This article presents the expected Bayesian (E‐Bayesian) estimation of the scale parameter, reliability and failure rate functions of two‐parameter bathtub‐shaped lifetime distribution under type‐II censoring data with. Squared error loss function and gamma distribution as a conjugate prior distribution for the unknown parameter are used to obtain the E‐Bayesian estimators. Also, three different prior distributions for the hyperparameters for the E‐Bayesian estimators are considered. Some properties of the E‐Bayesian estimators are studied. Using minimum mean square error criteria, a simulation study is conducted to compare the performance of the E‐Bayesian estimators and the corresponding Bayes and maximum likelihood estimators. A real data set is analysed to show the applicability of the different proposed estimators. The numerical results show that the E‐Bayesian estimators perform better than the classical and Bayesian estimators.

中文翻译：

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两参数浴缸形寿命分布可靠性特征的E-贝叶斯估计及其应用

本文介绍了在II型检查数据下使用的两参数浴缸形寿命分布的尺度参数，可靠性和失效率函数的预期贝叶斯（E-Bayesian）估计。平方误差损失函数和伽玛分布作为未知参数的共轭先验分布用于获得E-贝叶斯估计量。此外，考虑了E-贝叶斯估计量的超参数的三个不同的先验分布。研究了E-贝叶斯估计量的一些属性。使用最小均方误差标准，进行了仿真研究，以比较E-贝叶斯估计量以及相应的贝叶斯和最大似然估计量的性能。分析实际数据集以显示不同提议的估计量的适用性。