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A generalization of the classical secretary problem: dependent arrival sequences

Published online by Cambridge University Press:  14 July 2016

J. H. Reeves  and
V. F. Flack
J. H. Reeves*
Affiliation:
University of Georgia
V. F. Flack*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
∗∗ Postal address: Division of Biostatistics, School of Public Health, UCLA, CA 90024, USA.
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Abstract

This paper presents new methods for selecting the best population value under the classical secretary problem sequential selection rules. Unlike the classical case, the possible population arrival sequences considered here are not necessarily equally likely. When arrival orders in the sequence are rank dependent, the performance of the optimal solution to the standard problem (totally random arrival order assumed) is very poor, compared with procedures designed to guard against non-uniform arrival orders.

Keywords

DOWRY PROBLEMDEPENDENT ARRIVAL PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 97 - 105
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Freeman, P. R. (1983) The secretary problem and its extensions: A review. Internat. Statist. Rev. 51, 189–206.CrossRefGoogle Scholar
[2] Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.CrossRefGoogle Scholar
[3] Kendall, M. C. and Stuart, A. (1973) The Advanced Theory of Statistics , Vol. 2. Griffin, London.Google Scholar