Estimation of finite population distribution function in a complex survey sampling

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.