ABSTRACT

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton–Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model.

摘要

本文研究了自适应渐进II型删失样本下三参数指数幂Lindley分布的未知参数的统计推断。最大似然估计 (MLE) 无法明确表达，因此使用 Newton-Raphson 方法进行近似 MLE。研究了贝叶斯估计，并使用马尔可夫链蒙特卡罗方法计算贝叶斯估计。对于贝叶斯估计，我们考虑了两个损失函数，即：平方误差和线性指数（LINEX）损失函数，此外，我们对未知参数执行渐近置信区间和可信区间。使用模拟分析观察贝叶斯估计和 MLE 之间的比较，我们通过最小化参数点估计的偏差和均方误差来对一些建议的审查方案执行最佳标准。最后，使用一个真实的数据示例来说明该模型的拟合优度。