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Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution

Author

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  • Hassan Amal S.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Cairo, ; Egypt .)

  • Assar Salwa M.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Cairo, ; Egypt .)

  • Ali Kareem A.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Cairo, ; Egypt .)

  • Nagy Heba F.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research. Cairo, ; Egypt)

Abstract

The exponentiated Burr Type XII (EBXII) distribution has wide applications in reliability and economic studies. In this article, the estimation of the probability density function and the cumulative distribution function of EBXII distribution is considered. We examine the maximum likelihood estimator, the uniformly minimum variance unbiased estimator, the least squares estimator, the weighted least squares estimator, the maximum product spacing estimator, the Cramér–von-Mises estimator, and the Anderson–Darling estimator. We derive analytical forms for the bias and mean square error. A simulation study is performed to investigate the consistency of the suggested methods of estimation. Data relating to the wind speed and service times of aircraft windshields are used with the studied methods. The simulation studies and real data applications have revealed that the maximum likelihood estimator performs more efficiently than its remaining counterparts.

Suggested Citation

  • Hassan Amal S. & Assar Salwa M. & Ali Kareem A. & Nagy Heba F., 2021. "Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 171-189, December.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:4:p:171-189:n:1
    DOI: 10.21307/stattrans-2021-044
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    References listed on IDEAS

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    2. Yogesh Mani Tripathi & Amulya Kumar Mahto & Sanku Dey, 2017. "Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution," Annals of Data Science, Springer, vol. 4(1), pages 63-81, March.
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    5. Sanku Dey & Tanmay Kayal & Yogesh Mani Tripathi, 2018. "Evaluation and Comparison of Estimators in the Gompertz Distribution," Annals of Data Science, Springer, vol. 5(2), pages 235-258, June.
    6. Jan Mielniczuk & Małgorzata Wojtyś, 2010. "Estimation of Fisher information using model selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 163-187, September.
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