A new skew generalization of the normal distribution: properties and applications

Abstract

A new class of distribution functions with not-necessarily symmetric densities, which contains the normal one as a particular case, is introduced. The class thus obtained depends on a set of three parameters, with an additional one to the classical normal distribution being inserted. This new class of skewed distributions is presented as an alternative to the class of skew-normal and Balakrishnan skew-normal distributions, among others. The density and distribution functions of this new class are given by a closed expression which allows us to easily compute probabilities, moments and related measurements. Certain interesting regularity properties reduce the study of this class to one of a subset of standardized distributions. Finally, some applications are shown as examples.