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 journalArticlepeer-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 languageEnglish (US)
Pages (from-to)203-209
Number of pages7
JournalStatistics and Probability Letters
Volume23
Issue number3
DOIs
StatePublished - May 15 1995
Externally publishedYes

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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