Abstract
This paper suggests new estimators for cumulative distribution function (CDF) using L ranked set sampling (LRSS) and robust extreme ranked set sampling (RERSS) methods. The proposed estimators are deduced based on maximum likelihood estimation method and its asymptotic properties are theoretically investigated. Comparison study has been made to demonstrate the efficiency of the proposed estimators. It is found that when the data contain outliers, the proposed estimators are less sensitive and have a satisfied behavior compared to their analog in ranked set sampling as the population CDF is far away from the boundaries. Motivated by this efficiency gain, we provided new estimators for system reliability R. = P(Y > X) using LRSS and RERSS. Through a Monte Carlo simulation study, the performance of the introduced reliability estimators is also examined. A real data set is analyzed to illustrate the applicability of the proposed various estimators.