Finite mixture of semiparametric multivariate skew-normal distributions

Although the normal distribution is the most frequently used distribution for modeling a given data in many applications due to its desirable theoretical properties and computational convenience, it is often not suitable to model the data having asymmetric or heavy tailed distributions. The skew-normal distribution is an important alternative to the normal distribution as it can cover not only the normal distribution but also some asymmetric distributions. However, it cannot well approximate heavy tailed distributions. In this paper, we propose a semiparametric skew-normal distribution which contains skew-normal distributions using the nonparametric scale mixture of skew-normal distributions and apply the proposed model to finite mixture models so that we can obtain more efficient and insightful knowledge in the model-based cluster analysis. We provide a feasible algorithm to compute all parametric and nonparametric components in the proposed model. Numerical examples to show the applicability of the proposed model are also presented.