Abbas Tahir, Tahir Muhammad, Abid Muhammad, Munir Samavia, Ali Sajid
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates.
College of Statistical Sciences, University of the Punjab, Lahore, Pakistan.
Sci Rep. 2024 Apr 6;14(1):8074. doi: 10.1038/s41598-024-58245-x.
Mixture distributions are naturally extra attractive to model the heterogeneous environment of processes in reliability analysis than simple probability models. This focus of the study is to develop and Bayesian inference on the 3-component mixture of power distributions. Under symmetric and asymmetric loss functions, the Bayes estimators and posterior risk using priors are derived. The presentation of Bayes estimators for various sample sizes and test termination time (a fact of time after that test is terminated) is examined in this article. To assess the performance of Bayes estimators in terms of posterior risks, a Monte Carlo simulation along with real data study is presented.
在可靠性分析中，混合分布比简单概率模型更自然地吸引人们对过程的异质环境进行建模。本研究的重点是开发和进行关于幂分布的三成分混合的贝叶斯推断。在对称和非对称损失函数下，推导了使用先验的贝叶斯估计量和后验风险。本文研究了不同样本量和测试终止时间（测试终止后的时间事实）下贝叶斯估计量的表现。为了根据后验风险评估贝叶斯估计量的性能，进行了蒙特卡罗模拟以及实际数据研究。
