Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples

Mustafa Mohie El-Din; Yahia Abdel-Aty; Ahmed Shafay; Magdy Nagy

doi:doi:10.11648/j.ajtas.20140306.15

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Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples

Mustafa Mohie El-Din, Yahia Abdel-Aty, Ahmed Shafay, Magdy Nagy

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)

Received: 18 November 2014 Accepted: 28 November 2014 Published: 2 December 2014

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Abstract

In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)
DOI	10.11648/j.ajtas.20140306.15
Page(s)	202-210
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), 2024. Published by Science Publishing Group

Keywords

Bayesian Estimation, Pooled Type-II Censored Samples, Left Truncated Exponential Distribution, Bayesian Prediction, Maximum Likelihood Estimation

References

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APA Style

Mustafa Mohie El-Din, Yahia Abdel-Aty, Ahmed Shafay, Magdy Nagy. (2014). Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. American Journal of Theoretical and Applied Statistics, 3(6), 202-210. https://doi.org/10.11648/j.ajtas.20140306.15

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ACS Style

Mustafa Mohie El-Din; Yahia Abdel-Aty; Ahmed Shafay; Magdy Nagy. Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. Am. J. Theor. Appl. Stat. 2014, 3(6), 202-210. doi: 10.11648/j.ajtas.20140306.15

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AMA Style

Mustafa Mohie El-Din, Yahia Abdel-Aty, Ahmed Shafay, Magdy Nagy. Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. Am J Theor Appl Stat. 2014;3(6):202-210. doi: 10.11648/j.ajtas.20140306.15

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@article{10.11648/j.ajtas.20140306.15,
  author = {Mustafa Mohie El-Din and Yahia Abdel-Aty and Ahmed Shafay and Magdy Nagy},
  title = {Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {6},
  pages = {202-210},
  doi = {10.11648/j.ajtas.20140306.15},
  url = {https://doi.org/10.11648/j.ajtas.20140306.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.15},
  abstract = {In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.},
 year = {2014}
}

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TY  - JOUR
T1  - Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples
AU  - Mustafa Mohie El-Din
AU  - Yahia Abdel-Aty
AU  - Ahmed Shafay
AU  - Magdy Nagy
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PY  - 2014
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DO  - 10.11648/j.ajtas.20140306.15
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  - 202
EP  - 210
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140306.15
AB  - In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.
VL  - 3
IS  - 6
ER  -

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Author Information

Mustafa Mohie El-Din

Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt
Yahia Abdel-Aty

Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt
Ahmed Shafay

Nature Science Department, Community College of Riyadh, King Saud University, P.O. Box 28095, Riyadh 11437, Saudi Arabia; Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
Magdy Nagy

Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt

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APA Style

Mustafa Mohie El-Din, Yahia Abdel-Aty, Ahmed Shafay, Magdy Nagy. (2014). Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. American Journal of Theoretical and Applied Statistics, 3(6), 202-210. https://doi.org/10.11648/j.ajtas.20140306.15

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ACS Style

Mustafa Mohie El-Din; Yahia Abdel-Aty; Ahmed Shafay; Magdy Nagy. Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. Am. J. Theor. Appl. Stat. 2014, 3(6), 202-210. doi: 10.11648/j.ajtas.20140306.15

Copy | Download

AMA Style

Mustafa Mohie El-Din, Yahia Abdel-Aty, Ahmed Shafay, Magdy Nagy. Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples. Am J Theor Appl Stat. 2014;3(6):202-210. doi: 10.11648/j.ajtas.20140306.15

Copy | Download

@article{10.11648/j.ajtas.20140306.15,
  author = {Mustafa Mohie El-Din and Yahia Abdel-Aty and Ahmed Shafay and Magdy Nagy},
  title = {Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {6},
  pages = {202-210},
  doi = {10.11648/j.ajtas.20140306.15},
  url = {https://doi.org/10.11648/j.ajtas.20140306.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.15},
  abstract = {In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples
AU  - Mustafa Mohie El-Din
AU  - Yahia Abdel-Aty
AU  - Ahmed Shafay
AU  - Magdy Nagy
Y1  - 2014/12/02
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140306.15
DO  - 10.11648/j.ajtas.20140306.15
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  - 202
EP  - 210
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140306.15
AB  - In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.
VL  - 3
IS  - 6
ER  -

Copy | Download