Population proportion estimator in modified ranked set sampling methods

Ranked set sampling (RSS) is becoming an alternative sampling method in recent years. RSS method is used where sample units can be easily ranked, but where the exact measurement of sample units is time consuming, difficult or expensive. It is proved that the sample mean of RSS is always more efficient than the sample mean of SRS of the same sample size. Modified ranked set sampling methods have been developed for mean estimator to reduce the ranking errors of the units selected from the target population in RSS method. There are many studies for mean estimators based on modified RSS methods, but few contributions for proportion estimators to RSS research. In the literature, to estimate the population proportion and the variance of the proportion estimator were used only PRSS from the modified ranked set sampling methods. In this thesis, the proportion estimators and associated variance estimators are obtained for binary variable with a concomitant variable based on modified ranked set sampling methods which are Extreme Ranked Set Sampling (ERSS), Median Ranked Sampling (MRSS), Percentile Ranked Set Sampling (Per-RSS) and L Ranked Set Sampling (LRSS) methods. The Monte Carlo simulation study is performed to compare the performance of estimators based on bias, mean squared error and relative efficiency for different levels of correlation coefficient, set and cycle size under Normal and Log-Normal distributions.