On Moments of Folded and Truncated Multivariate Normal Distributions

Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online.

本文推导了涉及多元正态分布（multivariate normal distribution）密度的积分递推关系式。该递推关系可实现折叠型多元正态分布（folded multivariate normal distribution）与截尾型多元正态分布（truncated multivariate normal distribution）的矩的快速计算。该递推方法不仅具备优异的数值计算效率，还可直接获取折叠型与截尾型多元正态分布低阶矩的解析表达式。本文的补充材料可在线获取。