We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.
Bibliographical noteFunding Information:
The authors thank two anonymous referees for suggestions that improved the paper. This research was partially supported by Grant FONDECYT 1040865/7050091-Chile and by NSF Grant DMS-0504896.
- Elliptically contoured
- Fundamental skew distribution
- Selection mechanism
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty