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Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

Author

Listed:
  • M. M. Mohie El-Din

    (Al-Azhar University)

  • M. Nagy

    (King Saud University
    Fayoum University)

  • M. H. Abu-Moussa

    (Cairo University)

Abstract

In this paper, the statistical inference for the Gompertz distribution based on generalized progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is discussed using the maximum likelihood method and the Bayesian methods under different loss functions. The existence and uniqueness of the maximum likelihood estimation are proved. The point and interval Bayesian predictions for unobserved failures from the same sample and that from the future sample are derived. The Monte Carlo simulation is applied to compare the proposed methods. A real data example is used to apply the methods of estimation and to construct the prediction intervals.

Suggested Citation

  • M. M. Mohie El-Din & M. Nagy & M. H. Abu-Moussa, 2019. "Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data," Annals of Data Science, Springer, vol. 6(4), pages 673-705, December.
    • Handle: RePEc:spr:aodasc:v:6:y:2019:i:4:d:10.1007_s40745-019-00199-3
    DOI: 10.1007/s40745-019-00199-3
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    References listed on IDEAS

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    1. Raqab, Mohammad Z. & Asgharzadeh, A. & Valiollahi, R., 2010. "Prediction for Pareto distribution based on progressively Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1732-1743, July.
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    4. M. El-Din & A. Shafay, 2013. "One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data," Statistical Papers, Springer, vol. 54(2), pages 287-307, May.
    5. Shuo-Jye Wu & Chun-Tao Chang & Tzong-Ru Tsai, 2003. "Point and interval estimations for the Gompertz distribution under progressive type-II censoring," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 403-418.
    6. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.
    7. Lin, Chien-Tai & Chou, Cheng-Chieh & Huang, Yen-Lung, 2012. "Inference for the Weibull distribution with progressive hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 451-467.
    8. Erhard Cramer & George Iliopoulos, 2010. "Adaptive progressive Type-II censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 342-358, August.
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    Cited by:

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    2. A. M. Abd El-Raheem & M. H. Abu-Moussa & Marwa M. Mohie El-Din & E. H. Hafez, 2020. "Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study," Mathematics, MDPI, vol. 8(10), pages 1-19, October.

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