Bayesian inference for the Rayleigh distribution using ordered extreme k-records ranked set sampling with random sample sizes

This study presents an enhanced framework for statistical inference and prediction of the Rayleigh distribution using ordered extreme k-records ranked set sampling with both fixed and random sample sizes. We employ Bayesian methodologies to estimate the unknown parameter and develop predictive estimates under type II censoring, evaluating performance across three loss functions: Al-Bayyati, general entropy, and squared error. The approach extends to interval estimation via Bayesian probability intervals and highest posterior density intervals, as well as predictive frameworks for both point and interval forecasts. To validate our theoretical framework, we conduct extensive Monte Carlo simulations to evaluate the precision of our estimates and the reliability of confidence intervals. The practical applicability of these methodologies is demonstrated through their application to two empirical datasets, providing tangible evidence of their effectiveness in real-data scenarios.