On the exact distribution of order statistics arising from a doubly truncated bivariate elliptical distribution

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.