Método gerador de distribuições e classes de distribuições probabilísticas

Abstract

This work is divided into five chapters. The first one contains the objectives and the relevance of this study. In the second one, we review the literature presenting the state of the art in the field and we give an overview of the most used distributions which are the basis for the ones we generalize in later chapters. In the third chapter, the method for generating distributions is presented by means of a theorem and 7 corollaries. This method extends the probability distribution building process, so that the classes of distributions are constructed from pre-defined univariate monotonic functions and known distributions. In the fourth chapter, similarly to the third one, however, the construction was made from pre-defined multivariate monotonic functions and known multivariate distributions. We also conducted the development of new probability distributions and new generating functions of probability distribution classes. We illustrate the potentiality of this new univariate probability distribution we propose here by means of an application to an actual data set of excesses of flood peaks presented by Choulakian e Stephens (2001). For the application of the new multivariate distribution proposed, we used the database of measurements of Iris Flower exposed in Fisher’s work (1936). Six models were compared and, for their choice, we based on the Akaike Information Criterion (AIC), the Akaike Information Criterion corrected (AICc), Bayesian Information Criterion (BIC), the Hannan Quinn Information Criterion (HQIC) and the statistics of Cramér-von Mises and Anderson-Darling to assess the model fitting. Finally, we present the conclusions from de analyses, the comparisons from the results found in this thesis, the possibilities for research and ways to future works.