Skew-symmetric generalized normal and generalized t distributions

Abstract

In this paper, we introduce the skew-symmetric generalized normal and the skewsymmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions.