Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution

The competing risks model may be of great importance for an investigator in medical studies or in reliability analysis. In this article, Bayesian prediction bounds of order statistics based on progressively type-II censored competing risks data from a general class of distributions are obtained. The class of distributions includes, among others, Weibull, compound Weibull, Pareto, Gompertz, compound Gompertz and half-logistic distributions. The results are then applied to the half-logistic distribution. Based on three different progressive type-II censoring schemes, prediction intervals of the future order statistics are obtained. An illustrative example is presented to show the procedure. A Monte Carlo simulation study is performed and numerical computations are carried out to obtain the coverage probabilities and average interval lengths of the prediction intervals.