Bayesian approach for the reliability parameter of power Lindley distribution

Abstract

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.