Department of Mathematics and Statistics, College of Sciences, King Faisal University, Al-Ahsa, Saudi Arabia.
Faculty of Commerce, Department of Applied Statistics and Insurance, Mansoura University, Mansoura, Egypt.
PLoS One. 2022 Jul 27;17(7):e0270750. doi: 10.1371/journal.pone.0270750. eCollection 2022.
In this paper two prediction methods are used to predict the non-observed (censored) units under progressive Type-II censored samples. The lifetimes of the units follow Marshall-Olkin Pareto distribution. We observe the posterior predictive density of the non-observed units and construct predictive intervals as well. Furthermore, we provide inference on the unknown parameters of the Marshall-Olkin model, so we observe point and interval estimation by using maximum likelihood and Bayesian estimation methods. Bayes estimation methods are obtained under quadratic loss function. EM algorithm is used to obtain numerical values of the Maximum likelihood method and Gibbs and the Monte Carlo Markov chain techniques are utilized for Bayesian calculations. A simulation study is performed to evaluate the performance of the estimators with respect to the mean square errors and the biases. Finally, we find the best prediction method by implementing a real data example under progressive Type-II censoring schemes.
在本文中，使用两种预测方法来预测渐进式 II 型删失样本下的未观测（删失）单位。单位的寿命遵循马歇尔 - 奥尔金帕累托分布。我们观察未观测单位的后验预测密度，并构建预测区间。此外，我们对马歇尔 - 奥尔金模型的未知参数进行推断，因此我们通过最大似然和贝叶斯估计方法观察点估计和区间估计。贝叶斯估计方法是在二次损失函数下获得的。使用 EM 算法获得最大似然法的数值，以及使用 Gibbs 和蒙特卡罗马尔可夫链技术进行贝叶斯计算。进行了模拟研究，以根据均方误差和偏差评估估计量的性能。最后，我们通过在渐进式 II 型删失方案下实施真实数据示例来找到最佳预测方法。
