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del Castillo, Joan; Pérez-Casany, Marta

Overdispersed and underdispersed Poisson generalizations. (English) Zbl 1121.62015

J. Stat. Plann. Inference 134, No. 2, 486-500 (2005).
Summary: We consider a wide set of statistical models that extend the Poisson distribution. These models are obtained through weighted versions of the Poisson family and can be approximated by a log-linear model. Under general conditions, we prove that the new models contain overdispersed and underdispersed distributions and that they can be parametrized with the mean and variance. A classical data set is analyzed to show the usefulness of the new models.

Cited in 39 Documents

MSC:

62E15 Exact distribution theory in statistics
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions

Keywords:

Exponential models; Stochastic orders; Weighted distributions; Index of dispersion; Zero-inflated distributions
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References:

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