For the hierarchical inverse gamma and inverse gamma model, we calculate the Bayes posterior estimator of the rate parameter of the inverse gamma distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the rate parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the rate parameter of the inverse gamma distribution with a conjugate inverse gamma prior by the moment and MLE methods. In numerical simulations, we have illustrated four aspects: Consistency, goodness-of-fit, comparison, and marginal densities. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, the model could potentially be used to fit right skewed data, not left-skewed data.

对于分层逆伽马模型和逆伽马模型，我们计算了斯坦因损失函数下逆伽马分布速率参数的贝叶斯后验估计器，该函数对总高估和总低估均等进行惩罚，并对相应的后验斯坦因损失（PESL）进行惩罚。我们还获得了平方误差损失下的速率参数的贝叶斯后验估计器和相应的PESL。此外，我们通过矩量法和MLE方法获得了具有共轭反伽马的反伽马分布的速率参数的经验贝叶斯估计量。在数值模拟中，我们说明了四个方面：一致性，拟合优度，比较和边际密度。数值结果表明，在估计超参数时，MLE比矩估计器更好。最后，该模型可能会用于拟合右偏数据，而不是左偏数据。