Double Moving Extremes Ranked Set Sampling Design

Abstract

The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes.