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Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution

Received: 4 September 2013     Published: 30 September 2013
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Abstract

In this article, our main aim is to investigate the parameters estimation of inverse Weibull distribution in the frame work of progressively type II. We consider the censored sample from a two parameters inverse Weibull. The point estimators of the parameters derived by using the maximum likelihood method. The exact joint confidence region and confidence interval for the parameters are obtained. A numerical example is provided to illustrate the proposed. estimation methods developed here.

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)
DOI 10.11648/j.ajtas.20130206.11
Page(s) 149-153
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), 2013. Published by Science Publishing Group

Keywords

Joint Confidence Region, Maximum Likelihood Estimator, Progressively Type II Censored Sample, Confidence Interval

References
[1] A. C. Cohen, Progressively censored samples in life testing. Techno metrics, 5, 327-339, (1963).
[2] N. R. Mann, Best linear invariant estimation for Weibull parameters under progressive censoring, Technometrics, 13, 521-533, (1971).
[3] J. Y. Wong, Simultaneously estimating the three Weibull parameters from progressively censored samples, Microelectronics and Reliability, 33, 2217- 2224, (1993).
[4] N. Balakrishnan, and R. Aggarwala, Progressive Censoring-Theory, Methods, and Applications, Birkhauser, Boston, SBN 978-0-8176-4001-9 e-book package (2000).
[5] Wu. Shuo-Jye Estimation of the parameters of the weibull distribution with progressively censored data, Journal of Japan Statistical Society, 2, 155-163, (2002).
[6] W. B. Nelson, Applied Life Data Analysis. John Wiley & Sons, New York, (1982).
[7] R. Calaria, and G. Pulcini, On the maximum likelihood and least-squares estimation in the inverse Weibull distributions. Statistical Application, 2(1), 53-66, (1990).
[8] M. Maswedah, Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics. Journal of Statisticl Computation and Simulation, 73, 887-898, (2003).
[9] R. Dumonceaux, and C. E. Antle, Discrimination between the lognormal and Weibull distribution. Techno metrics, 15, 923-926, (1973).
[10] N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions. Vol. 2, second edition. John Wiley & Sons New York, (1995).
[11] D. N. P. Murthy, M. Xie, and R. Jiang, Weibull Model. John Wiley & Sons, New York, (2004).
[12] M. M, Mohie El-Din,,and F. H. Riad, Estimation and Prediction for the Inverse Weibull Distribution Based on Records, Journal of Advanced Research in Statistics and Probability (JARSP), 3(2), 20 – 27, (2011).
[13] P. Erto, New Practical Bayes estimators for the 2-Parameter Weibull distribution, IEEE Transactions on Reliability R-31, 194-197, (1982),
[14] M. Marušić, , D. Marković, and D. Jukić , Least squares fitting the three-parameter inverse Weibull density, Math. Commun., Vol. 15, No. 2, pp. 539-553, (2010).
[15] D. R. Thomas, and W. M. Wilson, Linear order statistic estimation for the two parameter Weibull and extreme value distribution from type-II progressively censored samples, Technometrics, 14, 679-691, (1972).
Cite This Article
  • APA Style

    Mostafa M. MohieEl-Din, Fathy H. Riad, Mohamed A. El-Sayed. (2013). Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution. American Journal of Theoretical and Applied Statistics, 2(6), 149-153. https://doi.org/10.11648/j.ajtas.20130206.11

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    ACS Style

    Mostafa M. MohieEl-Din; Fathy H. Riad; Mohamed A. El-Sayed. Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution. Am. J. Theor. Appl. Stat. 2013, 2(6), 149-153. doi: 10.11648/j.ajtas.20130206.11

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    AMA Style

    Mostafa M. MohieEl-Din, Fathy H. Riad, Mohamed A. El-Sayed. Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution. Am J Theor Appl Stat. 2013;2(6):149-153. doi: 10.11648/j.ajtas.20130206.11

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  • @article{10.11648/j.ajtas.20130206.11,
      author = {Mostafa M. MohieEl-Din and Fathy H. Riad and Mohamed A. El-Sayed},
      title = {Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {2},
      number = {6},
      pages = {149-153},
      doi = {10.11648/j.ajtas.20130206.11},
      url = {https://doi.org/10.11648/j.ajtas.20130206.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.11},
      abstract = {In this article, our main aim is to investigate the parameters estimation of inverse Weibull distribution in the frame work of progressively type II. We consider the censored sample from a two parameters inverse Weibull. The point estimators of the parameters derived by using the maximum likelihood method. The exact joint confidence region and confidence interval for the parameters are obtained. A numerical example is provided to illustrate the proposed. estimation methods developed here.},
     year = {2013}
    }
    

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    T1  - Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution
    AU  - Mostafa M. MohieEl-Din
    AU  - Fathy H. Riad
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    Y1  - 2013/09/30
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    DO  - 10.11648/j.ajtas.20130206.11
    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  - 149
    EP  - 153
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20130206.11
    AB  - In this article, our main aim is to investigate the parameters estimation of inverse Weibull distribution in the frame work of progressively type II. We consider the censored sample from a two parameters inverse Weibull. The point estimators of the parameters derived by using the maximum likelihood method. The exact joint confidence region and confidence interval for the parameters are obtained. A numerical example is provided to illustrate the proposed. estimation methods developed here.
    VL  - 2
    IS  - 6
    ER  - 

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Author Information
  • Dept. of Mathematics, Faculty of Science, Al-Azhar University, Egypt

  • Dept. of Mathematics, Faculty of Science, Minia University, Egypt

  • Dept. of Mathematics, Faculty of Science in Qena, South Valley University, Egypt

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