| Summary: | Tese de mestrado, Estatística e Investigação Operacional (Estatística), 2023, Universidade de Lisboa, Faculdade de Ciências The occurrence of earthquakes is an issue with an extreme importance for the society due to the effects that they can cause. There are specific areas in the world with great seismic activity, like the Pacific fire Ring, that includes North and South America the Kamchatka Peninsula and some islands in the western Pacific ocean. The main goal of this study is to model high magnitude earthquakes. For this purpose the data from the ISG-GEM Catalogue was chosen to study the moment magnitude, ????????. Only severe earthquakes were considered (???????? > 6). From the available types of magnitude, ???????? was the one selected to study due to the fact that for very large earthquakes it gives the most reliable estimate of earthquake size and it provides an estimate of the earthquake size valid over the complete range of magnitudes. Similar studies were developed in a worldwide perspective (Pisarenko et al., 2014) and in specific regions, such as China (Ma, Bai, and Meng, 2021) and the Ecuadorian coast (García-Bustos et al., 2018). In a first approach a worldwide study was conducted, followed by a study of a specific region with high seismic activity (Japan). Extreme Value Theory provides the appropriate methods for modeling earthquakes with high magnitudes. In this master thesis, for both data sets, a study of some of the available variables from the ISG-GEM catalogue, being the moment magnitude the main one, was conducted. Earthquakes with high magnitude, for both the worldwide and the Japan data sets, were modelled using the Block Maxima and the Peaks Over Threshold methods. The main purpose was to estimate the tail probabilities and extreme quantiles. For both the worldwide and the Japan data sets, applying the Block Maxima method, the Generalized Extreme Value distribution was adjusted to the data, as well as a Gumbel model. Methods to compare and evaluate the statistical models were performed in order to ...
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