平衡损失函数下Cox模型的可靠性分析:记录值样本情形

摘要

Based on record statistics, the empirical Bayes estimation and prediction problems are derived for a class of exponential distributions. The hyperparameter is estimated by using the ML-Ⅱ method. Under the balanced squared error loss and balanced linear-exponential (Linex) loss functions, the empirical Bayes estimators and the prediction bounds of future records are obtained, respectively. A numerical example is given through the Monte-Carlo simulation to investigate the estimation accuracy.%本文在记录值样本下,分别讨论了一类指数分布可靠性指标的经验贝叶斯估计以及未来失效样本的预测问题.通过ML-Ⅱ方法估计超参数,进而在平衡均方损失和平衡Linex损失下,获得了相关指标的经验贝叶斯估计,并给出未来记录值样本的经验贝叶斯预测区间.利用Monte-Carlo模拟方法给出了一个数值算例,研究了结果的精确性.