Modelo de dispersão Hiper-Poisson para variáveis discretas observáveis e não observáveis - Santos, Daiane de Souza (2019)
Poisson distribution is widely used to model count data, however it has the disadvantage the assumption that the data must have equal mean and variance, which is not always true, since in many situations the phenomenon of overdispersion (variance greater than average) or under- dispersion (variance lower than average) is common. Thus, we work with the hyper-Poisson distribution, which may accomodate data with overdispersion or underdispersion. The hyper- Poisson model is investigated here in two distinct scenarios, first modeling observable random variables in counting problems, and secondly representing an unobservable (latent) variable used in survival analysis models. In the first scenario, we take a classic approach for the estimation of the parameters of the hyper-Poisson distribution and we developed the usual likelihood ratio test, together with the gradient test to test the model dispersion parameter. In the survival analysis, we propose a new cure rate model induced by frailty discrete with hyper-Poisson probability distribution, since it is important to choose a distribution that takes into account the dispersion of risk factors. For this new model we developed inferential procedures from the classical and bayesian perspectives. All the models worked were analyzed through simulation studies and applied to real data sets.