Open Access
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

Abstract

Let Mn be the maximum of a sample X1,,Xn from a discrete distribution and let Wn be the number of i's, 1in, such that Xi=Mn. We discuss the asymptotic behavior of the distribution of Wn as n. 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.

Citation

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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. https://doi.org/10.1214/aoap/1069786498

Information

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

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

Subjects:
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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