Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution

Mohamed Abdul Wahab Mahmoud; Ahmed Abo-Elmagd Soliman; Ahmed Hamed Abd Ellah; Rashad Mohamed El-Sagheer

doi:doi:10.11648/j.ajtas.20130205.13

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Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution

Mohamed Abdul Wahab Mahmoud, Ahmed Abo-Elmagd Soliman, Ahmed Hamed Abd Ellah, Rashad Mohamed El-Sagheer

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 5)

Received: 17 August 2013 Published: 30 August 2013

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 5)
DOI	10.11648/j.ajtas.20130205.13
Page(s)	128-141
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Generalized Pareto Distribution, Progressive First-Failure Censored Sample, Gibbs and Metropolis Sampler, Bayesian and Non-Bayesian Estimations, Bootstrap Methods

References

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APA Style

Mohamed Abdul Wahab Mahmoud, Ahmed Abo-Elmagd Soliman, Ahmed Hamed Abd Ellah, Rashad Mohamed El-Sagheer. (2013). Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution. American Journal of Theoretical and Applied Statistics, 2(5), 128-141. https://doi.org/10.11648/j.ajtas.20130205.13

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ACS Style

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. Am. J. Theor. Appl. Stat. 2013, 2(5), 128-141. doi: 10.11648/j.ajtas.20130205.13

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AMA Style

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. Am J Theor Appl Stat. 2013;2(5):128-141. doi: 10.11648/j.ajtas.20130205.13

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@article{10.11648/j.ajtas.20130205.13,
  author = {Mohamed Abdul Wahab Mahmoud and Ahmed Abo-Elmagd Soliman and Ahmed Hamed Abd Ellah and Rashad Mohamed El-Sagheer},
  title = {Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {5},
  pages = {128-141},
  doi = {10.11648/j.ajtas.20130205.13},
  url = {https://doi.org/10.11648/j.ajtas.20130205.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130205.13},
  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.},
 year = {2013}
}

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TY  - JOUR
T1  - Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution
AU  - Mohamed Abdul Wahab Mahmoud
AU  - Ahmed Abo-Elmagd Soliman
AU  - Ahmed Hamed Abd Ellah
AU  - Rashad Mohamed El-Sagheer
Y1  - 2013/08/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajtas.20130205.13
DO  - 10.11648/j.ajtas.20130205.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 128
EP  - 141
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130205.13
AB  - 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.
VL  - 2
IS  - 5
ER  -

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Author Information

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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Plain Text BibTeX RIS

APA Style

Mohamed Abdul Wahab Mahmoud, Ahmed Abo-Elmagd Soliman, Ahmed Hamed Abd Ellah, Rashad Mohamed El-Sagheer. (2013). Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution. American Journal of Theoretical and Applied Statistics, 2(5), 128-141. https://doi.org/10.11648/j.ajtas.20130205.13

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ACS Style

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. Am. J. Theor. Appl. Stat. 2013, 2(5), 128-141. doi: 10.11648/j.ajtas.20130205.13

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AMA Style

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. Am J Theor Appl Stat. 2013;2(5):128-141. doi: 10.11648/j.ajtas.20130205.13

Copy | Download

@article{10.11648/j.ajtas.20130205.13,
  author = {Mohamed Abdul Wahab Mahmoud and Ahmed Abo-Elmagd Soliman and Ahmed Hamed Abd Ellah and Rashad Mohamed El-Sagheer},
  title = {Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {5},
  pages = {128-141},
  doi = {10.11648/j.ajtas.20130205.13},
  url = {https://doi.org/10.11648/j.ajtas.20130205.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130205.13},
  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.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Estimation Using MCMC Approach Based on Progressive First-Failure Censoring from Generalized Pareto Distribution
AU  - Mohamed Abdul Wahab Mahmoud
AU  - Ahmed Abo-Elmagd Soliman
AU  - Ahmed Hamed Abd Ellah
AU  - Rashad Mohamed El-Sagheer
Y1  - 2013/08/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajtas.20130205.13
DO  - 10.11648/j.ajtas.20130205.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 128
EP  - 141
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130205.13
AB  - 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.
VL  - 2
IS  - 5
ER  -

Copy | Download