IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v22y2021i4p171-189n1.html
   My bibliography  Save this article

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

Author

Listed:
  • 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, Statistics Poland, 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2021-044
    Download Restriction: no
    File URL: https://libkey.io/10.21307/stattrans-2021-044?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Badiollah Asrabadi, 1990. "Estimation in the pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 199-205, December.
    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.
    3. M. Alizadeh & S. Rezaei & S. Bagheri & S. Nadarajah, 2015. "Efficient estimation for the generalized exponential distribution," Statistical Papers, Springer, vol. 56(4), pages 1015-1031, November.
    4. F. Maleki & E. Deiri, 2017. "Efficient Estimation of the PDF and the CDF of the Frechet Distribution," Annals of Data Science, Springer, vol. 4(2), pages 211-225, June.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amal S. Hassan & Salwa M. Assar & Kareem A. Ali & Heba F. Nagy, 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.
    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.
    3. 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.
    4. Yogesh Tripathi & Somesh Kumar & Constantinos Petropoulos, 2016. "Estimating the shape parameter of a Pareto distribution under restrictions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 91-111, January.
    5. Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    6. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.
    7. Mehdi Jabbari Nooghabi, 2016. "Estimation of the Lomax Distribution in the Presence of Outliers," Annals of Data Science, Springer, vol. 3(4), pages 385-399, December.
    8. Xiao Wang & Xinmin Li, 2021. "Generalized Confidence Intervals for Zero-Inflated Pareto Distribution," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    9. Shama, M.S. & Dey, Sanku & Altun, Emrah & Afify, Ahmed Z., 2022. "The Gamma–Gompertz distribution: Theory and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 689-712.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:stintr:v:22:y:2021:i:4:p:171-189:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://stat.gov.pl/en/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.