任意n阶抽样样本量的最优分配

在抽样实践中，多阶抽样比单阶段抽样有更多的优点，而在各次具体抽样中，多阶抽样的阶数是一个变量，分析任意ｎ阶抽样的均值和均方误差及其估计是十分必要的，本文通过将文献（２）的（１０．２）式推广成定理１，在遵循简单随机抽样的原则下，解决了上述问题，获得定理２，并进一步讨论了在抽样费用或均方误差任意一方有限制的条件下，样本容量的最优分配方案，获得定理３，该方案能达到抽样费用最省或误差最小之目的。

Optimum Allocation for Sample Sizes in Random n-Stage Sampling

In practice, multi-stage sampling is more convenient than single-stage sampling. However, the number of stages of the n-stage sampling is a variable. It is very essential to estimate the mean, the mean square error and their estimates. In this paper, these problems are tackled and Theorem 2 is put forward using simple random method at all stages. Finally, the optimum allocation for sample sizes is discussed under limited conditions of sampling fees or mean square error. Theorem 3 is put forward accordingly.