Parametric inference and applications of a new exponentiated inverted lifetime distribution for the different cancer data modelling

In this study, we introduce a novel lifetime model, the exponentiated inverted exponentiated gamma distribution (EIEGD), which extends the classical inverted exponentiated gamma distribution to provide greater flexibility in modeling both complete and censored survival data. We rigorously derive the theoretical properties of the proposed distribution, including moments, moment generating function, conditional moments, order statistics, aging intensity, and other relevant hazard based characteristics, thereby highlighting its ability to capture a wide variety of hazard rate behaviors. For parameter estimation, we implement both classical maximum likelihood estimation and Bayesian approaches under Type-II censored data settings. Extensive simulation studies are conducted to assess the performance of these estimation methods across varying sample sizes and censoring levels. The findings demonstrate that Bayesian estimation generally provides improved accuracy and more robust parameter estimates. The practical applicability of the proposed distribution is illustrated using multiple cancer-related datasets, including AML (acute myelogenous leukemia), kidney transplant, and ovarian cancer datasets obtained from the R survival package, representing diverse survival patterns and clinical scenarios. The results indicate that the proposed model provides a better fit compared with several well-known existing distributions, making it a flexible and effective tool for survival and reliability analysis in biomedical research.