Burr III scaled inverse odds ratio-Rayleigh distribution for modeling asymmetric engineering, disease surveillance and epidemiological data

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. Supplementary Material File (bsiorr (7).pdf) - Download - 943.96 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 229views 163downloads Citations Download citation Okechukwu J. Obulezi, Mohamed Nejib Ouertani, Hanene Hamdani, et al. Burr III scaled inverse odds ratio-Rayleigh distribution for modeling asymmetric engineering, disease surveillance and epidemiological data. Authorea. 17 July 2025. DOI: https://doi.org/10.22541/au.175278602.28334107/v1 DOI: https://doi.org/10.22541/au.175278602.28334107/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.