Except-Extremes Ranked Set Sampling for Estimating the Population Variance with Two Applications of Real Data Sets

Abstract

The ranked set sampling (RSS) procedure was initially established by McIntyre (1952) for estimating the mean of forage and pasture yield as more precise than simple random sampling (SRS). Recently, Aldrabseh and Ismail (2023) suggested the except extreme RSS (EERSS) approach as a modification to RSS for estimating the population mean. In this paper, a new estimator of the population variance is proposed using the EERSS method. The mean squared error and bias equations of the new estimator are derived. When the underlying distribution is non-symmetric, a simulation study is conducted to evaluate the suggested estimator relative to SRS and RSS, based on the same number of measured units, in terms of the relative precision and bias values for several sample sizes. For symmetric distributions, the exact values of the bias and relative precision of the EERSS variance estimator are evaluated. Two real datasets are utilized to illustrate the performance of the suggested variance estimator. It is found that the EERSS variance estimator is more efficient than the SRS estimator and more precise than RSS in most cases, especially for small set sizes.