IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v65y2003i4p419-432.html
   My bibliography  Save this article

On optimal choosing of one of the k best objects

Author

Listed:
  • Porosinski, Zdzislaw

Abstract

A full-information continuous-time best choice problem is considered. A stream of objects being iid random variables with a known continuous distribution function is observed. The objects appear according to some renewal process independent of objects. The objective is to maximize the probability of selecting of one of the k best objects when observation is perfect, one choice can be made and neither recall nor uncertainty of selection is allowed. The horizon of observation is a positive random variable independent of objects. The natural case of a Poisson renewal process (with intensity [lambda]) and of exponentially distributed horizon (with parameter [mu]) is examined in detail. An optimal stopping rule stops at the first object which is greater than some constant level c(p) depending only on p=[mu]/([mu]+[lambda]). The probability of choosing the proper object P(win) is constant for all natural cases, i.e. when p is small. Simple formulae and numerical values for c(p) and P(win) are obtained. It is interesting that if p tends to 0, P(win) goes to 1 and c(p) goes to 0 at a much slower rate than exponentially fast.

Suggested Citation

  • Porosinski, Zdzislaw, 2003. "On optimal choosing of one of the k best objects," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 419-432, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:419-432
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00296-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Frank, Arthur Q. & Samuels, Stephen M., 1980. "On an optimal stopping problem of Gusein-Zade," Stochastic Processes and their Applications, Elsevier, vol. 10(3), pages 299-311, October.
    2. Bojdecki, Tomasz, 1978. "On optimal stopping of a sequence of independent random variables -- probability maximizing approach," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 153-163, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marek Skarupski, 2019. "Full-information best choice game with hint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 153-168, October.
    2. Demers, Simon, 2021. "Expected duration of the no-information minimum rank problem," Statistics & Probability Letters, Elsevier, vol. 168(C).
    3. Adam Woryna, 2017. "The solution of a generalized secretary problem via analytic expressions," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1469-1491, May.
    4. Abba M. Krieger & Ester Samuel-Cahn, 2014. "A generalized secretary problem," Discussion Paper Series dp668, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Ferenstein, Elzbieta Z. & Krasnosielska, Anna, 2010. "No-information secretary problems with cardinal payoffs and Poisson arrivals," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 221-227, February.
    6. Chris Dietz & Dinard van der Laan & Ad Ridder, 2010. "Approximate Results for a Generalized Secretary Problem," Tinbergen Institute Discussion Papers 10-092/4, Tinbergen Institute.
    7. Lazar Obradović, 2020. "Robust best choice problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 435-460, December.
    8. Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, June.
    9. You, Peng-Sheng, 2000. "Sequential buying policies," European Journal of Operational Research, Elsevier, vol. 120(3), pages 535-544, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:419-432. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.