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Full-information best-choice problems with recall of observations and uncertainty of selection depending on the observation

Published online by Cambridge University Press:  01 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

n i.i.d. random variables with known continuous distribution function F are observed sequentially with the object of choosing the largest. After any observation, say the kth, the observer may solicit any of the first k observations. If the (k – t)th is solicited, the probability of a successful solicitation may depend on t, the number of observations since the (k – t)th, and on the quantile of the (k – t)th observation. General properties of optimal selection procedures are obtained and the optimal procedures and their probabilities of success are derived in some special cases.

Keywords

OPTIMAL STOPPINGSECRETARY PROBLEMFULL INFORMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982 , pp. 340 - 358
Copyright
Copyright © Applied Probability Trust 1982 

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References

Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.CrossRefGoogle Scholar
Guttman, I. (1960) On a problem of L. Moser. Canad. Math. Bull. 3, 35–39.CrossRefGoogle Scholar
Haghighi-Talab, D. and Wright, C. (1973) On the distribution of records in a finite sequence of observations, with an application to a road traffic problem J. Appl. Prob. 10, 556–571.CrossRefGoogle Scholar
Moser, L. (1956) On a problem of Cayley. Scripta Math. 22, 289–292.Google Scholar
Petruccelli, J. D. (1981) Best choice problems involving uncertainty of selection and recall of observations. J. Appl. Prob. 18, 415–425.CrossRefGoogle Scholar
Smith, M. H. (1975) A secretary problem with uncertain employment. J. Appl. Prob. 12, 620–624.CrossRefGoogle Scholar
Yang, M. C. K. (1974) Recognizing the maximum of a sequence based on relative rank with backward solicitation J. Appl. Prob. 11, 504–512.CrossRefGoogle Scholar