Department of Statistics and Operation Research, Faculty of Science, King Saud University.
Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt.
Math Biosci Eng. 2022 Jul 8;19(10):9773-9791. doi: 10.3934/mbe.2022455.
The procedure of selecting the values of hyper-parameters for prior distributions in Bayesian estimate has produced many problems and has drawn the attention of many authors, therefore the expected Bayesian (E-Bayesian) estimation method to overcome these problems. These approaches are used based on the step-stress acceleration model under the Exponential Type-I hybrid censored data in this study. The values of the distribution parameters are derived. To compare the E-Bayesian estimates to the other estimates, a comparative study was conducted using the simulation research. Four different loss functions are used to generate the Bayesian and E-Bayesian estimators. In addition, three alternative hyper-parameter distributions were used in E-Bayesian estimation. Finally, a real-world data example is examined for demonstration and comparative purposes.
贝叶斯估计中先验分布超参数值的选择过程产生了许多问题，引起了许多作者的关注，因此期望贝叶斯（E-Bayesian）估计方法来克服这些问题。本研究在指数型 I 型混合截尾数据下的阶梯应力加速模型的基础上，采用了这些方法。本文推导了分布参数的值。为了将 E-Bayesian 估计与其他估计进行比较，通过模拟研究进行了比较研究。使用四种不同的损失函数生成贝叶斯和 E-Bayesian 估计量。此外，在 E-Bayesian 估计中还使用了三种替代的超参数分布。最后，为了演示和比较的目的，检查了一个实际的数据示例。
