Testing skew normality via the moment generating function

In this paper, goodness-of-fit tests are constructed for the skew normal law. The proposed tests utilize the fact that the moment generating function of the skew normal variable satisfies a simple differential equation. The empirical counterpart of this equation, involving the empiricalmoment generating function, yields appropriate test statistics. The consistency of the tests is investigated under general assumptions, and the finite-sample behavior of the proposed method is investigated via a parametric bootstrap procedure.