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On the best-choice problem when the number of observations is random

Published online by Cambridge University Press:  14 July 2016

Joseph D. Petruccelli
Joseph D. Petruccelli*
Affiliation:
Worcester Polytechnic Institute
*
∗ Postal address: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.
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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.

Keywords

OPTIMAL STOPPINGSECRETARY PROBLEMRELATIVE RANKSOPTIMIZATION THEORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 165 - 171
Copyright
Copyright © Applied Probability Trust 1983 

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References

Gianini-Pettitt, J. (1979) Optimal selection based on relative ranks with a random number of individuals. Adv. Appl. Prob. 11, 720–736.CrossRefGoogle Scholar
Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.CrossRefGoogle Scholar
Irle, A. (1980) On the best choice problem with random population size. Z. Operat. Res. 24, 177–190.Google Scholar
Presman, E. L. and Sonin, I. M. (1972) The best choice problem for a random number of objects. Theory Prob. Appl. 18, 657–668.Google Scholar
Rasmussen, W. T. (1975) A generalized choice problem. J. Optimization Theory Appl. 15, 311–325.CrossRefGoogle Scholar
Rasmussen, W. T. and Robbins, H. (1975) The candidate problem with unknown population size. J. Appl. Prob. 12, 692–701.CrossRefGoogle Scholar