Burr III Scaled Inverse Odds Ratio-Rayleigh Distribution for Modeling Asymmetric Engineering, Disease Surveillance and Epidemiological Data

Abstract

Modeling real-world dataâĂŤparticularly in fields like reliability engineering, survival analysis, and epidemiologyâĂŤoften requires distributions with the flexibility to accommodate heavy tails, skewness, and a range of hazard rate behaviors. Classical models such as the Rayleigh distribution, while analytically tractable, are limited to specific hazard shapes and symmetric forms and are therefore unsuitable for increasingly complex datasets. To surmount these limitations, we propose a novel and general distribution: the Burr III Scaled Inverse Odds Ratio-Rayleigh (B-SIOR-R) model, a special case of the broad B-SIOR-G family. By blending the inverse odds ratio transformation with Burr III scaling, the B-SIOR-R distribution offers extra control over tailweight, skewness, and hazard shapes. We derive key statistical properties like the quantile function, moments, entropy, extropy, and order statistics. The model parameters are estimated via maximum likelihood, with simulation studies verifying estimator consistency and efficiency. A group acceptance sampling plan (GASP) based on the novel distribution is also developed for application in industrial quality control contexts. Examples using real data setsâĂŤgroundwater contaminants, gauge data, and HIV/AIDS and COVID-19 epidemiological dataâĂŤdemonstrate the B-SIOR-R model’s improved fit and flexibility. These results suggest that it is a valuable addition to the modeler’s toolkit for real, asymmetric, heavy-tailed, and non-standard hazard behavior data.