Abstract
In this paper, by assuming that (X, Y 1, Y 2)T has a trivariate elliptical distribution, we derive the exact joint distribution of X and a linear combination of order statistics from (Y 1, Y 2)T and show that it is a mixture of unified bivariate skew-elliptical distributions. We then derive the corresponding marginal and conditional distributions for the special case of t kernel. We also present these results for an exchangeable case with t kernel and illustrate the established results with an air-pollution data.
Acknowledgements
The authors are thankful to the referees for their useful comments on an earlier version of this manuscript. The last two authors also thank the Mahani Mathematical Research Center (Kerman, Iran) for its support.