Location-scale mixture of skew-elliptical distributions: Looking at the robust modeling

Abstract

A flexible class of skew-slash distributions which is a location-scale mixture of skew-elliptically distributed random variable with power of a beta random variable is presented. This family of distributions, which is a generalization of location-scale mixture of normal and beta distributions, contain some existing and important distributions and is appropriate for modeling data with skewness and heavy tail structure. Some distributional properties and the moments of this new family of distributions are obtained. In the special case of location-scale mixture of skew-normal distribution, we estimate the parameters via an EM-type algorithm and a simulation study and an application to real data are provided for illustration. Finally we extend some results to multivariate case.