A new ranked set sampling design for estimating population mean and variance based on neoteric ranked set sampling

Abstract

This paper proposes a new ranked set sampling (RSS) design, termed modified neoteric RSS (MNRSS), for efficient estimation of the population mean and variance. The proposed method extends the neoteric RSS (NRSS) framework by selecting sampled units in a more dispersed manner while avoiding extreme ranks, thereby improving population representation and estimation accuracy, particularly for the population variance. The theoretical properties of the proposed mean estimator are examined. Under perfect ranking, the estimator is shown to be unbiased when the underlying distribution is symmetric; for asymmetric distributions, it exhibits only a small bias. The performance of MNRSS was evaluated through an extensive simulation study involving several symmetric and asymmetric distributions. The proposed design was compared with simple random sampling (SRS), RSS, median RSS (MRSS), extreme RSS (ERSS), NRSS, systematic RSS (SRSS), and centralized RSS (CRSS). Performance was assessed using bias and mean square error (MSE). The results show that MNRSS generally outperforms the competing methods, particularly for estimating population variance and under asymmetric distributions. An application to Scots pine tree measurements further supports the practical usefulness of the proposed sampling design.