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.

Barakat 等人基于 II 型删失样本。（预测混合指数分布的未来寿命，Commun Stat Simul Comput https://doi.org/10.1080/03610918.2020.1715434, 2020）考虑了从具有已知参数的混合指数分布中预测未观察到的删失单位的问题。然后，他们讨论了在所有参数已知的情况下，如何使用关键量来获得非随机和随机样本大小的预测区间。在这项工作中，我们考虑了相同的预测问题，其中涉及尺度参数以及混合比例参数的模型参数都是未知的。此外，我们提出了不同的预测方法来获得未来寿命的预测区间，包括可能性、最高条件中位数和参数引导方法。在此设置中，考虑了两种情况。在第一种情况下，我们假设样本量是非随机的，而在第二种情况下，我们假设样本量是随机数。从我们的数值结果中可以看出，与本文考虑的所有其他预测区间相比，基于参数的 bootstrap 预测区间在覆盖概率方面具有可比性，并且在平均长度方面非常具有竞争力。