On the multiplicity of the maximum in a discrete random sample

• 成果类型: Article
• 署名作者: Bruss, FT; Grübel, R
• 署名单位: Universite Libre de Bruxelles; Leibniz University Hannover
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 1252-1263
• 关键词: NUMBER

摘要

Let M-n be the maximum of a sample X-1,..., X-n from a discrete distribution and let W-n be the number of i's, 1 less than or equal to i less than or equal to n, such that X-i = M-n. We discuss the asymptotic behavior of the distribution of Wn as n --> infinity. 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-Renyi representation of exponential order statistics, which gives, as we think, a new insight into the problem.