On the exact distribution of order statistics arising from a doubly truncated bivariate elliptical distribution. (English) Zbl 1416.62290
Summary: This paper studies the “truncated extended skew elliptically contoured” (TESEC) distributions and their related properties, which have never been discussed in the literature. In particular, we show that the exact distributions of order statistics arising from a doubly truncated bivariate elliptical distribution can be formulated as a mixture of six TESEC distributions. The explicit formulae for computing the corresponding first two moments are also derived. The proposed results are illustrated with a real dataset relating to the mineral content in humerus bones on the dominant and non-dominant sides.
MSC:
| 62H10 | Multivariate distribution of statistics |
| 62G30 | Order statistics; empirical distribution functions |
| 62E15 | Exact distribution theory in statistics |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
generalized inverse Gaussian distribution; order statistics; symmetric generalized hyperbolic distribution; truncated extended skew elliptically contoured distributionReferences:
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