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

Yuliy Baryshnikov; Bennett Eisenberg; Gilbert Stengle

doi:10.1016/0167-7152(94)00114-N

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

Yuliy Baryshnikov, Bennett Eisenberg, Gilbert Stengle

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	203-209
Number of pages	7
Journal	Statistics and Probability Letters
Volume	23
Issue number	3
DOIs	https://doi.org/10.1016/0167-7152(94)00114-N
State	Published - May 15 1995
Externally published	Yes

Keywords

Existence of the limiting probability
Geometric distribution
Highest score
Logarithmic summability
Tauberian theorem
Tie

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/0167-7152(94)00114-N

Cite this

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

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AU - Eisenberg, Bennett

AU - Stengle, Gilbert

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N2 - Suppose that the scores of n players are unbounded, independent, integer valued random variables equal in distribution to X. We show that as n → ∞, the limiting probability of a tie for the highest score exists if and only if P(X = j)/P(X > j) → 0 as j → ∞.

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

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KW - Geometric distribution

KW - Highest score

KW - Logarithmic summability

KW - Tauberian theorem

KW - Tie

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

Abstract

Keywords

ASJC Scopus subject areas

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