Bimodality based on the generalized skew-normal distribution

This paper focuses on the development of a new extension of the generalized skew-normal distribution introduced in Gómez et al. [Generalized skew-normal models: properties and inference. Statistics. 2006;40(6):495–505]. To produce the generalization a new parameter is introduced, the signal of which has the flexibility of yielding unimodal as well as bimodal distributions. We study its properties, derive a stochastic representation and state some expressions that facilitate moments derivation. Maximum likelihood is implemented via the EM algorithm which is based on the stochastic representation derived. We show that the Fisher information matrix is singular and discuss ways of getting round this problem. An illustration using real data reveals that the model can capture well special data features such as bimodality and asymmetry.