On the rate of convergence of the sum of the sample extremes
type: Item
instance of: scholarly article
title: On the rate of convergence of the sum of the sample extremes
zbMATH Open document ID: 0658.62018
DOI: 10.1007/BF00342230
author: Joop Mijnheer
publication date: 1988-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). be independent random variables with a common distribution function in the domain of normal attraction of the completely asymmetric stable law F(\(\cdot;\alpha,1)\) with \(0<\alpha <1\). Let \(x_{n:1}\leq X_{n:2}\leq...\leq X_{n:n}\) denote the order statistics of \(X_ 1,X_ 2,...,X_ n\). The author derives the rate of convergence of \[ n^{-1/\alpha}(X_{n:n}+...+X_{n:n-k_ n+1}) \] to F(\(\cdot;\alpha,1)\) as both n and \(k_ n\to \infty\). As a consequence he obtains a representation of the sum \(X_{n:n}+...+X_{n:n-k_ n+1}\).
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4076304
zbMATH Keywords: stable limit law
zbMATH Keywords: domain of normal attraction
zbMATH Keywords: completely asymmetric stable law
zbMATH Keywords: order statistics
reviewed by: Wiesław Dziubdziela
MaRDI profile type: Publication
cites work: Q5558293
cites work: The Extreme Terms of a Sample and Their Role in the Sum of Independent Variables
cites work: Q5338485
cites work: What portion of the sample makes a partial sum asymptotically stable or normal?
cites work: The Influence of the Maximum Term in the Addition of Independent Random Variables
cites work: On the Extreme Terms of a Sample From the Domain of Attraction of a Stable Law
cites work: Q4197095
cites work: Q4085018
full work available at URL: https://doi.org/10.1007/bf00342230
OpenAlex ID: W2088035362
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4076304