Nonlinear regression in a trivariate elliptical distribution via a linear combination of order statistics |
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| Authors: | N. Balakrishnan S. H. Ong M. Habibi |
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| Affiliation: | 1. Department of Mathematics and Statistics , McMaster University , Hamilton , Canada;2. Institute of Mathematical Sciences, University of Malaya , Kuala Lumpur , Malaysia;3. Department of Statistics , Shahid Bahonar University , Kerman , Iran |
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| 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. |
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| Keywords: | trivariate elliptical distribution order statistics unified bivariate skew-elliptical distribution conditional distribution kernel function exchangeable distribution nonlinear regression |
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