Characterization of the monotone case for a best choice problem with a random number of objects
type: Item
instance of: scholarly article
title: Characterization of the monotone case for a best choice problem with a random number of objects
zbMATH Open document ID: 1009.60034
DOI: 10.1016/S0167-7152(02)00038-X
published in: Statistics \& Probability Letters
publication date: 2002-09-05T00:00:00Z
review text: The author considers the following full-information best choice problem with a random number of objects. When the number of objects \(N\) is a random variable, a sequence of i.i.d. random variables \(X_1,X_2,\dots, X_N\) with a known continuous distribution \(F\) is observed sequentially. The objective is to maximize the probability of choosing the largest. Such a problem was investigated by the author [Stochastic Processes Appl. 24, 293-307 (1987; Zbl 0623.60059)], in which the monotone case occurs for a class of distributions of \(N\), \(N\) is characterized by the number of sign changes of certain sequence, and the optimal stopping time is given. The author gives a more convenient way of checking whether the distribution of \(N\) gives the monotone case and shows that the new characterization forms a class of distributions which is a subclass of IFR distributions.
reviewed by: Yoshio Ohtsubo
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 1796703
zbMATH Keywords: best choice problem
zbMATH Keywords: optimal stopping
zbMATH Keywords: monotone case
zbMATH Keywords: IFR distribution
author: Zdzisław Porosiński
MaRDI profile type: Publication
cites work: Q5342246
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description: scientific article; zbMATH DE number 1796703