A necessary and sufficient condition for the existence of the limiting probability of a tie for first place

Suppose that the scores of n players are unbounded, independent, integer valued random variables equal in distribution to X. We show that as n --> [infinity], the limiting probability of a tie for the highest score exists if and only if P(X = j)/P(X > j) --> 0 as j --> [infinity].

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Year of publication:	1995
Authors:	Baryshnikov, Yuliy ; Eisenberg, Bennett ; Stengle, Gilbert
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 23.1995, 3, p. 203-209
Publisher:	Elsevier
Keywords:	Tie Existence of the limiting probability Logarithmic summability Geometric distribution Tauberian theorem Highest score

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254624