Bayesian Estimation and Prediction of Three-Parameter Complementary Exponential Power Distribution using MCMC Technique
Arun Kumar Chaudhary1, Vijay Kumar2

1Arun Kumar Chaudhary*, is an Associate Professor of Department of Management Science(Statistics), Nepal Commerce Campus, Tribhuwan University, Nepal.
2Vijay Kumar, Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, India. 

Manuscript received on December 02, 2020. | Revised Manuscript received on December 05, 2020. | Manuscript published on December 30, 2020. | PP: 164-174 | Volume-10 Issue-2, December 2020. | Retrieval Number: 100.1/ijeat.B20931210220 | DOI: 10.35940/ijeat.B2093.1210220
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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.
Keywords: Complementary exponential power model, Markov chain Monte Carlo, Bayesian estimation, Maximum likelihood estimation, Gamma Prior.