Skew Distributions Generated from Different Families

Following the recent paper by Gupta et al. [8], skew pdfs of the form $2 f (u) G (\lambda u)$ are generated, where the pdf $f$ and the cdf $G$ are taken to be different and to come from normal, Student's $t$, Cauchy, Laplace, logistic or the uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the $n$th moment and the characteristic function are derived. Graphical illustrations are also provided.