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Burr III Scaled Inverse Odds Ratio-Rayleigh Distribution for Modeling Asymmetric Engineering, Disease Surveillance and Epidemiological Data |
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PP: 69-93 |
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doi:10.18576/amis/200105
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Author(s) |
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Okechukwu J. Obulezi,
Sadia Nadir,
Gabriel O. Orji,
Chinyere P. Igbokwe,
Gaber Sallam Salem Abdalla,
Abdoulie Faal,
Mohammed Elgarhy,
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Abstract |
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| Reliability and epidemiology data in practice are of the type that require flexible distributions that fit heavy tails and varying hazard rates, which classical models like the Rayleigh distribution are not capable of. This work introduces the Burr III Scaled Inverse Odds Ratio-Rayleigh (B-SIOR-R) model, a novel model that overcomes such drawbacks. Our model, through the integration of Burr III scaling and inverse odds ratio transformation, provides more control over tail shapes, skewness, and hazards. We derive its statistical properties and estimate its parameters using the maximum likelihood method, which is affirmed by simulation studies. Our Monte Carlo simulations reveal the reduction and convergence towards zero of the bias and mean square error of the estimators with an increase in the sample size, where larger values show more stability and closer estimates to actual parameter values. We also derive a new group acceptance sampling plan (GASP) based on the B-SIOR-R model for quality control. The GASP results indicate that with an increasing true mean lifetime, the number of groups (g) and items in groups (m) to be sampled is reduced. For instance, using a consumer protection level 0.05 for β and a relative mean lifetime of 6 for r2, an optimal solution of (g,m,Paccept) = (1,1,0.958898) is achieved, demonstrating an extremely satisfactory acceptance probability of around 95.89% by testing one group of one item. Within the practical applications, B-SIOR-R distribution generated evenly high p-values for all datasets—0.9900, 0.9543, 0.9965, 0.9966, and 0.3105—demonstrating its statistical sufficiency and robustness. Exactly, for the COVID-19 Mortality and HIV/AIDS Mortality datasets, B-SIOR-R model attained low AIC values (−240.94 and −27.45, respectively), outperforming most of the competitors in goodness-of-fit tests. |
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