In this paper, we establish efficient recursive algorithms for the computation of the cumulative distribution function (cdf) of multivariate Student’s t and multivariate unified skew-t distributions. The recurrence relations are over \(\nu \) (the degrees of freedom), and starting from the explicit results for \(\nu \)=1 and \(\nu \)=2, they enable the recursive evaluation of the cdf for any positive integral value of \(\nu \). Using these, we obtain results for the computation of orthant probabilities of multivariate Student’s t distribution. We then demonstrate the usefulness of the established results in some problems involving order statistics and reliability systems. Finally, we use two real data sets to illustrate the methods established here.

在本文中，我们建立了高效的递归算法，可对多元学生的累积分布函数（CDF）的计算ŧ和多元统一skew-牛逼分布。递推关系超过\(\nu \)（自由度），并且从\(\nu \) =1 和\(\nu \) =2的显式结果开始，它们能够递归评估cdf 为\(\nu \) 的任何正整数值。使用这些，我们获得了计算多元学生t的正交概率的结果分配。然后，我们在涉及订单统计和可靠性系统的一些问题中证明了已建立的结果的有用性。最后，我们使用两个真实的数据集来说明这里建立的方法。