Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 5, September 2013, Pages: 128-141
Received: Aug. 17, 2013; Published: Aug. 30, 2013
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Authors
Mohamed Abdul Wahab Mahmoud, Mathematics Department, Faculty of Science, A1-Azhar University, Nasr-City 11884, Cairo, Egypt
Ahmed Abo-Elmagd Soliman, Mathematics Department, Faculty of Science, Islamic University, Madinh, Saudi Arabia
Ahmed Hamed Abd Ellah, Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
Rashad Mohamed El-Sagheer, Mathematics Department, Faculty of Science, A1-Azhar University, Nasr-City 11884, Cairo, Egypt
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Abstract
In this paper, based on a new type of censoring scheme called a progressive first-failure censored, the maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the Generalized Pareto (GP) distribution are derived. This type of censoring contains as special cases various types of censoring schemes used in the literature. A Bayesian approach using Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors. A numerical example is provided to illustrate the proposed methods. Finally, the maximum likelihood and different Bayes estimators are compared via a Monte Carlo simulation study.
Keywords
Generalized Pareto Distribution, Progressive First-Failure Censored Sample, Gibbs and Metropolis Sampler, Bayesian and Non-Bayesian Estimations, Bootstrap Methods
To cite this article
Mohamed Abdul Wahab Mahmoud, Ahmed Abo-Elmagd Soliman, Ahmed Hamed Abd Ellah, Rashad Mohamed El-Sagheer, Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 5, 2013, pp. 128-141. doi: 10.11648/j.ajtas.20130205.13
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