Series form of the characteristic functions of scale mixtures of multivariate skew-normal distributions

Abstract

Based on two series representations of the error function and a series representation of the Faddeeva function, the characteristic functions of scale mixtures of skew-normal distributions in univariate and multivariate cases are derived in series form instead of the previously suggested two-dimensional integral form without using contour integration. This is accomplished by applying the Lebesgue dominated convergence theorem to change the order of integral and limit. After integrating out each mixing variable, the series representation is expressed as in closed-form. Series form greatly reduces the computing times compared to the integral form, which is visualized via parallel box plots in a skew-t and a skew-slash distributions and a result of application on goodness-of-fit test.