Bayesian Predictive Inference for Future Order Statistics from the Two-Parameter Lomax Distribution under Type-II Censoring.

This study develops Bayesian predictive procedures for future order statistics from the two-parameter Lomax distribution under Type-II censored sampling schemes. The proposed framework combines predictive likelihood inference with Bayesian prediction based on independent gamma priors and Markov Chain Monte Carlo (MCMC) simulation using the Metropolis-Hastings algorithm. Bayesian point predictors are derived under the squared error, LINEX, and general entropy loss functions, and predictive intervals are constructed from posterior predictive samples. A detailed Monte Carlo simulation study compares the proposed methods with the classical predictive maximum-likelihood approach across varying sample sizes and censoring levels. For the small-sample scenario (n = 20, r = 14), the Bayesian-LINEX predictor reduced the mean squared prediction error (MSPE) from 0.1542-0.1182, decreased the average predictive interval width (APIW) from 2.4512-2.1985, and increased the coverage probability (CP) from 0.938-0.952 compared with the predictive maximum likelihood method. Overall, the Bayesian methods consistently outperformed the classical approach across all simulation settings, with the Bayesian-LINEX predictor achieving the best predictive performance. These findings demonstrate that the proposed Bayesian framework provides a more accurate and consistent approach for predicting future order statistics from the Lomax distribution while accounting for parameter uncertainty.