Flexibilidade da família exponencializada via divergências de Kullback-Leibler e Jeffreys e distância L1

Abstract

In recent years, new distributions have emerged, most of them based on generators, such as Exponentiated, Kumaraswamy, Beta, among others. These new distributions appear with the aim of being more flexible and accommodating several sets of data with special characteristics, such as, for example, heavy-tailed, skewness and bimodalities. However, there are no studies on how flexible these new distributions are when compared to their simpler peers, the base distributions. Therefore, in this work an analysis of divergence between the base distributions and those obtained considering the Exponentiated generator will be performed. The flexibility of the generalization of the base distribution was measured through the Kullback-Leibler and Jefferys divergences and the distance L1, and explicit expressions were obtained for the entire family of Exponentiated distributions. Special cases were also considered, such as the Exponentiatial Exponentiated and Weibull Exponentiated distribution to evidence the results obtained. Finally, simulation studies were carried out with the Exponentiatial Exponentiated and Weibull Exponentiated distribution models in order to assess the behavior of the additional parameter, as well as the model’s flexibility, in addition to a simulation study to evaluate each of the measures used.