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The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

Author

Listed:
  • Mahmoud El-Morshedy

    (Department of Mathematics, Faculty of Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Hassan M. Aljohani

    (Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohamed S. Eliwa

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Mazen Nassar

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44511, Egypt)

  • Mohammed K. Shakhatreh

    (Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan)

  • Ahmed Z. Afify

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

Abstract

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.

Suggested Citation

  • Mahmoud El-Morshedy & Hassan M. Aljohani & Mohamed S. Eliwa & Mazen Nassar & Mohammed K. Shakhatreh & Ahmed Z. Afify, 2021. "The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications," Mathematics, MDPI, vol. 9(18), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2277-:d:636808
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    Citations

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    Cited by:

    1. Xuanyi Gao & Wenhao Gui, 2023. "Statistical Inference of Burr–Hatke Exponential Distribution with Partially Accelerated Life Test under Progressively Type II Censoring," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    2. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.

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