ANALYSIS OF OVERDISPERSED COUNT DATA BY MIXTURES OF POISSON VARIABLESAND POISSON PROCESSES

Count data often show overdispersion compared to the Poisson distribut ion. Overdispersion is typically modeled by a random effect for the me an, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mi xture distributions, including the inverse Gaussian mixture distributi on. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation with in patients.