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November 2003 On the multiplicity of the maximum in a discrete random sample
F. Thomas Bruss, Rudolf Grübel
Ann. Appl. Probab. 13(4): 1252-1263 (November 2003). DOI: 10.1214/aoap/1069786498


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.


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F. Thomas Bruss. Rudolf Grübel. "On the multiplicity of the maximum in a discrete random sample." Ann. Appl. Probab. 13 (4) 1252 - 1263, November 2003.


Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1038.62047
MathSciNet: MR2023876
Digital Object Identifier: 10.1214/aoap/1069786498

Primary: 60C05
Secondary: 60F05 , 62G30

Keywords: Convergence in distribution , exponential distribution , order statistics , probabilistic constructions , quantile transformation , Sukhatme--Rényi representation

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 4 • November 2003
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