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2 results

  • 1 - Introduction: Count Data Containing Dispersion

  • Kimberly F. Sellers, Georgetown University, Washington DC
  • Book:
    The Conway–Maxwell–Poisson Distribution
    Published online:
    02 March 2023
    Print publication:
    09 March 2023, pp 1-21
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  • Summary

    This chapter is an overview summarizing relevant established and well-studied distributions for count data that motivate consideration of the Conway–Maxwell–Poisson distribution. Each of the discussed models provides an improved flexibility and computational ability for analyzing count data, yet associated restrictions help readers to appreciate the need for and usefulness of the Conway–Maxwell–Poisson distribution, thus resulting in an explosion of research relating to this model. For completeness of discussion, each of these sections includes discussion of the relevant R packages and their contained functionality to serve as a starting point for forthcoming discussions throughout subsequent chapters. Along with the R discussion, illustrative examples aid readers in understanding distribution qualities and related statistical computational output. This background provides insights regarding the real implications of apparent data dispersion in count data models, and the need to properly address it.

  • On A Model for the Claim Number Process*

  • Matti Ruohonen
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 18 / Issue 1 / April 1988
    Published online by Cambridge University Press:
    29 August 2014, pp. 57-68
    Print publication:
    April 1988
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  • A model for the claim number process is considered. The claim number process is assumed to be a weighted Poisson process with a three-parameter gamma distribution as the structure function. Fitting of this model to several data encountered in the literature is considered, and the model is compared with the two-parameter gamma model giving the negative binomial distribution. Some credibility theory formulae are also presented.