Decompositions for Sum-of-Power Statistics and the Sample Central Moments

Ben O'Neill

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arXiv · 2109.05801

Decompositions for Sum-of-Power Statistics and the Sample Central Moments

Ben O'Neill

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Abstract

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.

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Ben O'Neill. 2021-09-13. Decompositions for Sum-of-Power Statistics and the Sample Central Moments. https://arxiv.org/abs/2109.05801

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