O processo de Poisson estendido e aplicações

• Ano de defesa: 2007
• Autor(a) principal: Salasar, Luis Ernesto Bueno
• Orientador(a): Louzada Neto, Francisco
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Estatística - PPGEs
• País: BR
• Palavras-chave em Português: Processo estocástico; Simulação; Inferência bayesiana; Modelos discretos
• Palavras-chave em Inglês: Stochastic processes; Extended Poisson process; Chapman-Kolmogorov diferential equations; Discrete models; Poisson, Binomial and Negative Binomial dis-tributions; Maximum likelihood estimators, confidence intervals and hypothesis test of parameters
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/4509

Abstract In this dissertation we will study how extended Poisson process can be applied to construct discrete probabilistic models. An Extended Poisson Process is a continuous time stochastic process with the state space being the natural numbers, it is obtained as a generalization of homogeneous Poisson process where transition rates depend on the current state of the process. From its transition rates and Chapman-Kolmogorov di¤erential equations, we can determine the probability distribution at any …xed time of the process. Conversely, given any probability distribution on the natural numbers, it is possible to determine uniquely a sequence of transition rates of an extended Poisson process such that, for some instant, the unidimensional probability distribution coincides with the provided probability distribution. Therefore, we can conclude that extended Poisson process is as a very ‡exible framework on the analysis of discrete data, since it generalizes all probabilistic discrete models. We will present transition rates of extended Poisson process which generate Poisson, Binomial and Negative Binomial distributions and determine maximum likelihood estima- tors, con…dence intervals, and hypothesis tests for parameters of the proposed models. We will also perform a bayesian analysis of such models with informative and noninformative prioris, presenting posteriori summaries and comparing these results to those obtained by means of classic inference.