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The candidate problem with unknown population size

Published online by Cambridge University Press:  14 July 2016

Will T. Rasmussen  and
Herbert Robbins
Will T. Rasmussen
Affiliation:
Naval Electronics Laboratory Center, San Diego, California
Herbert Robbins
Affiliation:
Columbia University
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Abstract

The familiar problem of maximizing the probability of choosing the best from a group of N candidates, where N is known, is extended to the case of N unknown. An a priori distribution is assumed for N, and the case of a uniform distribution is examined. Let VN denote the probability of choosing the best from a group of at most N candidates, then it is shown that limN→∞VN = 2e–2.

Keywords

OPTIMAL STOPPINGDYNAMIC PROGRAMMINGOPTIMIZATION THEORYSEQUENTIAL DECISION ANALYSIS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 692 - 701
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Cayley, A. (1875) Mathematical questions and their solutions. Educational Times 22, 18–19.Google Scholar
[2] Chow, Y. S., Moriguti, S., Robbins, H. and Samuels, S. M. (1964) Optimal selection based on relative rank. Israel J. Math. 6, 81–90.Google Scholar
[3] Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin Co., Boston.Google Scholar
[4] Gilbert, J., and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.Google Scholar
[5] Rasmussen, W. T. (1974) A generalized secretary problem: choosing any of the d best from a sequence of independent values. To appear.Google Scholar
[6] Rasmussen, W. T. (1975) A generalized choice problem. J. Optimization Theory Appl. 15, 311–325.CrossRefGoogle Scholar