Investigating the performance of Systematic Ordered Ranked Set Samples for mean and quantile estimation

Sampling plays a fundamental role in empirical research by enabling efficient estimation of population characteristics when a complete enumeration is impractical or costly. Over the years, a variety of sampling schemes have been developed, each with its own strengths, limitations, and specific applications. In this study, a novel sampling approach that blends Ranked Set Sampling (RSS) with Systematic Sampling (Sys) to capitalize on the advantages offered by both methods is introduced. The proposed method, referred to as Systematic Ordered Ranked Set Sampling (SORSS), is evaluated for estimating the population mean and a set of quantiles in finite populations. Through extensive Monte Carlo simulations, SORSS is examined across continuous distributions exhibiting both symmetric and skewed features. A parallel assessment compares the performance of conventional schemes: Simple Random Sampling (SRS), RSS, Extreme Ranked Set Sampling (ERSS), and Median Ranked Set Sampling (MRSS) using mean squared error (MSE) and bias as comparative metrics. To ground the findings in practical applications, the paper includes analysis on two real life climate data that corroborates the simulation results and demonstrates the method’s applicability.