Abstract

In this paper, we develop unbiased estimators of the finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling. In addition, the ranked-set sampling scheme is also used in the secondary and tertiary sampling frames for further increasing the precision of the CDF estimators. This work is then extended to develop unbiased CDF estimators based on stratified two-stage and three-stage cluster sampling. Moreover, unbiased estimators of the variances of the proposed CDF estimators are also derived. Real datasets are considered to demonstrate the estimation of the CDF under these complex survey sampling schemes.

摘要

在本文中，我们使用两阶段和三阶段整群抽样开发了有限总体累积分布函数 (CDF) 的无偏估计量。此外，排序集抽样方案也用于二级和三级抽样框架，以进一步提高 CDF 估计器的精度。然后扩展这项工作以开发基于分层两阶段和三阶段整群抽样的无偏 CDF 估计量。此外，还导出了所提出的 CDF 估计量的方差的无偏估计量。真实数据集被认为是在这些复杂的调查抽样方案下证明 CDF 的估计。