Oncological data applications and risk measures of the heavy-tailed Weibull flexible-G family

We introduce the heavy-tailed Weibull flexible-G (HT-WF-G) family of distributions and derive its fundamental properties, including quantile functions and moments. A maximum likelihood estimation procedure is developed for the parameter inference, with its finite-sample performance and asymptotic properties validated through rigorous Monte Carlo simulation studies. Furthermore, we formulate key actuarial risk metrics including the value at risk (VaR), tail value at risk (TVaR), tail variance (TV), and tail variance premium (TVP) within this flexible framework. The model's practical effectiveness is demonstrated through its application to oncology time-to-event data (lung cancer and acute myeloid leukemia). Empirical results consistently affirm the model's superiority over leading benchmark distributions, as evidenced by significant improvements in the goodness-of-fit criteria, thus establishing the HT-WF-G family as an effective tool for statistical modeling in heavy-tailed and complex survival settings.