Distribuição Marshall-Olkin normal e aplicações

Abstract

Marshall and Olkin in 1997 introduced a new family of distributions by adding a new parameter in a primitive distribution G(x). However, the authors did not study the general properties of this new family of distributions. In this work, a generalization of the normal family using the mechanism of Marshall-Olkin called normal Marshall-Olkin (MON) distribution was studied. For this distribution we obtained the mathematical properties, such as general expansions for the probability density functions and cumulative distribution, expressions of the maximum likelihood estimators of the parameters, the expected information matrix and identi_ability. The usefulness of this distribution is illustrated by a set of data showing that the MON distribution is more exible than other existing distributions in the literature as the logistic, Student t and Cauchy distributions.