Skewed Reflected Distributions Generated by the Laplace Kernel

Abstract

In this paper we construct some skewed distributions with pdfs of the form 2f(u)G(¸u), where ¸ is a real number, f(¢) is taken to be a Laplace pdf while the cdf G(¢) comes from one of Laplace, double Weibull, reflected Pareto, reflected beta prime, or reflected generalized uniform distribution. Properties of the resulting distributions are studied. In particular, expressions for the moments of these distributions and the characteristic functions are derived. However, as some of these quantities could not be evaluated inclosed forms, special functions have been used to express them. Graphical illustrations of the pdfs of the skewed distributions are also given. Further, skewness-kurtosis graphs for these distributions have been drawn.