In this project a method of sampling called Moving Extremes Ranked Set Sampling (MERSS) introduced by Al-Odat and Al-Saleh (2001) has been investigated parametrically under some known distributions. The Maximum Likelihood Estimator (MLE), and a modified MLE were considered and their were properties were studied. The method has been studied under both cases; perfect ranking (no error in ranking) and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE's using the usual simple random sampling. The method is illustrated using some real life data.