IDEAS home Printed from https://ideas.repec.org/a/hin/jnljps/482462.html
   My bibliography  Save this article

Success Run Waiting Times and Fuss-Catalan Numbers

Author

Listed:
  • S. J. Dilworth
  • S. R. Mane

Abstract

We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of consecutive successes in a sequence of independent Bernoulli trials, that is, the geometric distribution of order . We show that the series coefficients are Fuss-Catalan numbers and write the roots in terms of the generating function of the Fuss-Catalan numbers. Our main result is a new exact expression for the distribution, which is more concise than previously published formulas. Our work extends the analysis by Feller, who gave asymptotic results. We obtain quantitative improvements of the error estimates obtained by Feller.

Suggested Citation

  • S. J. Dilworth & S. R. Mane, 2015. "Success Run Waiting Times and Fuss-Catalan Numbers," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-11, September.
    • Handle: RePEc:hin:jnljps:482462
    DOI: 10.1155/2015/482462
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JPS/2015/482462.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JPS/2015/482462.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/482462?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
    ---><---

    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:hin:jnljps:482462. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.