Moments of truncated scale mixtures of skew-normal distributions

Abstract

In this work, we consider the problem of finding the moments of a doubly truncated member of the class of scale mixtures of skew-normal (TSMSN) distributions. We obtain a general result and then use it to derive the moments in the case of doubly truncated versions of skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. Many properties of the TSMSN family are studied, inference procedures are developed and a simulation study is performed to assess the procedures. Two applications are also provided, one of them in the context of censored regression models and another in the field of actuarial sciences.