On the multiplicity of the maximum in a discrete random sample

Bruss, F. Thomas; Grübel, Rudolf

Ann. Appl. Probab., Tome 13 (2003) no. 1, p. 1252-1263 / Harvested from Project Euclid

Résumé

Let $M_n$ be the maximum of a sample $X_1,\ldots,X_n$ from a discrete distribution and let $W_n$ be the number of $i$'s, $1\le i \le n$, such that $X_i=M_n$. We discuss the asymptotic behavior of the distribution of $W_n$ as $n\to\infty$. The probability that the maximum is unique is of interest in diverse problems, for example, in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an approach based on the Sukhatme--Rényi representation of exponential order statistics, which gives, as we think, a new insight into the problem.

Publié le : 2003-11-14
Classification: Convergence in distribution, exponential distribution, order statistics, probabilistic constructions, quantile transformation, Sukhatme--Rényi representation, 60C05, 60F05, 62G30

@article{1069786498,
     author = {Bruss, F. Thomas and Gr\"ubel, Rudolf},
     title = {On the multiplicity of the maximum in a discrete random sample},
     journal = {Ann. Appl. Probab.},
     volume = {13},
     number = {1},
     year = {2003},
     pages = { 1252-1263},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069786498}
}

Bruss, F. Thomas; Grübel, Rudolf. On the multiplicity of the maximum in a discrete random sample. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp.  1252-1263. http://gdmltest.u-ga.fr/item/1069786498/