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August, 1993 The Asymptotic Probability of a Tie for First Place
Bennett Eisenberg, Gilbert Stengle, Gilbert Strang
Ann. Appl. Probab. 3(3): 731-745 (August, 1993). DOI: 10.1214/aoap/1177005360

Abstract

Suppose that the scores of $n$ players are independent integer-valued random variables with probabilities $p_j$. We study the probability $P(T_n)$ that there is a tie for the highest score. The asymptotic behavior of this probability is surprising. Depending on the limit of $p_{j+1}/p_j$, we find different limits of different subsequences $P(T_{n(m)})$. These limits are evaluated for several families of discrete distributions.

Citation

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Bennett Eisenberg. Gilbert Stengle. Gilbert Strang. "The Asymptotic Probability of a Tie for First Place." Ann. Appl. Probab. 3 (3) 731 - 745, August, 1993. https://doi.org/10.1214/aoap/1177005360

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0787.60029
MathSciNet: MR1233622
Digital Object Identifier: 10.1214/aoap/1177005360

Subjects:
Primary: 60G70
Secondary: 60F05

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 3 • August, 1993
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