A necessary and sufficient condition for the existence of the limiting probability of a tie for first place
type: Item
instance of: scholarly article
title: A necessary and sufficient condition for the existence of the limiting probability of a tie for first place
zbMATH Open document ID: 0823.60029
DOI: 10.1016/0167-7152(94)00114-N
author: Bennett Eisenberg
author: G. Stengle
author: Yuliy M. Baryshnikov
published in: Statistics \& Probability Letters
publication date: 1995-10-23T00:00:00Z
review text: Suppose that the scores of \(n\) players are unbounded, independent, non- negative integer-valued random variables equal in distribution to \(X\). \(P(T_ n)\) denotes the probability of a tie \(T_ n\) for the highest score. The authors show that as \(n \to \infty\), \(\lim P(T_ n)\) exists if and only if \(P(X = j)/P(X > j) \to 0\) as \(j \to \infty\). In this case \(P(T_ n) \to 0\).
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 768766
zbMATH Keywords: tie
zbMATH Keywords: limiting probability
reviewed by: Zhengyan Lin
MaRDI profile type: Publication
cites work: On the number of maxima in a discrete sample
cites work: On the maximum and its uniqueness for geometric random samples
cites work: The asymptotic probability of a tie for first place
cites work: Q3871318
full work available at URL: 0167-7152(94)00114-n
OpenAlex ID: W1990522598
description: scientific article; zbMATH DE number 768766