Construção de uma Priori para os parâmetros do modelo de valores extremos generalizado baseada em quantis com distribuição gumbel

• Ano de defesa: 2006
• Autor(a) principal: Beijo, Luiz Alberto
• Orientador(a): Muniz, Joel Augusto
• Banca de defesa: Sáfadi, Thelma, Carvalho, Luiz Gonsaga de, Cancho, Vicente Garibay
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: UNIVERSIDADE FEDERAL DE LAVRAS
• Programa de Pós-Graduação: DEX - Departamento de Ciências Exatas
• País: BRASIL
• Palavras-chave em Português: Inferência bayesiana; Distribuição generalizada de valores extremos; Conhecimento a priori; Precipitação máxima; Generalized extreme value distribution; Bayesian approach; Maximum rainfall; Prior knowledge
• Área do conhecimento CNPq: CNPQ_NÃO_INFORMADO
• Link de acesso: https://repositorio.ufla.br/handle/1/4415

The generalized extreme value distribution (GEV) plays a key role in studies related to physical measurements where it is applied to describe the behavior of the extreme values or rare event As these values are extracted from the upper (or lower) tail of the original distribution, a scarce amount of data is obtained in most cases This can be usually a problem in the acquirement of reliable estimates on some measure of interest An alternative to overcome this potential problem and as a consequence to obtain an improvement in the quality of the estimates would be to use available information that certain specialists possess One theme of this paper is to propose an alternative prior distribution for the Bayesian approach of the GEV distribution that makes easier the incorporation of the information supplied by specialists The form proposed to introduce the prior knowledge of experts consists of using quantis of the GEV distribution assuming that they have a Gumbel distribution This approach makes easier the incorporation of the information once extreme quantis and Gumbel distribution parameters are standard quantities to specialists in extreme values analyses To evaluate the performance of this new approach 36 series of data for samples of different sizes and different values of parameters have been simulated It was also aimed to determine the punctual and the upper limit 95% estimates of the probable maximum rainfall for return periods of 10 and 20 years for the annual and month periods of the rainy station at region of Jaboticabal Sao Paulo States Brazil Posterior inference is obtained through Markov Chain Monte Carlo (MCMC) methods The proposed prior presented good results in the estimation of parameters of GEV distribution for samples of different sizes and in the determination of values of probable maximum rainfall estimates for the region of Jaboticabal It presented itself as a good alternative in the incorporation of prior knowledge in the study of extreme data.