: Item
instance of: scholarly article
title: Strong domain of attraction of extreme generalized order statistics
zbMATH Open document ID: 1035.60052
DOI: 10.1023/A:1025176209750
author: Frank Marohn
published in: Extremes
publication date: 2004-03-16T00:00:00Z
review text: For the ordinary order statistics it is known that under the von Mises conditions the distribution function \(F\) belongs to the strong domain of attraction of an extreme value distribution \(G\), i.e. the convergence with respect to the variational distance holds true \(\sup_{B}| P\{a_{n}^{-1}(X_{n,n}-b_{n})\in B\}-G(B)|\to0\) as \(n\to\infty\), where \(\sup\) is taken over all Borel sets \(B\subset R\). The author proves that the von Mises conditions imply that the underlying distribution function \(F\) belongs to the strong domain of attraction of a generalized extreme value distribution. Moreover, it turns out that the strong domains of attractions of joint distributions of the fixed number of generalized extreme order statistics can be characterized by means of the corresponding result for generalized maxima. The author determines the asymptotic joint distribution of (upper and lower) extreme generalized order statistics, and shows that the Hill estimator based on extreme generalized order statistics is asymptotically normal.
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 2059075
zbMATH Keywords: strong domain of attraction
zbMATH Keywords: extreme generalized order statistics
zbMATH Keywords: von Mises condition
MaRDI profile type: Publication
full work available at URL: a:1025176209750
OpenAlex ID: W139744271
description: scientific article; zbMATH DE number 2059075