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

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), 2014. 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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[14] AL-Hussaini, E. K., Jaheen, Z. F. (1999). Parametric prediction bounds for the future median of the exponential distribution. Statistics, 32, 267-275.
[15] Abdel-Aty, Y., Franz, J., Mahmoud, M. A. W. (2007). Bayesian prediction based on generalized order statistics using multiply type-II censoring. Statistics, 41, 495-504.
[16] Schenk, N., Burkschat, M., Cramer, E., Kamps, U. (2011). Bayesian estimation and prediction with multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions. Journal of Statistical Planning and Inference, 141, 1575-1587.
[17] Mohie El-Din, M. M., Abdel-Aty, Y., Shafay, A. R. (2012). Two-sample Bayesian prediction intervals of generalized order statistics based on multiply Type II censored data. Communications in Statistics – Theory and Methods, 41, 381-392.
[18] Mohie El-Din, M. M., Shafay, A. R. (2013). One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data. Statistical Papers, 54, 287-307.
[19] Shafay A. R., Balakrishnan, N., Sultan, K. s. (2014). Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples. Journal of Statistical Computation and Simulation, 84, 526-544.
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Cite This Article
  • 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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    T1  - Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples
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    AU  - Yahia Abdel-Aty
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    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    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.
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Author Information
  • Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt

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

  • 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

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