A generalized skew two-piece skew-normal distribution

In this paper, we discuss a general class of skew two-piece skew-normal distributions, denoted by GSTPSN(λ1, λ2, ρ). We derive its moment generating function and discuss some simple and interesting properties of this distribution. We then discuss the modes of these distributions and present a useful representation theorem as well. Next, we focus on a different generalization of the two-piece skew-normal distribution which is a symmetric family of distributions and discuss some of its properties. Finally, three well-known examples are used to illustrate the practical usefulness of this family of distributions.