Note on a new generalization of the skew-normal distribution

In this paper we define and study a three-parameter distribution, referred to as the Beta skew-normal distribution (BSN), which is a generalization of the skewnormal distribution introduced by Azzalini [1]. This family is obtained using the generator approach suggested by Eugene et al. [2] and Jones [3]. Some properties of the proposed distribution are discussed: among others the moment generating function, a recursion formula for its moments and two different methods which allow to simulate a BSN distribution. The densities in the family have a symmetric or asymmetric, unimodal or bimodal shape, depending on the values of the parameters. Some of the results presented in this work can be adapted for other distributions belonging to the family of the Beta-generated distribution, such as the Beta-normal (see [2]).