A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF THE LIMITING PROBABILITY OF A TIE FOR FIRST PLACE

Autor(en): BARYSHNIKOV, Y
EISENBERG, B
STENGLE, G
Stichwörter: EXISTENCE OF THE LIMITING PROBABILITY; GEOMETRIC DISTRIBUTION; HIGHEST SCORE; LOGARITHMIC SUMMABILITY; Mathematics; Statistics & Probability; TAUBERIAN THEOREM; TIE
Erscheinungsdatum: 1995
Herausgeber: ELSEVIER SCIENCE BV
Journal: STATISTICS & PROBABILITY LETTERS
Volumen: 23
Ausgabe: 3
Startseite: 203
Seitenende: 209
Zusammenfassung: 
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.
ISSN: 01677152
DOI: 10.1016/0167-7152(94)00114-N

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