Distributions of Ratios of Two Correlated Skew-Normal Variables and of Ratios of Two Linear Functions of Order Statistics from Bivariate Normal Distribution

In this article, we first derive the distribution of the ratio of two correlated skew-normal variables. Then, with , where |ρ|< 1, and (X 1:2, X 2:2) T denoting the corresponding order statistics, we consider two linear functions of these order statistics, viz., a 1 X 1:2 + a 2 X 2:2 and b 1 X 1:2 + b 2 X 2:2, and derive explicit expressions for the cumulative distribution function (cdf) and probability density function (pdf) of the ratios and .