Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes. (English) Zbl 0911.62101

Hougaard, Philip; Lee, Mei-Ling Ting; Whitmore, G. A.

Biometrics 53, No. 4, 1225-1238 (1997).

Summary: Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. 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 within patients.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62M99	Inference from stochastic processes

Keywords:

frailty; inverse Gaussian; negative binomial; power variance function; mixture distributions; epileptic seizures