A generalization of the Balakrishnan skew-normal distribution

The skew-normal distribution belongs to a family of distributions which includes the normal distribution along with an extra parameter to regulate skewness. Azzalini [Azzalini A., 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12, 171-178] was the first to introduce the skew-normal distribution and studied some of its properties. Balakrishnan [Balakrishnan, N., 2002. Discussion of "skewed multivariate models related to hidden truncation and/or selective reporting". Test 11, 37-39], as a discussant of Arnold and Beaver [Arnold, B.C., Beaver, R.J., 2002. Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test II, 7-54], later proposed a generalization of this distribution. In this paper, we introduce a new generalization of the Balakrishnan skew-normal distribution by explaining some important properties of this distribution. Also, we have described three methods for constructing this distribution. Finally, its multivariate extension has been presented.