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Negative binomial distributions for point processes

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  • Gregoire, Gérard

Abstract

Negative binomial point processes are defined for which all finite-dimensional distributions associated with disjoint bounded Borel sets are negative binomial in the usual sense. For these processes we study classical notions such as infinite divisibility, conditional distributions, Palm probabilities, convergence, etc. Negative binomial point processes appear to be of interest because they are mathematically tractable models which can be used in many situations. The general results throw some new light on some well-known special cases like the Polya process and the Yule process.

Suggested Citation

  • Gregoire, Gérard, 1984. "Negative binomial distributions for point processes," Stochastic Processes and their Applications, Elsevier, vol. 16(2), pages 179-188, February.
    • Handle: RePEc:eee:spapps:v:16:y:1984:i:2:p:179-188
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    Cited by:

    1. Yuguang Ipsen & Ross Maller & Soudabeh Shemehsavar, 2020. "Limiting Distributions of Generalised Poisson–Dirichlet Distributions Based on Negative Binomial Processes," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1974-2000, December.
    2. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2019. "Ratios of ordered points of point processes with regularly varying intensity measures," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 205-222.
    3. Ipsen, Yuguang & Maller, Ross & Shemehsavar, Soudabeh, 2020. "Size biased sampling from the Dickman subordinator," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6880-6900.

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