Prediction of future censored lifetimes from mixture exponential distribution

On the basis of a Type-II censored sample, Barakat et al. (Predicting future lifetimes of mixture exponential distribution, Commun Stat Simul Comput https://doi.org/10.1080/03610918.2020.1715434, 2020) considered the problem of predicting the unobserved censored units from a mixture exponential distribution with known parameters. They then discussed how to use the pivotal quantity for obtaining prediction intervals for non-random and random sample size when all parameters are known. In this work, we consider the same problem of prediction where the model parameters involving the scale parameters as well as the mixing proportion parameter are all unknown. Further, we propose different prediction methods for obtaining prediction intervals of future lifetimes including likelihood, highest conditional median, and parametric bootstrap methods. In this set-up, two cases are considered. In the first case, we assume that the sample size is non-random, while in the second case, the sample size is assumed to be random number. It is shown from our numerical results that the parametric bootstrap-based prediction intervals are comparable in terms of coverage probability and very competitive in terms of average length when compared to all other prediction intervals considered in this paper.