  Empirical distribution functions (EDFs) based on ranked set sampling (RSS)
and its modifications have been examined by many authors. In these studies, the
proposed estimators have been investigated for infinite population setting.
However, developing EDF estimators in finite population setting would be more
valuable for areas such as environmental, ecological, agricultural, biological,
etc. This paper introduces new EDF estimators based on level-0, level-1 and
level-2 sampling designs in RSS. Asymptotic properties of the new EDF
estimators have been established. Numerical results have been obtained for the
case when ranking is imperfect under different distribution functions. It has
been observed that level-2 sampling design provides more efficient EDF
estimator than its counterparts of level-0, level-1 and simple random sampling.
In real data application, we consider a pointwise estimate of distribution
function and estimation of the median of sheep's weights at seven months using
RSS based on level-2 sampling design.
