Some Relationships Between Skew-Normal Distributions and Order Statistics from Exchangeable Normal Random Vectors

The article explores the relationship between distributions of order statistics from random vectors with exchangeable normal distributions and several skewed generalizations of the normal distribution. In particular, we show that the order statistics of exchangeable normal observations have closed skew-normal distributions, and that the corresponding density function is log-concave when the order statistic is extreme. Special attention is given to the bivariate case, which is related to the univariate skew-normal distribution. The applications discussed focus on the lifetimes of coherent systems.