Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1469" altimg="si259.svg"><mml:mi>t</mml:mi></mml:math> distribution

In this paper, we compute doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions well-known such as normal, Student’s t, slash, among others. We address members family, establishing neat formulation high-order and its first two moments. establish sufficient necessary conditions existence these Further, propose optimized methods to handle extreme setting parameters, partitions with almost zero volume or no truncation, which are validated numerical studies. All results have been particularized unified skew-t distribution, a complex heavy-tailed distribution includes extended skew-t, skew-normal, skew-normal distributions particular limiting cases.