In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

中文翻译：

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通过应用程序推断来自 Chen 分布的逐步 II 型删失的竞争风险数据

在本文中，在存在竞争故障原因的情况下，考虑在渐进型 II 审查下对 Chen 分布的未知参数的估计。假设失效的潜在原因具有独立的陈分布，具有共同的形状参数，但不同的尺度参数。从频率论者的角度来看，通过期望最大化（EM）算法获得了参数的最大似然估计。此外，计算基于缺失信息原理的预期Fisher信息矩阵。通过使用获得的 MLE 的预期 Fisher 信息矩阵，构造参数的渐近 95% 置信区间。我们还应用 bootstrap 方法（Bootstrap-p 和 Bootstrap-t）来构建置信区间。从贝叶斯角度来看，通过应用马尔可夫链蒙特卡罗（MCMC）程序计算未知参数的贝叶斯估计，还进行了可信区间的平均长度和覆盖率。贝叶斯推理基于平方误差、LINEX 和一般熵损失函数。通过模拟研究评估点估计器和置信区间的性能。最后，为了说明的目的，考虑了一个真实的例子。