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- Análise de sobrevivência e valores extremos em RPublication . Abreu, Ana Maria; Gouveia-Reis, DéliaO software R ´e uma ferramenta extremamente u´til para a investiga¸c˜ao estat´ıstica. No entanto, a prolifera¸c˜ao de bibliotecas (na ordem dos milhares) dificulta o r´apido e eficiente acesso a todas as possibilidades em cada uma das ´areas desta ciˆencia. Uma forma de limitar esta procura ´e aceder `a task view correspondente, se existir. Pelos motivos descritos, neste trabalho procura-se compilar informac¸˜ao relevante nas ´areas de an´alise de sobrevivˆencia e de valores extremos, de modo a minimizar as dificuldades referidas. A abordagem na an´alise de sobrevivˆencia, que possui task view, ser´a sobretudo atrav´es de exemplos. Nos valores extremos ser´a dada uma vis˜ao geral do que existe, uma vez que nesta ´area n˜ao h´a task view.
- Funções teste e funções generalizadas em dimensão 1. Descrição e caracterizaçãoPublication . Ferreira, Jorge; Gouveia, Délia; Reis, Maurício; Silva, José LuísNeste trabalho introduzimos uma família de espaços de funções teste definidas em R associadas à medida Gaussiana µ. Por dualidade obtemos a correspondente família de espaços de distribuições (ou funções generaliza das). A caracterização destas famílias à custa de funções inteiras com um certo tipo de crescimento é feita usando a transformada S. Como exemplo de aplicação apresentamos o produto de Wick entre funções generalizadas.
- Statistical modelling of extreme rainfall in Madeira IslandPublication . Réis, Délia Canha Gouveia; Lopes, Luiz Carlos Guerreiro; Mendonça, Sandra Maria FreitasExtreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.