The Generalized Flexible Family of Distributions: Theory, Estimation, and Applications to Cancer Data

This study introduces a new flexible family of continuous probability distributions, termed the generalized flexible family, developed for the effective modeling of cancer data. The proposed family extends the recently introduced new flexible generalized family by incorporating an additional shape parameter to enhance flexibility in capturing various data behaviors, including skewness and heavy tails. Fundamental statistical properties such as the quantile function, Shannon entropy, moments, and moment-generating function are derived and discussed. The behavior of the proposed model is examined through probability density function and hazard rate function plots, demonstrating its ability to model diverse hazard shapes commonly observed in biomedical datasets. Parameter estimation is carried out using the maximum likelihood estimation method, and a Monte Carlo simulation study is performed to evaluate the efficiency of the estimators. The practical utility of the new model is demonstrated through applications to three real cancer datasets, where the new model outperforms several existing distributions in terms of goodness-of-fit criteria. Overall, the proposed new model provides a robust and adaptable framework for analyzing complex lifetime and biomedical data.