Skew-Symmetric Generalized Normal and Generalized <i>t</i> Distributions

Abstract

In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric 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.

Keywords

• skew-normal distribution
• skew-t distribution
• generalized skew-normal distribution
• generalized skew-t distribution
• skew-symmetric distributions
• recurrence relations