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Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm

Received: 16 March 2017     Accepted: 6 April 2017     Published: 27 April 2017
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Abstract

This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as well as the asymptotic variance-covariance matrix. By using the obtained variance-covariance matrix of the MLEs, the asymptotic 95% confidence interval for the parameters are constructed. Through simulation, the behavior of these estimates are studied and compared under different censoring schemes and parameter values. It is concluded that for an increasing sample size; the estimated value of the parameters converges to the true value, the variances decrease and the width of the confidence interval become narrower.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3)
DOI 10.11648/j.ajtas.20170603.12
Page(s) 141-149
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), 2017. Published by Science Publishing Group

Keywords

Poisson-Exponential Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm

References
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Cite This Article
  • APA Style

    Joseph Nderitu Gitahi, John Kung’u, Leo Odongo. (2017). Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm. American Journal of Theoretical and Applied Statistics, 6(3), 141-149. https://doi.org/10.11648/j.ajtas.20170603.12

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    ACS Style

    Joseph Nderitu Gitahi; John Kung’u; Leo Odongo. Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm. Am. J. Theor. Appl. Stat. 2017, 6(3), 141-149. doi: 10.11648/j.ajtas.20170603.12

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    AMA Style

    Joseph Nderitu Gitahi, John Kung’u, Leo Odongo. Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm. Am J Theor Appl Stat. 2017;6(3):141-149. doi: 10.11648/j.ajtas.20170603.12

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  • @article{10.11648/j.ajtas.20170603.12,
      author = {Joseph Nderitu Gitahi and John Kung’u and Leo Odongo},
      title = {Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {3},
      pages = {141-149},
      doi = {10.11648/j.ajtas.20170603.12},
      url = {https://doi.org/10.11648/j.ajtas.20170603.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170603.12},
      abstract = {This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as well as the asymptotic variance-covariance matrix. By using the obtained variance-covariance matrix of the MLEs, the asymptotic 95% confidence interval for the parameters are constructed. Through simulation, the behavior of these estimates are studied and compared under different censoring schemes and parameter values. It is concluded that for an increasing sample size; the estimated value of the parameters converges to the true value, the variances decrease and the width of the confidence interval become narrower.},
     year = {2017}
    }
    

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    T1  - Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm
    AU  - Joseph Nderitu Gitahi
    AU  - John Kung’u
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    DO  - 10.11648/j.ajtas.20170603.12
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajtas.20170603.12
    AB  - This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as well as the asymptotic variance-covariance matrix. By using the obtained variance-covariance matrix of the MLEs, the asymptotic 95% confidence interval for the parameters are constructed. Through simulation, the behavior of these estimates are studied and compared under different censoring schemes and parameter values. It is concluded that for an increasing sample size; the estimated value of the parameters converges to the true value, the variances decrease and the width of the confidence interval become narrower.
    VL  - 6
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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