Extreme value Birnbaum - Saunders distribution : regression models and L - moments / Camilo Miguel Lillo Flores.

Magíster en Estadística.

The Birnbaum-Saunders model is a life distribution originated from a problem of material fatigue that has been largely studied and applied in recent decades. This distribution is receiving considerable attention due to its physical arguments and its good properties. A random variable following the Birnbaum-Saunders distribution can be stochastically represented by another random variable used as basis. Then, the Birnbaum-Saunders model can be generalized by switching the distribution of the basis variable using diverse arguments allowing to construct more general classes of models. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme measures. In this thesis, we describe, implement and apply an extreme value version of the Birnbaum-Saunders distribution. This distribution is useful to determinate the probability of events that are larger or smaller than others previously observed, based in the properties of the traditional Birnbaum-Saunders and the extreme value theory. We propose a methodology based on extreme value Birnbaum-Saunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with realworld extreme value environmental data using the methodology is provided as illustration. Furthermore, we propose a parameter estimator and goodness-of-fit methodology based on L-moments for extreme value Birnbaum-Saunders distribution. We further conduct a simulation study for evaluating the properties of the L-moments estimators. A statistical analysis of earthquake magnitudes in the global centroid moment tensor catalog from 1962 to 2015 based on regional frequency analysis and goodness-of-fit is developed.