A note on the number of records near the maximum
type: Item
instance of: scholarly article
title: A note on the number of records near the maximum
zbMATH Open document ID: 0942.60036
DOI: 10.1016/S0167-7152(98)00253-3
author: Yun Li
published in: Statistics \& Probability Letters
publication date: 2000-08-21T00:00:00Z
review text: Continuing work by \textit{A. G. Pakes} and the reviewer [Aust. J. Stat. 39, No. 2, 179-192 (1997; Zbl 0908.60040)], the author considers the quantity \(K_n(a)\), the number of values within a distance \(a\) from the maximum in a random sample of size \(n\). It is proved that \(EK_n(a)\to 1\) if and only if \(K_n(a)\to 1\) in probability. A necesary and sufficient condition for this in terms of tail behaviour is given, and a sufficient condition for \(K_n(a)\to 1\) almost surely.
reviewed by: Fred W. Steutel
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1310366
zbMATH Keywords: records
zbMATH Keywords: extreme values
MaRDI profile type: Publication
cites work: A necessary and sufficient condition for the existence of the limiting probability of a tie for first place
cites work: On the number of maxima in a discrete sample
cites work: The asymptotic probability of a tie for first place
cites work: ON THE NUMBER OF RECORDS NEAR THE MAXIMUM
cites work: A note on the number of maxima in a discrete sample
cites work: The limit behavior of maxima modulo one and the number of maxima
full work available at URL: s0167-7152(98)00253-3
OpenAlex ID: W1996245962
description: scientific article; zbMATH DE number 1310366