Volume 4, Issue 1, January 2015, Page: 26-32
Bayesian Estimation Based on Record Values from Exponentiated Weibull Distribution: An Markov Chain Monte Carlo Approach
Rashad Mohamed El-Sagheer, Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
Received: Jan. 10, 2015;       Accepted: Jan. 13, 2015;       Published: Jan. 23, 2015
DOI: 10.11648/j.ajtas.20150401.15      View  2657      Downloads  191
Abstract
In this paper, we consider the Bayes estimators of the unknown parameters of the exponentiated Weibull distribution (EWD) under the assumptions of gamma priors on both shape parameters. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are proposed. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. The approximate Bayes estimators obtained under the assumptions of non-informative priors are compared with the maximum likelihood estimators using Monte Carlo simulations. A numerical example is also presented for illustrative purposes.
Keywords
Exponentiated Weibull Distribution (EWD), Record Values, Bootstrap Methods, Bayes Estimation, Gibbs and Metropolis Sampler
To cite this article
Rashad Mohamed El-Sagheer, Bayesian Estimation Based on Record Values from Exponentiated Weibull Distribution: An Markov Chain Monte Carlo Approach, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 1, 2015, pp. 26-32. doi: 10.11648/j.ajtas.20150401.15
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