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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
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    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.

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