On the Rayleigh Exponentiated Odd Generalized‐Inverse Exponential Distribution With Properties and Applications

ABSTRACT This research centers on the creation of an innovative statistical model that extends the inverse exponential (IE) distribution by employing the Rayleigh‐exponentiated odd generalized (REOG) family of distributions, which is designated as the REOG‐IE distribution. Various structural characteristics of the REOG‐IE distribution have been derived, encompassing moments, skewness, kurtosis, and the behavior of the hazard function. The parameters of the proposed distribution were estimated through the maximum likelihood estimation (MLE) technique, and a simulation study was performed to assess the performance and consistency of the parameter estimates. The REOG‐IE distribution was utilized on several real‐world datasets, including the fatigue life of 6061‐T6 aluminium coupons, the remission time of bladder cancer patients, and the radiation susceptibility data of peppermint exposed to gamma and microwave radiation. These applications illustrate the model's versatility and robustness in managing various types of survival and reliability data. The performance of the REOG‐IE distribution was compared against several competing models. The findings indicate that the REOG‐IE distribution consistently surpassed all rival models, achieving the lowest values for AIC, BIC, HQIC, and CAIC across all datasets. Notably, its application to radiation exposure data demonstrated exceptional adaptability in modeling the impacts of gamma and microwave radiation on the susceptibility of peppermint to pest infestation, further underscoring its practical significance. These results validate the REOG‐IE distribution as a more flexible and dependable model for analyzing intricate data patterns in survival analysis, engineering, and biomedical research.