IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v69y2017i5d10.1007_s10463-016-0578-5.html
   My bibliography  Save this article

On coupon collector’s and Dixie cup problems under fixed and random sample size sampling schemes

Author

Listed:
  • James C. Fu

    (University of Manitoba)

  • Wan-Chen Lee

    (Health Canada)

Abstract

Suppose an urn contains m distinct coupons, labeled from 1 to m. A random sample of k coupons is drawn without replacement from the urn, numbers are recorded and the coupons are then returned to the urn. This procedure is done repeatedly and the sample sizes are independently identically distributed. Let W be the total number of random samples needed to see all coupons at least l times $$(l \ge 1)$$ ( l ≥ 1 ) . Recently, for $$l=1$$ l = 1 , the approximation for the first moment of the random variable W has been studied under random sample size sampling scheme by Sellke (Ann Appl Probab, 5:294–309, 1995). In this manuscript, we focus on studying the exact distributions of waiting times W for both fixed and random sample size sampling schemes given $$l \ge 1$$ l ≥ 1 . The results are further extended to a combination of fixed and random sample size sampling procedures.

Suggested Citation

  • James C. Fu & Wan-Chen Lee, 2017. "On coupon collector’s and Dixie cup problems under fixed and random sample size sampling schemes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1129-1139, October.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0578-5
    DOI: 10.1007/s10463-016-0578-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-016-0578-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-016-0578-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Brad C. Johnson & Thomas M. Sellke, 2010. "On the Number of i.i.d. Samples Required to Observe All of the Balls in an Urn," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 139-154, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kiyoshi Inoue, 2021. "On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1129-1153, September.

    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. Tung-Lung Wu, 2013. "On Finite Markov Chain Imbedding and Its Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 453-465, June.

    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:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0578-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.