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Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process

Published online by Cambridge University Press:  14 July 2016

Minoru Yoshida
Minoru Yoshida*
Affiliation:
Osaka University
*
∗ Department of Applied Mathematics, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan.
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Abstract

Before some random moment θ, independent identically distributed random variables x1, · ··, xθ–1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.

In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.

Keywords

OPTIMAL STOPPING OF MARKOV RANDOM SEQUENCESBAYES FORMULASMALLEST EXCESSIVE MAJORANT
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 98 - 107
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Bojedecki, T. (1979) Probability maximizing approach to optimal stopping and its application to a disorder problem. Stochastics 3, 61–71.CrossRefGoogle Scholar
[2] Degroot, M. H. (1970) Optimal Statistical Decision. McGraw-Hill, New York.Google Scholar
[3] Liptser, R. S. and Shiryayev, A. N. (1977) Statistics of Random Processes I. Springer-Verlag, New York.Google Scholar
[4] Shiryaev, A. N. (1973) Statistical Sequential Analysis. Translations of Mathematical Monographs 38, American Mathematical Society, Providence, RI.Google Scholar
[5] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar