<p> The problem of obtaining a prediction interval at specified confidence level to contain k future observations from the Gumbel distribution, based on an observed sample from the same distribution, is considered. An existing method due to Hahn, which is originally valid for the normal, is adapted to the Gumbel case. Motivated by the equivalence between Hahn's prediction intervals and Bayesian predictive intervals for the normal, we develop Bayesian predictive intervals for the Gumbel in the case where the scale parameter b is both known and unknown. Furthermore, we perform comparison of Hahn's and Bayesian intervals. We find that the Bayesian is better in the b known case, while Hahn and Bayes perform about the same in the other case when b is unknown. We then consider the maximum of the Hahn's and Bayesian predicted lower limits which is shown to be a better predictor when b is unknown. All the discussions are based on Monte Carlo simulations. In the end, the results are applied to Ontario Power Generation data on feeder thicknesses.</p> / Thesis / Master of Science (MSc)

The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

Nos últimos anos, diversos autores têm concentrado seus esforços na generalização de distribuições de probabilidades obtendo, dessa forma, maior flexibilidade e, consequentemente, ganho na análise de dados e na capacidade de incorporar um grande número de sub-modelos nas distribuições generalizadas. Neste trabalho, serão apresentadas duas novas distribuições de probabilidade: McGumbel e gama Burr XII; e uma nova família de distribuições de probabilidade: Marshall-Olkin binomial negativa. Algumas propriedades das novas distribuições são apresentadas e o método de máxima verossimilhança foi utilizado para estimar os parâmetros dos modelos propostos. / In recent years, several authors have concentrated their efforts on the generalization of probability distributions obtained in this way more flexibility and hence gain in data analysis and the ability to incorporate a large number of sub-models in the generalized distributions. In this work, two new probability distributions will be presented: MacDonald Gumbel and gamma Burr XII; and a new family of probability distributions: negative binomial Marshall-Olkin. Some properties of the new distributions are presented and the method of maximum likelihood was used to estimate the parameters of the proposed models.

Submitted by Fernando Souza (fernandoafsou@gmail.com) on 2017-08-21T16:29:54Z No. of bitstreams: 1 arquivototal.pdf: 917941 bytes, checksum: e85ae298ee652a63fa17fc43f8fc6b8f (MD5) / Made available in DSpace on 2017-08-21T16:29:54Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 917941 bytes, checksum: e85ae298ee652a63fa17fc43f8fc6b8f (MD5) Previous issue date: 2016-03-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this paper, we analyze the problem of evaluating the influence of observations in the extreme value regression model (Gumbel regression) under type I censorship. This model is very important in the analysis of lifetime data. First, we obtain the log-likelihood function, the score function and Fisher's information matrix. Then we will discuss some methods of influence, such as global influence and the influence local. In the local influence analysis will derive the normal curvatures under various perturbation schemes. We conclude the work obtaining a closed-form expression for the generalized leverage. / Neste trabalho, analisaremos o problema de avaliar a influência de observações no modelo de regressão de valor extremo (regressão Gumbel) sob censura tipo I. Tal modelo é muito importante na análise de dados de tempo de vida. Primeiramente, obteremos a função log-verossimilhança, a função escore e a matriz de informação de Fisher. Em seguida discutiremos alguns métodos de influência, tais como a influência global e a influência local. Na análise de influência local, derivaremos expressões para as curvaturas normais sob diferentes esquemas de perturbações. Finalizaremos obtendo uma expressão de forma fechada para a alavancagem generalizada.

Nos últimos anos, diversos autores têm concentrado seus esforços na generalização de distribuições de probabilidades obtendo, dessa forma, maior flexibilidade e, consequentemente, ganho na análise de dados e na capacidade de incorporar um grande número de sub-modelos nas distribuições generalizadas. Neste trabalho, serão apresentadas duas novas distribuições de probabilidade: McGumbel e gama Burr XII; e uma nova família de distribuições de probabilidade: Marshall-Olkin binomial negativa. Algumas propriedades das novas distribuições são apresentadas e o método de máxima verossimilhança foi utilizado para estimar os parâmetros dos modelos propostos. / In recent years, several authors have concentrated their efforts on the generalization of probability distributions obtained in this way more flexibility and hence gain in data analysis and the ability to incorporate a large number of sub-models in the generalized distributions. In this work, two new probability distributions will be presented: MacDonald Gumbel and gamma Burr XII; and a new family of probability distributions: negative binomial Marshall-Olkin. Some properties of the new distributions are presented and the method of maximum likelihood was used to estimate the parameters of the proposed models.

In the case of soil chemical analyses, frequency distributions for some elements show a dissymmetrical aspect, with a very marked spread to the right or to the left. A high frequency of extreme values is also observed and a possible mixture of several distributions, due to the presence of various soil types within a single geographical unit, is encountered. Then, for the outliers detection and the establishment of detection limits, an original outliers detection procedure has been developed; it allows estimating extreme quantiles above and under which observations are considered as outliers. The estimation of these detection limits is based on the right and the left of the distribution tails. A first estimation is realised for each elementary geographical unit to determine an appropriate truncation level. Then, a spatial classification allows creating adjoining homogeneous groups of geographical units to estimate robust limit values based on an optimal number of observations. / Dans le cas des analyses chimiques de sols, les distributions de fréquences des résultats présentent, pour certains éléments étudiés, un caractère très dissymétrique avec un étalement très marqué à droite ou à gauche. Une fréquence importante de valeurs extrêmes est également observée et un mélange éventuel de plusieurs distributions au sein dune même entité géographique, lié à la présence de divers types de sols, peut être rencontré. Dès lors, pour la détection des valeurs aberrantes et la fixation des limites de détection, une méthode originale, permettant destimer des quantiles extrêmes au-dessus et en dessous desquelles les observations sont considérées comme aberrantes, a été élaborée. Lestimation des limites de détection est établie de manière distincte à partir des queues des distributions droite et gauche. Une première estimation par entité géographique élémentaire est réalisée afin de déterminer un niveau de troncature adéquat. Une classification spatiale permet ensuite de créer des groupes dentités homogènes contiguës, de manière à estimer des valeurs limites robustes basées sur un nombre dobservations optimal.