Modelo de dispersão Hiper-Poisson para variáveis discretas observáveis e não observáveis

• Ano de defesa: 2019
• Autor(a) principal: Santos, Daiane de Souza
• Orientador(a): Cancho, Vicente Garibay
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
• Palavras-chave em Português: Distribuição hiper-Poisson; Teste gradiente; Modelos de fragilidade; Modelos com fração de cura; Algoritmo EM; Inferência bayesiana
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA
• Link de acesso: https://repositorio.ufscar.br/handle/ufscar/12175

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.