逐步Ⅰ型混合截尾下广义Pareto分布的参数估计

Parameter Estimation of Generalized Pareto Distribution under StepwiseⅠ-Type Mixed Censorship

为精准研判工业产品失效规律,得到更为准确的工业产品寿命,探讨逐步Ⅰ型混合截尾下广义Pareto分布的参数估计问题。构建了广义Pareto分布中形状参数?的极大似然估计(MLE)和Bayes估计。分别利用Bootstrap方法和Gibbs抽样法,获得了形状参数的Bootstrap置信区间和最大后验密度(HPD)置信区间。通过Monte Carlo数值模拟方法对形状参数的MIE和Bayes估计效果进行比较。设计了两种移走方案,开展了数值模拟试算和案例研究,结果表明:样本量方面,当样本量较小时,Bayes估计的平均相对偏差在0.3以下,好于MLE,当样本量较大时,MLE更为精准;方案选择方面,移走数目较多的方案更能节约试验成本,在相同置信度下,HPD置信区间优于Student-t置信区间。

In order to accurately judge the law of failure of industrial products and obtain a more accurate life of industrial products,the parameter estimation of generalized Pareto distribution under stepwiseⅠ-type mixed censorship was discussed.The maximum likelihood estimation(MLE)and Bayes estimation of shape parameters in the generalized Pareto distribution were constructed.Bootstrap confidence interval and highest posterior density(HPD)confidence interval of shape parameters were obtained by Bootstrap method and Gibbs sampling method respectively.Monte Carlo numerical simulation method was used to compare the MIE and Bayes estimation effects of shape parameters.Two removal schemes were designed,and the trial calculation by numerical simulation and a case study were carried out.The results show:when the sampling size is small,the average relative deviation of Bayes estimation is below 0.3,which is better than MLE,and while the sampling size is large,the MLE is more accurate;in terms of scheme selection,the scheme with a large amount of removal can save testing cost,and under the same confidence level,the HPD confidence interval is better than the Student-t confidence interval.