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Recognizing both the maximum and the second maximum of a sequence

Published online by Cambridge University Press:  14 July 2016

M. Tamaki
M. Tamaki*
Affiliation:
Otemon Gakuin University
*
∗Postal address: Otemon Gakuin University, School of Economics, Ai 230 Ibaraki City, Osaka, Japan.
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Abstract

We consider the situation in which the decision-maker is allowed to have two choices and he must choose both the best and the second best from a group of N applicants. The optimal stopping rule and the maximum probability of choosing both of them are derived.

Keywords

OPTIMAL STOPPING RULESECRETARY PROBLEMDYNAMIC PROGRAMMINGMARKOV DECISION PROCESSOLA POLICYSEQUENTIAL DECISION ANALYSIS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 803 - 812
Copyright
Copyright © Applied Probability Trust 1979 

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References

Chow, Y. S., Moriguti, S., Robbins, H. and Samuels, S. M. (1964) Optimum selection based on relative rank (the ‘Secretary Problem’). Israel J. Math. 2, 81–90.CrossRefGoogle Scholar
Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.CrossRefGoogle Scholar
Gusein–Zade, S. M. (1966) The problem of choice and optimal stopping rule for a sequence of independent trials. Theory Prob. Appl. 11, 472–476.CrossRefGoogle Scholar
Lindley, D. V. (1961) Dynamic programming and decision theory. Appl. Statist. 10, 39–51.CrossRefGoogle Scholar
Mucci, A. G. (1973a) Differential equations and optimal choice problems. Ann. Statist. 1, 104–113.CrossRefGoogle Scholar
Mucci, A. G. (1973b) On a class of Secretary Problems. Ann. Prob. 1, 417–427.CrossRefGoogle Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden Day, San Francisco, CA.Google Scholar
Sakaguchi, M. (1978) Dowry problems and OLA policies. Rep. Stat. Appl. Res. JUSE 25, 124–128.Google Scholar