Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T13:05:26.819Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References

Abdel-Hamid, A. R., Bather, J. A. and Trustrum, G. B. (1982) The secretary problem with an unknown number of candidates. J. Appl. Prob. 19, 619–630.CrossRefGoogle Scholar
Berger, J. O. (1980) Statistical Decision Theory. Springer-Verlag, Berlin.Google Scholar
Bruss, F. T. (1984) A unified approach to a class of best choice problems with an unknown number of options. Ann. Prob. 12, 882–889.CrossRefGoogle Scholar
Bruss, F. T. (1986) Identities in connection with the Pascal distribution. Rapport Interne 86/7, Dépt. Math., F.U. Notre-Dame, Namur.Google Scholar
Ciesielski, J. and Zabczyk, J. (1979) A note on a selection problem. Prob. Theory 5, 47–51.Google Scholar
Cowan, R. and Zabczyk, J. (1978) An optimal selection problem associated with the Poisson process. Theory Prob. Appl. 23, 584–592.CrossRefGoogle Scholar
Dynkin, E. B. and Juschkewitsch, A. A. (1969) Markov Prozesse — Sätze und Aufgaben. Springer-Verlag, Berlin.Google Scholar
Irle, A. (1980) On the best choice problem with random population size. Z. Operat. Res. 24, 177–190.Google Scholar
Petruccelli, J. D. (1983) On the best choice problem when the number of observations is random. J. Appl. Prob. 20, 165–171.CrossRefGoogle Scholar
Presman, E. L. and Sonin, I. M. (1972) The best choice problem for a random number of objects. Theory Prob. Appl. 17, 657–668.CrossRefGoogle Scholar
Stewart, T. J. (1981) The secretary problem with an unknown number of options. Operat. Res. 29, 130–145.Google Scholar
Yasuda, M. (1984) Asymptotic results for the best choice problem with a random number of objects. J. Appl. Prob. 21, 521–536.CrossRefGoogle Scholar

References added in proof

Sakaguchi, M. (1986) Best choice problems for randomly arriving offers during a random lifetime. Math. Japonica 31, 107–117.Google Scholar
Sakaguchi, M. and Tamaki, M. (1980) Optimal stopping problems associated with a non-homogeneous Markov process. Math. Japonica 25, 681–696.Google Scholar