An Efficient CDF Estimator Based on Dual-Rank Ranked Set Sampling with an Application to Body Mass Index Data

The dual-rank ranked set sampling (DRRSS) technique is recently proposed for estimating the population mean. The DRRSS-based estimator is verified to be superior to its analog under the traditional ranked set sampling (RSS) and simple random sampling (SRS) when the underlying distribution is symmetric. The main target of this study is to extend the work for estimating the cumulative distribution function (CDF) based on DRRSS. Using the empirical distribution function, a new CDF estimator is proposed and its basic properties are also discussed. Under perfect ranking as well as imperfect ranking setups, a comparison study is then conducted to demonstrate the performance of the proposed estimator relative to the RSS competitor for the same number of measured units. It is pointed out that the traditional RSS estimator is surpassed by the proposed estimator for the majority of the considered cases even if the quality ranking is not much well. Finally, the proposed DRRSS-CDF estimator is applied to a popular dataset in the context of the medical field known as "National Health and Nutrition Examination Survey" for illustrative purposes.