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Extreme order statistics with cost of sampling

Published online by Cambridge University Press:  01 July 2016

James Pickands III
James Pickands III*
Affiliation:
University of Pennsylvania
*
∗Postal address: Wharton Analysis Center, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.
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Abstract

Let X1, X2, …, Xn, … be mutually independent with common CDF F and, for each m, n, let Xm:n be the mth largest among the first n. We consider max1≤n<∞ (X1:n – cn) and the ‘optimal stopping rule' N which maximizes where all l and In particular, we consider and All of these are considered for c ϵ (0,∞) as well as asymptotically as c → 0+.

Keywords

EXTREME VALUESOPTIMAL STOPPING
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 783 - 797
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research supported by the United States Department of Energy Contract DE-AC01-81RG10494.

References

Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton-Mifflin, New York.Google Scholar
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Ross, S. (1970) Applied Probability with Optimization Applications. Holden-Day, San Francisco.Google Scholar