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Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms

Received: 15 November 2016     Accepted: 30 November 2016     Published: 20 December 2016
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Abstract

In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 1)
DOI 10.11648/j.ajtas.20170601.11
Page(s) 1-9
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), 2016. Published by Science Publishing Group

Keywords

Two-Parameter Rayleigh Distribution, Maximum Likelihood Estimation, EM Algorithm, NR Method, Progressive Type-II Censoring

References
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Cite This Article
  • APA Style

    Murithi Daniel Fundi, Edward Gachangi Njenga, Kemboi George Keitany. (2016). Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms. American Journal of Theoretical and Applied Statistics, 6(1), 1-9. https://doi.org/10.11648/j.ajtas.20170601.11

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    ACS Style

    Murithi Daniel Fundi; Edward Gachangi Njenga; Kemboi George Keitany. Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms. Am. J. Theor. Appl. Stat. 2016, 6(1), 1-9. doi: 10.11648/j.ajtas.20170601.11

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    AMA Style

    Murithi Daniel Fundi, Edward Gachangi Njenga, Kemboi George Keitany. Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms. Am J Theor Appl Stat. 2016;6(1):1-9. doi: 10.11648/j.ajtas.20170601.11

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  • @article{10.11648/j.ajtas.20170601.11,
      author = {Murithi Daniel Fundi and Edward Gachangi Njenga and Kemboi George Keitany},
      title = {Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {1},
      pages = {1-9},
      doi = {10.11648/j.ajtas.20170601.11},
      url = {https://doi.org/10.11648/j.ajtas.20170601.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170601.11},
      abstract = {In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.},
     year = {2016}
    }
    

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    T1  - Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms
    AU  - Murithi Daniel Fundi
    AU  - Edward Gachangi Njenga
    AU  - Kemboi George Keitany
    Y1  - 2016/12/20
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    DO  - 10.11648/j.ajtas.20170601.11
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20170601.11
    AB  - In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.
    VL  - 6
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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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