On the identifiability of finite mixture of Skew-Normal and Skew-t distributions

In this paper, the class of all finite mixtures of skew-normal distributions is proved to be identifiable. Also, the class of all finite mixtures of Skew-t distributions with null location parameter is proved to be identifiable. In order to achieve the results, the real moments of a Skew-t random variable are explicitly obtained in a closed-form. The latter is given in terms of the Meijer G-function.