Bayesian Estimation and Prediction of Three-Parameter Complementary Exponential Power Distribution using MCMC Technique

Abstract

The Markov chain Monte Carlo (MCMC) technique is applied for estimating the Complementary Exponential Power (CEP) distribution's parameters through the analysis of complete sample in this article. With the help of the Bayesian and the Maximum Likelihood techniques, the unknown parameters of the model are estimated. To find Complementary Exponential Power distribution's parameters' Bayesian estimates, a new methodology is developed, via simulation method of MCMC through the application of OpenBUGS platform. To demonstrate under the gamma and uniform sets of priors, a real data set is taken. The generations of posterior MCMC samples is conducted with OpenBUGS software. For analyzing the output of so generated MCMC samples, and studying the statistical properties, distribution's comparison tools and model validation the functions of R have been used. The credible interval and predicted of the reliability, hazard and modal parameters' values are also estimated. We have shown that Bayesian estimators are more efficient than classical estimators for any real data set.