IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v38y1991i1p167-183.html
   My bibliography  Save this article

The distributions of certain record statistics from a random number of observations

Author

Listed:
  • Bunge, J. A.
  • Nagaraja, H. N.

Abstract

Suppose we observe a random number N of independent identically distributed random variables in sequence. The record values are the successive maxima of this sequence. Assuming that N and the observations are independent, we obtain the joint distribution of the number of records and their values. Using this, the dependence structures of record values and interrecord counts are studied; this yields a necessary and sufficient condition for N to have geometric tail. In addition, we obtain the distribution of the number of records. When N is negative binomial, the expressions can be simplified; in one case the number of records has an exact Poisson distribution. Our results are applied to point process models considered by Gaver (1976) and Westcott (1977). Our results remain applicable when the assumption of identical distribution is relaxed to allow the distribution to change after a record event, as proposed by Pfeifer (1982).

Suggested Citation

  • Bunge, J. A. & Nagaraja, H. N., 1991. "The distributions of certain record statistics from a random number of observations," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 167-183, June.
    • Handle: RePEc:eee:spapps:v:38:y:1991:i:1:p:167-183
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(91)90077-P
    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.

    Citations

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


    Cited by:

    1. Gadi Barlevy, 2003. "Estimating models of on-the-job search using record statistics," Working Paper Series WP-03-18, Federal Reserve Bank of Chicago.
    2. Gadi Barlevy & H. N. Nagaraja, 2006. "Identification of Search Models with Initial Condition Problems," 2006 Meeting Papers 4, Society for Economic Dynamics.
    3. Gadi Barlevy & H. N. Nagaraja, 2010. "Estimating Mobility Rates in Search Models with Initial Condition Problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(4), pages 780-799, October.
    4. Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.
    5. Barranco-Chamorro, I. & Moreno-Rebollo, J.L. & Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2015. "Estimation of the sample size n based on record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 58-72.

    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:spapps:v:38:y:1991:i:1:p:167-183. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/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.