双边定数截尾下Topp-Leone分布的Bayes估计与预测

The Bayesian Estimation and Prediction for the Topp-Leone Distribution under Type-Ⅱ Doubly Censored Sample

在双边定数截尾样本下得到了Topp-Leone分布中参数的极大似然估计.基于无信息先验分布和Gamma先验分布,在平方损失和预防损失下分别得到了参数的Bayes估计.根据后验密度函数得到了未知参数的Bayes可信区间和未来观测值的预测密度,进而可得预测值和预测区间.利用Monte-Carlo模拟计算了参数的各种估计的均方误差,研究结果表明:当取Gamma先验分布时,在平方损失下参数的Bayes估计是最优的.最后通过一个寿命数据的例子计算出未知参数的估计以及未来观测值的预测值和预测区间.

In this paper,the maximum likelihood estimation of the parameter in the Topp-Leone distribution is obtained under type-II doubly censored sample.Based on the non-information prior distribution and Gamma prior distribution,the Bayesian estimation of the parameter is obtained under the squared loss and precautionary loss respectively.According to the posterior density function,the Bayesian credible interval of the unknown parameter and the predictive density of future observation are obtained,and then the predictive values and predictive intervals can be obtained.The mean square errors of various estimators are calculated by means of Monte-Carlo simulation,the conclusion is that the Bayesian estimation of the parameter is optimal under the Gamma prior distribution and the squared loss function.Finally,an example of life data is used to calculate the estimation of the unknown parameter,the predictive values and predictive intervals of future observation.