Bayesian approach for the reliability parameter of power Lindley distribution

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• 作者：Iman Makhdoom ; Parviz Nasiri ; Abbas Pak
• 刊名：International Journal of Systems Assurance Engineering and Management
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：7
• 期：3
• 页码：341-355
• 全文大小：943 KB
• 刊物类别：Engineering
• 刊物主题：Operating Procedures and Materials Treatment
  Quality Control, Reliability, Safety and Risk
  
• 出版者：Springer India
• 卷排序：7

文摘

This study investigates Bayesian inference on the reliability parameter \(R=P(X>Y)\) from the power Lindley (PL) distribution where X and Y are independent power Lindley random variables. Gamma distribution is used as the priors of parameters. Bayes and empirical Bayes (EB) approaches are provided in details. Based on an EB approach, hyperparameters in the prior distributions, are estimated using the method of moments and maximum likelihood estimates (MLEs). Further, noninformative and less informative priors are opted as the Bayes approaches. To estimate the reliability parameter, the posterior mode (PM) and posterior mean methods are obtained. Markov Chain Monte Carlo (MCMC) method is performed for the implementation of the posterior mean method. The accuracy of the estimation methods involving the MLEs in frequency school and the Bayesian estimate methods are investigated through the Monte Carlo simulations. An application example on a real data is performed for illustrative purpose. Finally, we will bring this research to the end with discussion on the results.KeywordsBayesian estimationPower Lindley distributionMaximum likelihood estimatesMarkov chain Monte CarloStress-strength modelPosterior mode method