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Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis

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  • Hanan Haj Ahmad

    (Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia)

  • Dina A. Ramadan

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt)

  • Ehab M. Almetwally

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Riyadh, Saudi Arabia
    Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt)

Abstract

Various discrete lifetime distributions have been observed in real data analysis. Numerous discrete models have been derived from a continuous distribution using the survival discretization method, owing to its simplicity and appealing formulation. This study focuses on the discrete analog of the newly generalized Rayleigh distribution. Both classical and Bayesian statistical inferences are performed to evaluate the efficacy of the new discrete model, particularly in terms of relative bias, mean square error, and coverage probability. Additionally, the study explores different important submodels and limiting behavior for the new discrete distribution. Various statistical functions have been examined, including moments, stress–strength, mean residual lifetime, mean past time, and order statistics. Finally, two real data examples are employed to evaluate the new discrete model. Simulations and numerical analyses play a pivotal role in facilitating statistical estimation and data modeling. The study concludes that the discrete generalized Rayleigh distribution presents a notably appealing alternative to other competing discrete distributions.

Suggested Citation

  • Hanan Haj Ahmad & Dina A. Ramadan & Ehab M. Almetwally, 2024. "Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis," Mathematics, MDPI, vol. 12(2), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:183-:d:1314141
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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. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    3. S. Goliforushani & M. Asadi, 2008. "On the discrete mean past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 209-217, September.
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