IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i1p63-68.html
   My bibliography  Save this article

A fast and simple algorithm for finding the modes of a multinomial distribution

Author

Listed:
  • White, W.T.J.
  • Hendy, M.D.

Abstract

Suppose a trial has r possible outcomes, with the i-th outcome having probability pi, and . The outcome of n independent trials can be described by the frequencies , , where outcome i was selected with frequency . A mode (there can be multiple modes) is an outcome with maximal likelihood over all possible outcomes. Despite the ubiquity of multinomial distributions in statistical applications, the best algorithm to date for finding modes has unknown computational complexity and highly variable performance in practice. It is also vulnerable to precision problems due to accumulated roundoff error. We propose a new algorithm, GreedyModeFind, for calculating the mode(s) of this distribution, given n and . GreedyModeFind is simple, efficient and numerically robust, requiring O(rlogr) time and O(r) space to find one mode. A concise representation of the full set of joint modes can be found for an additional time cost of O(rlogr). In practice this algorithm drastically improves on the performance of earlier algorithms. We provide a freely available C++ implementation of GreedyModeFind.

Suggested Citation

  • White, W.T.J. & Hendy, M.D., 2010. "A fast and simple algorithm for finding the modes of a multinomial distribution," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 63-68, January.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:1:p:63-68
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00354-X
    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. Gall, Françoise Le, 2003. "Determination of the modes of a Multinomial distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 325-333, May.
    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. Gall, Françoise Le, 2006. "The modes of a negative multinomial distribution," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 619-624, March.

    More about this item

    Statistics

    Access and download statistics

    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:80:y:2010:i:1:p:63-68. 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.