We give some useful decompositions of sum-of-powers statistics, leading to decompositions for the sample mean, sample variance, sample skewness and sample kurtosis. We solve two related problems: computing these sample moments for a pooled sample composed of subgroups with known moments; and computing these sample moments for a subgroup using known moments from other subgroups and the overall pooled sample. Each task is accomplished via decompositions of the sums-of-squares, sums-of-cubes and sums-of-quads from which the sample central moments (up to fourth order) are formed. We give decomposition results and we implement these in a user-friendly R function.

翻译：我们对能量总和统计数据进行一些有用的分解,导致样本平均值、样本差异、样本毛细度和样本毛细度分解。我们解决了两个相关的问题:为由已知时间分组组成的集成样本计算这些样本时间;利用其他分组和总体集成样本的已知时间为分组计算这些样本时间。每一项任务都是通过对样本中央时间(直至第四顺序)的形成所根据的方块总和、立方体总和和方块分解完成的。我们给出分解结果,并在方便用户的R函数中执行这些结果。