Aslam Muhammad, Tahir Muhammad, Hussain Zawar, Al-Zahrani Bander
A Department of Basic Sciences, Riphah International University, Islamabad, 44000, Pakistan.
Department of Statistics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan.
PLoS One. 2015 May 20;10(5):e0126183. doi: 10.1371/journal.pone.0126183. eCollection 2015.
To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given.
为了研究某些工程过程的寿命，需要一个能够适应此类过程性质的寿命模型。与简单模型相比，潜在寿命分布的混合模型在直观上更适合且更有吸引力来对过程的异质性进行建模。本文旨在从贝叶斯视角研究瑞利分布的三成分混合模型。由于其在可靠性理论和生存分析中的广泛应用，本文考虑了删失抽样环境。在不同情况下推导了贝叶斯估计量及其后验风险的表达式。在没有或几乎没有先验信息的情况下，给出了超参数的确定方法。为了从数值上检验在不同损失函数下使用非信息先验和信息先验的贝叶斯估计量的性能，我们针对不同的样本量和测试终止时间模拟了它们的统计性质。此外，为了突出实际意义，还给出了一个基于实际工程数据的示例。
