A unified formula for various moments of the multivariate normal distribution with sectional truncation is derived using a non-recursive method, where sectional truncation is given by several sections (regions) for selection including single and double truncation as special cases. The moments include raw, central, arbitrarily deviated, non-absolute, absolute and partially absolute moments with non-integer orders for variables taking absolute values. The formula is alternatively shown using weighted Kummer’s confluent hypergeometric function and, in the bivariate case, the weighted Gauss hypergeometric function, where the weighted functions have advantages of fast convergence. Numerical illustrations with simulations show that the methods employed are relatively free from accumulating cancellation errors.

使用非递归方法推导了具有截断的多元正态分布各个矩的统一公式，其中截断由几个部分（区域）给出，供选择，包括单截和双截。力矩包括原始力矩，中心力矩，任意偏离力矩，非绝对力矩，绝对力矩和部分绝对力矩，对于采用绝对值的变量，它们具有非整数阶。该公式也可以使用加权的Kummer融合超几何函数显示，在双变量情况下，可以使用加权的高斯超几何函数显示，其中加权函数具有快速收敛的优点。带有仿真的数字说明表明，所采用的方法相对没有累积消除误差的现象。