STRATIFIED FOLDED RANKED SET SAMPLING FOR ASYMMETRIC DISTRIBUTIONS

This study evaluates the comparative efficiency of Stratified Folded ranked set sampling (SFRSS) in estimating the population mean against three other sampling methods: Simple Random Sampling (SRS), Stratified Simple Random Sampling (SSRS), and Random Sampling (RSS). The analysis spans various probability distributions, Exp(1), Geo(0.5), Gamma, Weibull, Log N(0,1), CHI(1). The results show that SFRSS outperforms or remains competitive with the other sampling methods, especially in simpler conditions (r=2), across a wide range of distributions. For instance, in the Exponential and Geometric distributions, SFRSS demonstrates superior efficiency at r=2, indicating its effectiveness in less complex scenarios. Similarly, for the Gamma and Weibull distributions, SFRSS maintains high efficiency at r=2, showcasing its adaptability and robustness in various conditions. Notably, in the Log-Normal distribution at r=5, SFRSS’s efficiency dramatically improves against SSRS, suggesting its particular suitability for skewed data under certain conditions. Additionally, SFRSS exhibits exceptional efficiency in the Chi-Square distribution at r=2, underscoring its effectiveness across diverse statistical landscapes. However, at the more complex condition (r=5), although the efficiency of SFRSS generally decreases, it still competes closely with SRSS and outperforms SSRS in certain cases, retaining its relevance and demonstrating a degree of adaptability to complex scenarios. This comprehensive analysis highlights the importance of selecting appropriate sampling strategies based on the study’s distribution characteristics and conditions. SFRSS emerges as a highly efficient method for estimating population means, particularly in less complex scenarios, and remains a competitive choice in more demanding conditions. The findings underscore the potential of SFRSS in optimizing estimation accuracy across various statistical distributions and study designs, affirming its value in statistical research and applications.