Estimation of the mean of the exponential distribution using extreme ranked set sampling with unequal samples

Abstract

In many environmental studies, the main focus is on observational economy, that is to obtain data on the basis of cost effective and efficient sampling methods. In this paper, a ranked set sampling procedure with unequal samples based on extremes (ERSSU) is proposed, which reduces the cost and increases the precision of the estimator. Maximum likelihood estimator and modified maximum likelihood estimators are obtained and their properties are studied when the underlying distribution is exponential. These methods are studied under both perfect and imperfect ranking (with errors in ranking). These estimators are then compared with estimators based on simple random sampling (SRS) and ranked set sampling (RSS) procedures. It is shown that relative efficiencies of the estimators based on ERSSU are better than those of the estimator based on SRS. Simulation results show that efficiency of proposed estimator is better than estimators based on SRS and RSS, when errors in ranking are present.