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.
Publié le : 1993-08-14
Classification:
Tie,
asymptotic probability,
record value,
order statistics,
logarithmic summability,
geometric distribution,
60G70,
60F05
@article{1177005360,
author = {Eisenberg, Bennett and Stengle, Gilbert and Strang, Gilbert},
title = {The Asymptotic Probability of a Tie for First Place},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 731-745},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005360}
}
Eisenberg, Bennett; Stengle, Gilbert; Strang, Gilbert. The Asymptotic Probability of a Tie for First Place. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 731-745. http://gdmltest.u-ga.fr/item/1177005360/