Evaluating Advanced Ranked Set Sampling Methods for Parameter Estimation in the Lehmann Family of Distributions

This study focuses on improving parameter estimation for the Lehmann family of distributions (LEM_F) by employing advanced ranked set sampling (RSS) techniques. We evaluate three sampling methods—traditional RSS, neoteric RSS (NRSS), and double neoteric RSS (DNRSS)—with an emphasis on maximum likelihood estimators (MLEs) for the generalized exponential distribution (GE), a key member of the LEM_F. Through extensive simulation studies and analysis of real-world data, we demonstrate that NRSS and DNRSS outperform traditional RSS in terms of estimation accuracy and efficiency. Specifically, DNRSS consistently achieves the lowest mean square errors (MSEs) and the highest efficiency across various sample sizes and parameter configurations. These results underscore the enhanced precision and cost-effectiveness of NRSS and DNRSS, making them valuable tools for statistical inference in applications requiring accurate life testing and reliability analysis, such as engineering, medical research, and other fields where precise parameter estimation is critical. The findings advocate for the adoption of these advanced sampling methods to achieve more reliable and efficient statistical outcomes.