Weighted Extreme Ranked Set Sample for Skewed Population

Abstract

Samawi et al. (1996) investigated the use of a variety of extreme ranked set samples (ERSSs) for estimating the population mean. They indicated that ERSSs give unbiased and more efficient estimators of the population mean , compared to simple random samples (SRSs), in case of symmetric distributions. Also, ERSSs are more practical than ranked set samples (RSSs) and reduce the ranking judgment error. However, ERSSs produce biased estimators for the population mean when the underlying distribution has a skewed shape. In this paper a generalization of ERSS namely the weighted extreme ranked set sample (WERSS) is suggested. WERSS gives an unbiased and more efficient estimate for the population mean of scale and location families of distributions, compared with SRS, using the same number of quantified units. Also, a sequential approach is introduced to estimate the population mean when a limited knowledge of the underlying distribution is available. Simulation as well as a real data example about the bilirubin level in jaundice neonatal babies are used to investigate and to illustrate the method.