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Generalized poisson models arising from Markov processes

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  • Bosch, Ronald J.
  • Ryan, Louise M.

Abstract

We develop a family of distributions which allow for over- and underdispersion relative to the Poisson. This latter feature is particularly appealing since many existing methods only allow for overdispersion. These distributions arise from underlying continuous-time Markov processes in which event rates depend on how many events have already occurred. The results are illustrated with underdispersed count data from a polyspermy study and overdispersed data from the Canadian Sickness Survey.

Suggested Citation

  • Bosch, Ronald J. & Ryan, Louise M., 1998. "Generalized poisson models arising from Markov processes," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 205-212, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:3:p:205-212
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    References listed on IDEAS

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    1. R. W. Morgan, 1975. "Some Stochastic Models to Describe the Fertilization of an Egg," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(1), pages 137-138, March.
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    Cited by:

    1. Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    2. M. J. Faddy & R. J. Bosch, 2001. "Likelihood-Based Modeling and Analysis of Data Underdispersed Relative to the Poisson Distribution," Biometrics, The International Biometric Society, vol. 57(2), pages 620-624, June.

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