Abstract
An extension of the Poisson distribution is derived by considering a stochastic point process where the duration has a generalized Weibull distribution. This distribution is able to represent under, equi and over dispersion, a useful feature in data analysis. The computation of the probabilities and renewal function (expected number of renewals) are examined. Parameter estimation by the method of maximum likelihood is considered with applications of the count distribution to real frequency count data exhibiting under and over dispersion. It is shown that the generalized Weibull count distribution fits much better than the Weibull and gamma duration models.
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