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Pascal processes and their characterization

Author

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  • Bruss, F. T.
  • Rogers, L. C. G.

Abstract

Let ([Pi]t) be a counting process on + with the property that for any t, T with 0[less-than-or-equals, slant]t[less-than-or-equals, slant]T the distribution of [Pi]T given the past t is Pascal (negative binomial) with one parameter being [Pi]t+1 and the probability parameter depending only on t and T. Does such a process exist? If so, how is it characterized? Finally, what is the most convenient way to model such a process? These questions are motivated by the distinguished role of the Pascal distribution in finding explicit solutions of optimal selection problems based on relative ranks. We answer them completely.

Suggested Citation

  • Bruss, F. T. & Rogers, L. C. G., 1991. "Pascal processes and their characterization," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 331-338, April.
    • Handle: RePEc:eee:spapps:v:37:y:1991:i:2:p:331-338
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    Cited by:

    1. 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.
    2. Bruss, F. Thomas & Rogers, L.C.G., 2022. "The 1/e-strategy is sub-optimal for the problem of best choice under no information," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1059-1067.

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