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A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data

Author

Listed:
  • Mohamed S. Eliwa

    (Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt)

Abstract

This paper introduces a new flexible probability tool for modeling extreme and zero-inflated count data under different shapes of hazard rates. Many relevant mathematical and statistical properties are derived and analyzed. The new tool can be used to discuss several kinds of data, such as “asymmetric and left skewed”, “asymmetric and right skewed”, “symmetric”, “symmetric and bimodal”, “uniformed”, and “right skewed with a heavy tail”, among other useful shapes. The failure rate of the new class can vary and can take the forms of “increasing-constant”, “constant”, “monotonically dropping”, “bathtub”, “monotonically increasing”, or “J-shaped”. Eight classical estimation techniques—including Cramér–von Mises, ordinary least squares, L-moments, maximum likelihood, Kolmogorov, bootstrapping, and weighted least squares—are considered, described, and applied. Additionally, Bayesian estimation under the squared error loss function is also derived and discussed. Comprehensive comparison between approaches is performed for both simulated and real-life data. Finally, four real datasets are analyzed to prove the flexibility, applicability, and notability of the new class.

Suggested Citation

  • Mohamed S. Eliwa & Mahmoud El-Morshedy & Haitham M. Yousof, 2022. "A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3348-:d:915804
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    2. Hafida Goual & Haitham M. Yousof, 2020. "Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(3), pages 393-423, February.
    3. Haitham M. Yousof & M. Masoom Ali & Hafida Goual & Mohamed Ibrahim, 2021. "A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and a modified right-censored test for validation," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 99-121, September.
    4. M. El-Morshedy & M. S. Eliwa & H. Nagy, 2020. "A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 354-375, January.
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