A Study of Skew-normal Distribution and Skew-t Distribution

Abstract

A Study of Skew-normal Distribution and Skew-t Distribution Professor Nan-Cheng Su. The distribution of weighted function of independent skew-normal random variables is useful in many applications. In this work first we will study properties of this distribution. The joint distribution of a linear form and a quadratic form will also be discussed. Next, through ratio of two independent skew-symmetric random variables, we propose a new family of univariate skew-t distributions, which can capture skewness and heavy tails. Properties of our skew-t distribution will be given. We also present some illustrative examples for the simulated data and the volcano height data.