IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v35y1981i1p49-55.html
   My bibliography  Save this article

On the unimodality of passage time densities in birth‐death processes

Author

Listed:
  • J. Keilson

Abstract

It has been shown [2] that for any ergodic birth‐death process the p.d.f. of Ton, the passage time from the reflecting state 0 to any level n is log‐concave and hence strongly unimodal. It is also known (cf [2]) that the p.d.f. of Tn, n+1 or Tn+1, n for such a process is completely monotone and hence unimodal. It has been conjectured that the p.d.f. for the passage time Tmn between any two states is unimodal. An analytical proof of the result is presented herein, based on underlying renewal structure and methods in the complex plane. It is further shown that the p.d.f. of Tmn can always be written as the convolution of two p.d.f.s, one completely monotone and the second PF and hence log‐concave.

Suggested Citation

  • J. Keilson, 1981. "On the unimodality of passage time densities in birth‐death processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 35(1), pages 49-55, March.
    • Handle: RePEc:bla:stanee:v:35:y:1981:i:1:p:49-55
    DOI: 10.1111/j.1467-9574.1981.tb00710.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9574.1981.tb00710.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9574.1981.tb00710.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
    ---><---

    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:bla:stanee:v:35:y:1981:i:1:p:49-55. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.