A Poisson approximation with applications to the number of maxima in a discrete sample
type: Item
instance of: scholarly article
title: A Poisson approximation with applications to the number of maxima in a discrete sample
zbMATH Open document ID: 0961.60036
DOI: 10.1016/S0167-7152(98)00288-0
author: Peter Olofsson
published in: Statistics \& Probability Letters
publication date: 1999-01-01T00:00:00Z
review text: The joint distribution of the \(k\) largest values of a sample of \(n\) independent and identically distributed random variables is asymptotically the same as that of a Poisson distributed number \(N\), if \(EN= n\) and \(k\) is fixed. The author uses this well known fact to simplify the proofs of some results concerning the number of maxima in discrete samples; see, for example, \textit{B. Eisenberg}, \textit{G. Stengle} and \textit{G. Strang} [Ann. Appl. Probab. 3, No. 3, 731--745 (1993; Zbl 0787.60029)].
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1395116
reviewed by: A. D. Barbour
MaRDI profile type: Publication
cites work: Probability approximations via the Poisson clumping heuristic
cites work: Q4002919
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: Q4004226
description: scientific article; zbMATH DE number 1395116