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Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records

Author

Listed:
  • Ajit Chaturvedi

    (University of Delhi)

  • Reza Arabi Belaghi

    (University of Tabriz)

  • Ananya Malhotra

    (University of Delhi)

Abstract

Some improved estimators and confidence interval of the parametric functions are proposed based on records from three parameters Burr XII distribution. We propose preliminary test estimators (PTES) of the powers of the parameter and reliability functions based on uniformly minimum variance unbiased estimator, maximum likelihood estimator, best invariant estimator and empirical Bayes estimator. We compare the performance of the proposed PTES with the usual estimators by studying their relative efficiencies based on Monte Carlo simulations. We also construct preliminary test confidence interval (PTCI) for the parameter and study its coverage probability and expected length. The results show that the proposed PTES dominate the usual estimators in a wide range of the parametric space. Also it is seen that the proposed PTCI have higher coverage probability while keeping the shorter width in some domain of parametric space. The paper ends up by analysing a real data set.

Suggested Citation

  • Ajit Chaturvedi & Reza Arabi Belaghi & Ananya Malhotra, 2018. "Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1260-1278, December.
    • Handle: RePEc:spr:ijsaem:v:9:y:2018:i:6:d:10.1007_s13198-018-0710-4
    DOI: 10.1007/s13198-018-0710-4
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    References listed on IDEAS

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    1. M. Arashi & M. Emadi, 2008. "Evidential inference based on record data and inter-record times," Statistical Papers, Springer, vol. 49(2), pages 291-301, April.
    2. R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    3. R. Arabi Belaghi & M. Arashi & S. M. M. Tabatabaey, 2015. "On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 1-23, January.
    4. Shao, Quanxi, 2004. "Notes on maximum likelihood estimation for the three-parameter Burr XII distribution," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 675-687, April.
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    Cited by:

    1. Hua Xin & Zhifang Liu & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution," Mathematics, MDPI, vol. 8(2), pages 1-23, January.

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