Some skew-symmetric models

The skew-normal distributions have been introduced by many authors, e.g. Azzalini (1985), Arnold et al. (1993), Aigner et al. (1977), Andel et al. (1984). This class of distributions includes the normal distribution and possesses several properties which coincide or are close to the properties of the normal family. However, this class has a skewness parameter which makes it possible to have a reasonable model for a skewed population distribution thus providing a more flexible model which represents the data as adequately as possible. Besides being useful in modeling, they are helpful in studying the robustness, and in Bayesian analysis as priors. The construction of such models is based on the following lemma (see Azzalini, 1985).