中文摘要：

首先通过巧妙利用贝塔分布、F分布与t分布三者之间的关系,推导给出三大抽样分布高阶原点矩的计算公式;其次借助递推关系、二项展开式和伽玛积分推导出正态分布、威布尔分布和对数正态分布高阶原点矩的计算公式;最后利用上述公式给出这些分布的数学期望和方差的一些相关推论.

英文摘要：

The calculation formula for higher-order origin moment are derived for three sampling distributions by skillfully using beta distribution, F distribution and t distribution, then the calculation formula for higher-order origin moment are derived for normal distribution, Weibull distribution and logarithm normal distribution by recursive relation, binominal expansion and gamma integral, and finally some related generalizations on the mathematical expectations and variance by using the above formula are given.