Uniform convergence of sums of order statistics to stable laws
type: Item
instance of: scholarly article
title: Uniform convergence of sums of order statistics to stable laws
zbMATH Open document ID: 0628.60034
DOI: 10.1007/BF00322023
publication date: 1988-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index \(0<\alpha <1\). Under a von Mises condition we show that the sum of order statistics \[ a_ n^{-1}(\sum ^{k(n)}_{i=1}X_{i:n}+\sum ^{n}_{i=n+1-r(n)}X_{i:n}) \] converges to Q with respect to the norm of total variation if for instance min(k(n),r(n))\(\to \infty\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 4022264
zbMATH Keywords: domain of attraction of a stable law
zbMATH Keywords: von Mises condition
zbMATH Keywords: order statistics
author: Arnold Janssen
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4022264