Abstract
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.
Mathematics Subject Classification:
Acknowledgments
We would like to thank Professor Azzalini for several helpful comments. We also thank the referees and guest editor Arthur Pewsey for thoughtful and useful feedback on previous versions of the article. Jorge Navarro and José M. Ruiz are partially supported by the Spanish Ministerio de Ciencia y Tecnología under grant BFM2003-02947 and the Fundación Séneca under grant 00698/PI/04.