The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.

中文翻译：

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基于递推关系的折叠和截断多元学生-t 分布的矩

截断多元学生 t 分布的前两个矩的使用引起了广泛应用的越来越多的关注。本文开发了涉及多元学生 t 分布密度的积分的递推关系。所提出的技术允许快速计算折叠和截断多元学生 t 分布的任意阶乘积矩，并提供折叠和截断多元学生 t 分布的低阶矩的显式表达式。应用包含正删失响应的真实数据示例来说明所提出方法的有效性和重要性。R MomTrunc 包已开发并在 CRAN 存储库上公开可用。