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The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution

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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
    Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia)

Abstract

In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed, symmetric, and monotonic datasets. Statistical analyses were conducted using maximum likelihood estimation and Bayesian approaches to assess these models. The Bayesian analysis, in particular, was implemented with the squared error and LINEX loss functions, incorporating a modified Lwin Prior distribution for parameter estimation. Through simulation studies and numerical methods, we evaluated the estimators’ performance and compared the effectiveness of the two discrete adaptations of the Rayleigh–Lindley distribution. The simulations reveal that Bayesian methods are especially effective in this setting due to their flexibility and adaptability. They provide more precise and dependable estimates for the discrete Rayleigh–Lindley model, especially when using the hazard rate preservation method. This method is a compelling alternative to the traditional survival discretization approach, showcasing its significant potential in enhancing model accuracy and applicability. Furthermore, two real data sets are analyzed to assess the performance of each analog.

Suggested Citation

  • Hanan Haj Ahmad, 2024. "The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1261-:d:1380140
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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.
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