双边I型删失下Topp-Leone分布的参数及可靠度的估计

Estimation of the Parameter and Reliability for the Topp-Leone Distribution Under Type-Ⅰ Doubly Censoring

首先,在双边Ⅰ型删失样本下得到Topp-Leone分布中参数的极大似然估计、渐近置信区间和Bootstrap置信区间,并进一步得到可靠度函数的渐近置信区间.其次,在不同的损失函数下得到了参数和可靠度函数的Bayes估计.通过蒙特卡罗模拟,计算出参数估计的均值和平均相对误差.最后,为了说明目的,还采用了一个真实的数据集.

Firstly, the maximum likelihood estimation, asymptotic confidence interval and Bootstrap confidence interval of the unknown parameter for the Topp-Leone distribution are obtained under Type-Ⅰ doubly censored samples. Furthermore, the asymptotic confidence interval of the reliability function is also given. Secondly, under different loss functions, Bayesian estimates of the unknown parameter and reliability function are obtained. Monte Carlo simulation is carried out to calculate the mean values and average relative errors of the parameter estimation. Finally, a real life data set is also taken up for illustrative purpose.