Asian Journal of Probability and Statistics

In this paper, we develop maximum likelihood (ML) estimation procedures and derive the Fisher information matrix for two Weibull populations under Joint Modified Maximum Ranked Set Sampling (JMxRSS), a sampling framework in which units from two populations are jointly ranked and selected for measurement. The Fisher information matrix is derived to facilitate statistical inference for the ML estimators. We also develop the likelihood ratio test (LRT) for testing the equality of scale parameters of two Weibull populations when the shape parameters are assumed to be known. The performance of the proposed methodology is evaluated under Joint Modified Maximum Ranked Set Sampling (JMxRSS), Joint Modified Minimum Ranked Set Sampling (JMnRSS), and Joint Simple Random Sampling (JSRS). A Monte Carlo simulation study conducted in RStudio demonstrates that the joint ranked set sampling schemes generally outperform JSRS in terms of ML estimation efficiency and statistical power of the LRT. Moreover, the proposed sampling schemes achieve reliable inference with fewer measured observations, highlighting their cost-effectiveness in situations where data collection is expensive or time-consuming. A real-data analysis further supports the practical applicability of the proposed methods and yields conclusions consistent with the simulation results.