Decompositions for Sum-of-Power Statistics and the Sample Central Moments
Applications
2021-09-14 v1 Statistics Theory
Computation
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2109.05801,
title = {Decompositions for Sum-of-Power Statistics and the Sample Central Moments},
author = {Ben O'Neill},
journal= {arXiv preprint arXiv:2109.05801},
year = {2021}
}