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Random record processes and state dependent thinning

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  • Browne, Sid
  • Bunge, John

Abstract

Suppose that a point process , ... if [0, [infinity]) is thinned by independently retaining Tn with probability pn. Our main examples are the classical p-thinning (pn [reverse not equivalent] p) and the random record process (pn = 1/n). When is a mixed, nonhomogeneous Poisson process, we find conditions under which the thinned process is Poisson. When is a pure birth process (gamma-mixed Poisson with exponential rate), we show that the record process is Markov renewal, with an interesting structure, and we compare this with related asymptotic results. When is a Mittag-Leffler renewal process (the homogeneous Poisson is a special case), we give a "Deheuvels-type" representation of the record process (Deheuvels, 1982) and related characterization results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:131-142
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    References listed on IDEAS

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    6. 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.
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    Cited by:

    1. Gnedin, Alexander, 2022. "The best choice problem with random arrivals: How to beat the 1/e-strategy," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 226-240.

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