Statistical inference for the generalized exponential distribution using ordered lower k-record ranked set sampling with random sample sizes

This article presents an innovative sampling strategy, ordered moving extremes lower k-record ranked set sampling, designed to enhance parameter estimation and prediction for the generalized exponential distribution. By incorporating k-record values with random sample sizes, we develop maximum likelihood estimation, classical Bayes estimation, and empirical Bayes estimators, leveraging informative priors under balanced loss functions, including balanced squared error and balanced linear exponential. Additionally, we utilize the pivotal prediction method to construct prediction intervals for future observations under double type-II censoring. Extensive simulation studies demonstrate that our approach significantly improves estimation accuracy by achieving lower mean squared errors and reduced bias compared to conventional methods. The efficacy of the proposed sampling method is further validated through its application to real-world medical datasets, showcasing its practical utility in enhancing statistical inferences for lifetime data analysis. The key findings highlight that ordered moving extremes lower k-record ranked set sampling effectively balances efficiency and accuracy, making it particularly well-suited for reliability studies and survival analysis.