The newly modified Weibull distribution defined in the literature is a model based on combining the Weibull and modified Weibull distributions. It has been demonstrated as the best model for fitting to the bathtub-shaped failure rate data sets. However, another new model based on combining the modified Weibull and Gompertz distributions has been demonstrated later to be even better than the first model. In this article, we have shown how to improve the former model into a better model, and more importantly, we have provided a full Bayesian analysis of the improved model. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. Bayes estimators have been obtained using Hamiltonian Monte Carlo for posterior simulations. Bayesian model checking has also been provided in order to check the validation of the model when fitting to real data sets. We have also provided the maximum likelihood estimators of the model parameters using the cross-entropy method to optimize the log-likelihood function. The results derived from the analysis of two well-known data sets show that the improved model is much better than its original form.

文献中定义的新修改的Weibull分布是基于Weibull和修改的Weibull分布相结合的模型。它已被证明是拟合浴缸形故障率数据集的最佳模型。然而，后来又证明了另一种基于修改后的Weibull和Gompertz分布的新模型比第一个模型更好。在本文中，我们展示了如何将以前的模型改进为更好的模型，更重要的是，我们提供了对改进模型的完整贝叶斯分析。汉密尔顿蒙特卡罗方法和交叉熵方法已被用来增强传统的统计估计方法。使用汉密尔顿蒙特卡洛方法进行后验模拟可获得贝叶斯估计量。还提供了贝叶斯模型检查，以便在拟合实际数据集时检查模型的有效性。我们还使用交叉熵方法提供了模型参数的最大似然估计量，以优化对数似然函数。对两个著名数据集的分析得出的结果表明，改进的模型比其原始形式要好得多。