Frequency-Based Prediction Study of Burr X Distribution Under Type II Censoring

This paper investigates frequentist prediction methods for the Burr X distribution under Type II censored data. To address the challenges of small sample sizes and high censoring rates commonly encountered in survival analysis, we derive four point prediction methods: best unbiased prediction (BUP), maximum likelihood prediction (MLP), conditional median prediction (CMP), and median unbiased prediction (MUP). For interval prediction, we examine four approaches—the pivotal method, the Wald method, the highest conditional density (HCD) method, and the shortest-length method to construct prediction intervals. The finite-sample performance of these methods is evaluated through Monte Carlo simulations and illustrated using three real-world datasets. The results demonstrate that CMP provides the most stable point predictions, with its advantage being particularly pronounced in small samples due to the conditional median’s robustness to extreme values. For interval prediction, the pivotal method yields the most consistently reliable coverage. The shortest-length method exhibits high accuracy and efficiency. Analyses of three real datasets further validate the applicability of these methods to both complete and right-censored data.