Estimation of the distribution function of a finite population utilizing auxiliary information in the context of non-response within complex survey sampling

This study focuses on estimating a finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling under non-response. This work is then extended to estimate the finite population CDF under non-response using stratified two-stage and three-stage cluster sampling. We propose two distinct families of CDF estimators, specifically designed for these complex surveys, namely classical ratio/product-type and exponential ratio/product-type. Furthermore, we introduce a difference estimator for the CDF under non-response, utilizing ancillary information about the variances and covariances of the estimators under these complex schemes. We provide mathematical expressions for the biases and mean squared errors of the proposed CDF estimators, based on first-order approximation. To evaluate the performance of the proposed estimators, we conduct extensive simulations and assess their efficiency. The simulation results demonstrate that the proposed families of estimators perform well under different sampling scenarios. Our findings indicate that difference CDF estimators are more explicit than the other estimators discussed. We support our theoretical claims by analyzing real datasets.