Balakrishnan Skew-t Distribution and Associated Statistical Characteristics

As a discussant of Arnold and Beaver (2002), Balakrishnan proposed a generalized skew-normal (BSN) distribution. This new model has been encountered in the literature for modeling various data sets. In this paper, we propose a new generalization of skew t-distribution of Azzalini and Capitanio (2003), denoted by BST$\textit{BST}$, as a scale mixture of the BSN-distribution. This new model may be used for modeling data sets exhibiting a unimodal density function having some skewness as well as heavy tails with respect to the skew-normal distribution. An explicit expression for the probability density function and a recurrence formula for the cumulative distribution function of the BST$\textit{BST}$-distribution are derived. Some statistical characteristics of the proposed model including central moments, unimodality, and stochastic orders are investigated. Two representation theorems for BST$\textit{BST}$-distribution which may be used for generating copies from the new model are given. The problem of estimation of the unknown parameters on the basis of a random sample arising from BST$\textit{BST}$-distribution is considered. For illustration proposes, a real data set on strength of glass fibers, due to Smith and Naylor (1987), is analyzed using the procedures obtained.