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Probabilities of choosing applicants of arbitrary rank in the secretary problem

Published online by Cambridge University Press:  14 July 2016

Peter A. Rogerson
Peter A. Rogerson*
Affiliation:
State University of New York at Buffalo
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Abstract

Gilbert and Mosteller (1966) derive the probability of obtaining the best secretary when a fixed number of potential employees of varying quality are interviewed sequentially by an employer. This paper extends these results by deriving the probability of selecting an applicant of arbitrary rank under a variety of circumstances concerning the objective of employers and the amount of information employers have about applicant quality.

Keywords

DECISION NUMBERSORDER STATISTICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 527 - 533
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This paper was written while the author was in the Departments of Civil Engineering and Geography, Northwestern University, Evanston, IL 60201, USA.

The support of NSF Grant SES 84-19773 is gratefully acknowledged.

References

Chow, Y., Moriguti, S., Robbins, H. and Samuels, S. (1964) Optimal selection based on relative rank. Israel J. Math. 2, 81–90.Google Scholar
Gilbert, J. P. and Mosteller, F. (1986) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 58, 35–73.Google Scholar
Rogerson, P. (1985) Alternative strategies for selling land to the highest bidder. Submitted for publication.Google Scholar