Estimating of the distribution function under ranked set sampling with unequal probabilities

Ranked set sampling (RSS), suggested by McIntyre(1952), is a popular sampling strategy when the measurements of the sampleunits are relatively difficult (expensive and/or time-consuming). Theestimation of distribution function has received considerable attention in theliterature of RSS. Because many practical problems involve estimation ofdistribution function from experimental data. Many authors have proposedempirical distribution functions (EDFs) based on RSS and its modifications(see, for example, Stokes and Sager, 1988; Samawi and Al-Sagher, 2001, Nazariet al., 2016 and Zamanzade, 2019). For finite population setting, there are afew studies on estimation of distribution function (see, for example, Sevil andYildiz, 2017, 2020; Yildiz and Sevil, 2019). In this study, design-basedestimators for distribution function have been developed using RSS designs(level-0, level-1 and level-2). Some of their asymptotic properties have beeninvestigated. Theoretical and numerical results show that the level-2 samplingdesign provides a more efficient EDF estimator than its counterparts oflevel-0, leve-1 and simple random sampling.