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Statistics
A Journal of Theoretical and Applied Statistics
Volume 46, 2012 - Issue 5
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Original Articles

Nonlinear regression in a trivariate elliptical distribution via a linear combination of order statistics

, , &
Pages 605-619 | Received 13 May 2010, Accepted 17 Nov 2010, Published online: 04 May 2011
 

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.

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