Alyami Salem A, Hassan Amal S, Elbatal Ibrahim, Albalawi Olayan, Elgarhy Mohammed, El-Saeed Ahmed R
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
PLoS One. 2024 Dec 20;19(12):e0312937. doi: 10.1371/journal.pone.0312937. eCollection 2024.
This article examines the estimate of ϑ = P [T < Q], using both Bayesian and non-Bayesian methods, utilizing progressively first-failure censored data. Assume that the stress (T) and strength (Q) are independent random variables that follow the Burr III distribution and the Burr XII distribution, respectively, with a common first-shape parameter. The Bayes estimator and maximum likelihood estimator of ϑ are obtained. The maximum likelihood (ML) estimator is obtained for non-Bayesian estimation, and the accompanying confidence interval is constructed using the delta approach and the asymptotic normality of ML estimators. Through the use of non-informative and gamma informative priors, the Bayes estimator of ϑ under squared error and linear exponential loss functions is produced. It is suggested that Markov chain Monte Carlo techniques be used for Bayesian estimation in order to achieve Bayes estimators and the associated credible intervals. To evaluate the effectiveness of the several estimators created, a Monte Carlo numerical analysis is also carried out. In the end, for illustrative reasons, an algorithmic application to actual data is investigated.
本文使用贝叶斯方法和非贝叶斯方法，利用逐步首次失效删失数据，研究了ϑ = P [T < Q]的估计。假设应力（T）和强度（Q）是分别服从 Burr III 分布和 Burr XII 分布的独立随机变量，且具有共同的第一形状参数。得到了ϑ的贝叶斯估计量和最大似然估计量。通过非贝叶斯估计得到最大似然（ML）估计量，并使用德尔塔方法和 ML 估计量的渐近正态性构建了相应的置信区间。通过使用无信息先验和伽马信息先验，得到了平方误差损失函数和线性指数损失函数下ϑ的贝叶斯估计量。建议使用马尔可夫链蒙特卡罗技术进行贝叶斯估计，以获得贝叶斯估计量和相关的可信区间。为了评估所创建的几种估计量的有效性，还进行了蒙特卡罗数值分析。最后，出于说明目的，研究了对实际数据的算法应用。
