On a class of two-piece skew-normal distributions

In this article, a class of uni/bimodal distributions is proposed as a model for data concentrated about two directions in roughly equal proportions. This is an extension of earlier work on the skew-normal distribution introduced by Azzalini [Azzalini, A., 1985, A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.]. The class, which depends on a shape parameter θ ∈ (−∞, ∞), includes the normal distribution as a special case. Further, it defines yet another conditional distribution of compositely truncated bivariate normal distributions. Some distributional properties and inferences of the class are studied and further extensions are described. A sample of 850 KEBIX (Korea e-business index) scores is shown to be well described by this model.