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.
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