IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i4d10.1007_s11009-022-09966-x.html
   My bibliography  Save this article

An Examination of the Negative Occupancy Distribution and the Coupon-Collector Distribution

Author

Listed:
  • Ben O’Neill

    (Australian National University)

Abstract

We examine the negative occupancy distribution and the coupon-collector distribution, both of which arise as distributions relating to hitting times in the extended occupancy problem. These distributions constitute a full solution to a generalised version of the coupon collector problem, by describing the behaviour of the number of items we need to collect to obtain a full collection or a partial collection of any size. We examine the properties of these distributions and show how they can be computed and approximated. We give some practical guidance on the feasibility of computing large blocks of values from the distributions, and when approximation is required.

Suggested Citation

  • Ben O’Neill, 2022. "An Examination of the Negative Occupancy Distribution and the Coupon-Collector Distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3229-3260, December.
  • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09966-x
    DOI: 10.1007/s11009-022-09966-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-022-09966-x
    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/s11009-022-09966-x?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. Sen, Ananda & Balakrishnan, N., 1999. "Convolution of geometrics and a reliability problem," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 421-426, July.
    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. Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
    2. Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1717-1723, August.
    3. Chaoran Hu & Vladimir Pozdnyakov & Jun Yan, 2020. "Density and distribution evaluation for convolution of independent gamma variables," Computational Statistics, Springer, vol. 35(1), pages 327-342, March.
    4. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    5. Thierry E. Huillet, 2019. "Partitioning Problems Arising From Independent Shifted-Geometric and Exponential Samples With Unequal Intensities," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-31, November.
    6. George P. Yanev, 2020. "Exponential and Hypoexponential Distributions: Some Characterizations," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    7. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    8. Zhao, Xuejing & Fouladirad, Mitra & Bérenguer, Christophe & Bordes, Laurent, 2010. "Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 921-934.
    9. Zhao, Peng & Balakrishnan, N., 2010. "Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 969-974, June.
    10. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
    11. Zhao, Peng & Hu, Taizhong, 2010. "On hazard rate ordering of the sums of heterogeneous geometric random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 44-51, January.

    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:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09966-x. 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.