Ranked set sampling from location-scale families of symmetric distributions

Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on r independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.