Population moments and moments of the sample mean

Abstract

This paper presents new formulae which simultaneously express and estimate moments of the sample mean and estimate population moments, from a simple random sample drawn without replcement from a finite population. By avoiding the generality of the multivariate case, these two problems are not only unified but are made significantly more tractable. Explicit solution are given up to eighth moments. Asymptotic results for infinite populations are also given.

Keywords:

• finite population
• sampling without replacement
• estimation of moments
• symmetric mean
• h–statistics