Abstract
We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
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