Classe de distribuições multivariadas para dados extremos dependentes, limitados e não estacionários - Leonardo Brandão Freitas do Nascimento (2023)
The model proposed in this work belongs to the class of Min-stable distributions and was obtained through the marginalization of a baseline distribution V conditioned on a latent random field with a positive alfa-stable distribution. It is suitable for modeling dependent extreme values that are non-stationary and within limited intervals. The model can be applied to time series and data with space-time interactions. Considering the interval (0,1), properties measuring dependence, such as the temporal and spatial extremogram, were obtained, along with conditional probabilities useful for making inferences and obtaining relevant practical results. In the context of time series, an EM algorithm was developed to estimate the model parameters, and an analytical expression for the observed information matrix was obtained, enabling confidence intervals and hypothesis tests to be conducted based on the asymptotic distribution of the estimators. Applying the model to air relative humidity data in Manaus identified months with a high probability of minimum humidity exceeding 0.70, indicating potential risks to human health. In the space-time analysis, the model proved suitable for modeling spatial dependence in extreme minima. The analysis revealed extreme climatic spatial patterns of humidity in the state of Amazonas that could pose risks to human health. Parameter estimates were obtained using the conditional MCEM algorithm, where the variance and hypothesis tests of the estimators were performed using the conditional bootstrap method.