American Journal of Theoretical and Applied Statistics

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Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm

Received: 03 May 2016    Accepted: 23 May 2016    Published: 01 June 2016
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Abstract

This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. Also the expected Fisher information matrix based on the missing value principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. Through simulations, the behaviour of these estimates are studied and compared under different censoring schemes and parameter values. It’s concluded that for an increasing sample; the estimated parameter values become closer to the true values, the variances and widths of the confidence intervals reduce. Also, more efficient estimates are obtained with censoring schemes concerned with removals of units from their right.

DOI 10.11648/j.ajtas.20160503.21
Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3, May 2016)
Page(s) 154-161
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

Kumaraswamy Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm

References
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[2] Kumaraswamy P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46, 79-88.
[3] Ponnambalam K., Seifi A. and Vlach J. (2001). Probabilistic design of systems with general distributions of parameters. Integrated Journals on Circuit Theory Applications, 29, 527-536.
[4] Jones M. C (2009). Kumaraswamy's Distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6, 70-81.
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[6] Tabassum N. S, Navid Feroze and Muhammed Aslam (2013). Bayesian analysis of the Kumaraswamy distribution under failure censoring sampling scheme. International Journal of Advanced Science and Technology, 51, 39-58.
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[9] Mahmoud, M. A. W., El-Sagheer, R. M., Soliman, A. A. and Abd Ellah, A. H., Inferences of the lifetime performance index with Lomax distribution based on progressive Type-II censored data. Economic Quality Control, 29(1), 39–51, (2014).
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[18] Tahmasbi R. and Rezaei S. (2008). A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis, 52, 3889-3901.
[19] Amal Helu, Hani Samawi and Mohammad Z. Raqab (2013). Estimation on lomax progressive censoring using the EM algorithm. Journal of Statistical Computation and Simulation, 837-861.
[20] Juan Li and Lina Ma (2015). Inference for the Generalized Rayleigh Distribution Based on Progressively Type II hybrid Censored data. Journal of Information and Computational Science, 1101-1112.
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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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    Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga. (2016). Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm. American Journal of Theoretical and Applied Statistics, 5(3), 154-161. https://doi.org/10.11648/j.ajtas.20160503.21

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    ACS Style

    Wafula Mike Erick; Kemei Anderson Kimutai; Edward Gachangi Njenga. Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm. Am. J. Theor. Appl. Stat. 2016, 5(3), 154-161. doi: 10.11648/j.ajtas.20160503.21

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    AMA Style

    Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga. Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm. Am J Theor Appl Stat. 2016;5(3):154-161. doi: 10.11648/j.ajtas.20160503.21

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  • @article{10.11648/j.ajtas.20160503.21,
      author = {Wafula Mike Erick and Kemei Anderson Kimutai and Edward Gachangi Njenga},
      title = {Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {5},
      number = {3},
      pages = {154-161},
      doi = {10.11648/j.ajtas.20160503.21},
      url = {https://doi.org/10.11648/j.ajtas.20160503.21},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20160503.21},
      abstract = {This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. Also the expected Fisher information matrix based on the missing value principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. Through simulations, the behaviour of these estimates are studied and compared under different censoring schemes and parameter values. It’s concluded that for an increasing sample; the estimated parameter values become closer to the true values, the variances and widths of the confidence intervals reduce. Also, more efficient estimates are obtained with censoring schemes concerned with removals of units from their right.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm
    AU  - Wafula Mike Erick
    AU  - Kemei Anderson Kimutai
    AU  - Edward Gachangi Njenga
    Y1  - 2016/06/01
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    N1  - https://doi.org/10.11648/j.ajtas.20160503.21
    DO  - 10.11648/j.ajtas.20160503.21
    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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    EP  - 161
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20160503.21
    AB  - This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. Also the expected Fisher information matrix based on the missing value principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. Through simulations, the behaviour of these estimates are studied and compared under different censoring schemes and parameter values. It’s concluded that for an increasing sample; the estimated parameter values become closer to the true values, the variances and widths of the confidence intervals reduce. Also, more efficient estimates are obtained with censoring schemes concerned with removals of units from their right.
    VL  - 5
    IS  - 3
    ER  - 

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