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Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

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  • Musleh, Rola M.
  • Helu, Amal

Abstract

In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley׳s approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness (PN) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators.

Suggested Citation

  • Musleh, Rola M. & Helu, Amal, 2014. "Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 216-227.
    • Handle: RePEc:eee:reensy:v:131:y:2014:i:c:p:216-227
    DOI: 10.1016/j.ress.2014.07.006
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    1. Mahmoud, M. A. W. & Sultan, K. S. & Amer, S. M., 2003. "Order statistics from inverse weibull distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 149-163, February.
    2. Chansoo Kim & Keunhee Han, 2010. "Estimation of the scale parameter of the half-logistic distribution under progressively type II censored sample," Statistical Papers, Springer, vol. 51(2), pages 375-387, June.
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    5. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    6. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    7. Mohamed Abdel Wahab Mahmoud & Khalaf Salman Sultan & Safaa Mousa Amer, 2003. "Order statistics from inverse Weibull distribution and characterizations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 389-401.
    8. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    9. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
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    Cited by:

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    4. Leonardo Leoni & Farshad BahooToroody & Saeed Khalaj & Filippo De Carlo & Ahmad BahooToroody & Mohammad Mahdi Abaei, 2021. "Bayesian Estimation for Reliability Engineering: Addressing the Influence of Prior Choice," IJERPH, MDPI, vol. 18(7), pages 1-16, March.
    5. Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.
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    7. Sarah R. Al-Dawsari & Khalaf S. Sultan, 2021. "Inverted Weibull Regression Models and Their Applications," Stats, MDPI, vol. 4(2), pages 1-22, April.

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