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From Theory to Practice: The Ristic ́-Balakrishnan- Harris-G Family of Distributions and Its Applications |
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PP: 383-402 |
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doi:10.18576/jsap/140305
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Author(s) |
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Shusen Pu,
Thatayaone Moakofi,
Broderick Oluyede,
Achraf Cohen,
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Abstract |
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| This research introduces the Ristic ́-Balakrishnan-Harris-G (RB-Harris-G) family of distributions, a novel framework designed to address critical gaps in survival analysis and reliability modeling. The paper systematically explores the mathematical foundations and statistical properties of this family, emphasizing its capacity to model complex hazard rate behaviors such as bathtub-shaped, increasing, and decreasing failure patterns. Key innovations include a reparameterized quantile function for enhanced simulation capabilities and comprehensive analyses of reliability metrics, Re ́nyi entropy, and order statistics. Parameters are estimated via maximum likelihood estimation, with rigorous simulations confirming estimator consistency. The RB-Harris-Weibull subfamily demonstrates exceptional flexibility, outperforming established models across four diverse datasets (silicon nitride fracture toughness, unemployment insurance, COVID-19 survival, and chemotherapy outcomes) through advanced goodness-of-fit tests. Visual diagnostics, including Kaplan-Meier curves and hazard rate plots, underscore the model’s alignment with empirical trends. These advancements provide researchers with robust tools for medical and engineering applications while establishing a foundation for future extensions in time-dependent covariate modeling.
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