在逐步增加II型截尾寿命数据下,本研究深入探讨了比例危险率模型的参数以及可靠性指标的贝叶斯估计与样本预测问题。首先,通过频率方法对模型参数进行了预先估计,并分析了其相关性质。随后,在平衡损失函数框架下,本文得到了可靠性指标...在逐步增加II型截尾寿命数据下,本研究深入探讨了比例危险率模型的参数以及可靠性指标的贝叶斯估计与样本预测问题。首先,通过频率方法对模型参数进行了预先估计,并分析了其相关性质。随后,在平衡损失函数框架下,本文得到了可靠性指标的贝叶斯估计,同时也得出平衡损失比一般损失更加灵活的实用性结论。本文还进行了一系列数值模拟示例,其模拟结果与理论分析相一致。以上的理论研究和示例均证实了所提出的平衡损失下贝叶斯方法的实用性和有效性。This study delves into the Bayesian estimation and sample prediction issues of the proportional hazard rate model’s parameters and reliability indicators under progressive type-II censored lifetime data. Firstly, a preliminary estimation of the model parameters was conducted through frequency methods, and their related properties were analyzed. Subsequently, within the framework of the balanced loss function, this paper obtained the Bayesian estimation of the reliability indicators and also concluded that the balanced loss is more flexible and practical than the general loss. A series of numerical simulation examples were also conducted, and the simulation results were consistent with the theoretical analysis. The theoretical research and examples presented above all confirm the practicality and effectiveness of the proposed Bayesian method under balanced loss.展开更多
针对一种具浴盆型失效率曲线的寿命分布,本文在记录值数据场合研究了模型参数的置信集估计问题。首先,基于记录值样本构造枢轴量,进而分别建立模型参数的精确置信区间和置信域。其次,为补充起见,进一步利用大样本原理构造了模型参数的...针对一种具浴盆型失效率曲线的寿命分布,本文在记录值数据场合研究了模型参数的置信集估计问题。首先,基于记录值样本构造枢轴量,进而分别建立模型参数的精确置信区间和置信域。其次,为补充起见,进一步利用大样本原理构造了模型参数的渐近置信区间估计。最后,通过数值模拟和算例分析比较了不同置信集结果的优良性。This paper investigates the confidence set estimation problem of model parameters for a lifetime distribution with a bathtub-shaped failure rate curve in the case of recorded data. Firstly, based on the recorded value samples, pivotal quantities are constructed, and then exact confidence intervals and confidence regions for the model parameters are established separately. Secondly, for the sake of supplementation, the asymptotic confidence interval estimation of the model parameters was further constructed using the large sample principle. Finally, the superiority of different confidence set results was compared through numerical simulation and case analysis.展开更多
文摘在逐步增加II型截尾寿命数据下,本研究深入探讨了比例危险率模型的参数以及可靠性指标的贝叶斯估计与样本预测问题。首先,通过频率方法对模型参数进行了预先估计,并分析了其相关性质。随后,在平衡损失函数框架下,本文得到了可靠性指标的贝叶斯估计,同时也得出平衡损失比一般损失更加灵活的实用性结论。本文还进行了一系列数值模拟示例,其模拟结果与理论分析相一致。以上的理论研究和示例均证实了所提出的平衡损失下贝叶斯方法的实用性和有效性。This study delves into the Bayesian estimation and sample prediction issues of the proportional hazard rate model’s parameters and reliability indicators under progressive type-II censored lifetime data. Firstly, a preliminary estimation of the model parameters was conducted through frequency methods, and their related properties were analyzed. Subsequently, within the framework of the balanced loss function, this paper obtained the Bayesian estimation of the reliability indicators and also concluded that the balanced loss is more flexible and practical than the general loss. A series of numerical simulation examples were also conducted, and the simulation results were consistent with the theoretical analysis. The theoretical research and examples presented above all confirm the practicality and effectiveness of the proposed Bayesian method under balanced loss.
文摘针对一种具浴盆型失效率曲线的寿命分布,本文在记录值数据场合研究了模型参数的置信集估计问题。首先,基于记录值样本构造枢轴量,进而分别建立模型参数的精确置信区间和置信域。其次,为补充起见,进一步利用大样本原理构造了模型参数的渐近置信区间估计。最后,通过数值模拟和算例分析比较了不同置信集结果的优良性。This paper investigates the confidence set estimation problem of model parameters for a lifetime distribution with a bathtub-shaped failure rate curve in the case of recorded data. Firstly, based on the recorded value samples, pivotal quantities are constructed, and then exact confidence intervals and confidence regions for the model parameters are established separately. Secondly, for the sake of supplementation, the asymptotic confidence interval estimation of the model parameters was further constructed using the large sample principle. Finally, the superiority of different confidence set results was compared through numerical simulation and case analysis.
