We introduce an extension of the skew generalized normal distribution called shape-skew generalized normal distribution. The proposed distribution has certain type of flexibility which is different from those given in other flexible skew normal distributions. It possesses properties such as uni/bimodality, skewness, wider range of the Pearson’s excess kurtosis coefficient ( γ2γ2 ) with respect to skew generalized normal distribution and preserving the most desirable features of the skew generalized normal distribution. Some basic distributional properties of the new extension including moments, moment generating function, characterization and relation to other distributions are derived. Also, the multivariate case of our proposed distribution is introduced and some of its properties are studied. The suitability of our model is demonstrated via comparisons with other generalized models.
