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On an optimal selection problem of Cowan and Zabczyk

Published online by Cambridge University Press:  14 July 2016

F. Thomas Bruss
F. Thomas Bruss*
Affiliation:
Facultés Universitaires Notre-Dame de la Paix, Namur
*
∗ Postal address: Statistics Program, Department of Mathematics, University of California, Santa Barbara CA 93106, USA.
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Abstract

Cowan and Zabczyk (1978) have studied a continuous-time generalization of the so-called secretary problem, where options arise according to a homogeneous Poisson processes of known intensity λ. They gave the complete strategy maximizing the probability of accepting the best option under the usual no-recall condition. In this paper, the solution is extended to the case where the intensity λ is unknown, and also to the case of an inhomogeneous Poisson process with intensity function λ (t), which is either supposed to be known or known up to a multiplicative constant.

Keywords

OPTIMAL STOPPINGAPARTMENT PROBLEM(IN)HOMOGENEOUS POISSON PROCESSBAYESIAN INFERENCESTATIONARY STRATEGYELEMENTARY RENEWAL THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 918 - 928
Copyright
Copyright © Applied Probability Trust 1987 

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References

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References added in proof

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