Abstract A generalization of the linear failure rate called non-linear failure rate is introduced, analyzed, and applied to real data sets for both censored and uncensored data. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. We have obtained the Bayes estimators of parameters and reliability characteristics using Hamiltonian Monte Carlo and these estimators are considered under both symmetric and asymmetric loss functions. Additionally, the maximum likelihood estimators of parameters are obtained by using the cross-entropy method to optimize the log-likelihood function. The superiority of the proposed model and estimation procedures are demonstrated on real data sets adopted from references.

中文翻译：

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非线性故障率：使用哈密顿蒙特卡罗模拟的贝叶斯研究

摘要 引入、分析了称为非线性故障率的线性故障率的推广，并将其应用于审查和未审查数据的实际数据集。哈密​​顿蒙特卡罗和交叉熵方法已被用来增强传统的统计估计方法。我们已经使用哈密顿蒙特卡罗获得了参数和可靠性特征的贝叶斯估计量，这些估计量在对称和非对称损失函数下都被考虑。此外，通过使用交叉熵方法优化对数似然函数来获得参数的最大似然估计量。所提出的模型和估计程序的优越性在参考文献中采用的真实数据集上得到了证明。