American Journal of Theoretical and Applied Statistics

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Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring

Received: Mar. 13, 2020    Accepted: Apr. 10, 2020    Published: Apr. 23, 2020
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Abstract

This paper considers the problem of estimating the parameters of Poisson-Exponential (PE) distribution under progressive type-I interval censoring scheme. PE is a two-parameter lifetime distribution having an increasing hazard function. It has been applied in complementary risks problems in latent risks, that is in scenarios where maximum lifetime values are observed but information concerning factors accounting for component failure is unavailable. Under progressive type-I interval censoring, observations are known within two consecutively pre-arranged times and items would be withdrawn at pre-scheduled time points. This scheme is most suitable in those cases where continuous examination is impossible. Maximum likelihood estimates of Poisson-Exponential parameters are obtained via Expectation-Maximization (EM) algorithm. The EM algorithm is preferred as it has been confirmed to be a more superior tool when dealing with incomplete data sets having missing values, or models having truncated distributions. Asymptotic properties of the estimates are studied through simulation and compared based on bias and the mean squared error under different censoring schemes and parameter values. It is concluded that for an increasing sample size, the estimated values of the parameters tend to the true value. Among the four censoring schemes considered, the third scheme provides the most precise and accurate results followed by fourth scheme, first scheme and finally the second scheme.

DOI 10.11648/j.ajtas.20200902.11
Published in American Journal of Theoretical and Applied Statistics ( Volume 9, Issue 2, March 2020 )
Page(s) 14-20
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

Poisson-exponential, Progressive Type I Interval Censoring, Maximum Likelihood Estimation, EM Algorithm

References
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  • APA Style

    Peter Tumwa Situma, Leo Odongo. (2020). Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring. American Journal of Theoretical and Applied Statistics, 9(2), 14-20. https://doi.org/10.11648/j.ajtas.20200902.11

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    ACS Style

    Peter Tumwa Situma; Leo Odongo. Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring. Am. J. Theor. Appl. Stat. 2020, 9(2), 14-20. doi: 10.11648/j.ajtas.20200902.11

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    AMA Style

    Peter Tumwa Situma, Leo Odongo. Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring. Am J Theor Appl Stat. 2020;9(2):14-20. doi: 10.11648/j.ajtas.20200902.11

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  • @article{10.11648/j.ajtas.20200902.11,
      author = {Peter Tumwa Situma and Leo Odongo},
      title = {Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {9},
      number = {2},
      pages = {14-20},
      doi = {10.11648/j.ajtas.20200902.11},
      url = {https://doi.org/10.11648/j.ajtas.20200902.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20200902.11},
      abstract = {This paper considers the problem of estimating the parameters of Poisson-Exponential (PE) distribution under progressive type-I interval censoring scheme. PE is a two-parameter lifetime distribution having an increasing hazard function. It has been applied in complementary risks problems in latent risks, that is in scenarios where maximum lifetime values are observed but information concerning factors accounting for component failure is unavailable. Under progressive type-I interval censoring, observations are known within two consecutively pre-arranged times and items would be withdrawn at pre-scheduled time points. This scheme is most suitable in those cases where continuous examination is impossible. Maximum likelihood estimates of Poisson-Exponential parameters are obtained via Expectation-Maximization (EM) algorithm. The EM algorithm is preferred as it has been confirmed to be a more superior tool when dealing with incomplete data sets having missing values, or models having truncated distributions. Asymptotic properties of the estimates are studied through simulation and compared based on bias and the mean squared error under different censoring schemes and parameter values. It is concluded that for an increasing sample size, the estimated values of the parameters tend to the true value. Among the four censoring schemes considered, the third scheme provides the most precise and accurate results followed by fourth scheme, first scheme and finally the second scheme.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring
    AU  - Peter Tumwa Situma
    AU  - Leo Odongo
    Y1  - 2020/04/23
    PY  - 2020
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    DO  - 10.11648/j.ajtas.20200902.11
    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  - 14
    EP  - 20
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20200902.11
    AB  - This paper considers the problem of estimating the parameters of Poisson-Exponential (PE) distribution under progressive type-I interval censoring scheme. PE is a two-parameter lifetime distribution having an increasing hazard function. It has been applied in complementary risks problems in latent risks, that is in scenarios where maximum lifetime values are observed but information concerning factors accounting for component failure is unavailable. Under progressive type-I interval censoring, observations are known within two consecutively pre-arranged times and items would be withdrawn at pre-scheduled time points. This scheme is most suitable in those cases where continuous examination is impossible. Maximum likelihood estimates of Poisson-Exponential parameters are obtained via Expectation-Maximization (EM) algorithm. The EM algorithm is preferred as it has been confirmed to be a more superior tool when dealing with incomplete data sets having missing values, or models having truncated distributions. Asymptotic properties of the estimates are studied through simulation and compared based on bias and the mean squared error under different censoring schemes and parameter values. It is concluded that for an increasing sample size, the estimated values of the parameters tend to the true value. Among the four censoring schemes considered, the third scheme provides the most precise and accurate results followed by fourth scheme, first scheme and finally the second scheme.
    VL  - 9
    IS  - 2
    ER  - 

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

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

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