Flexible families of symmetric and asymmetric distributions based on the two-piece skew normal distribution

In this article, we first introduce a procedure for the construction of a general family of symmetric distributions. Then, using Azzalini's approach, we build a rich family of asymmetric distributions. Next, we focus our attention on a specific case of this general class of asymmetric distributions, which subsumes and extends several well-known uni/bimodal asymmetric distributions. Also, the 0-truncated version of the new distribution is studied as a flexible extension of the half-normal model. Finally, the practical utility of the proposed distribution in the modeling of empirical data is investigated through a set of real-life data.