Bell-generated family of mixture cure rate models with application to credit default

Abstract

Time-to-default data in credit risk modeling are often characterized by heavy tails, skewness, non-monotonic hazard functions, and a non-negligible proportion of long-term survivors. To address these features, we propose a new class of mixture cure rate models based on the Bell-generated (Bell-G) class of distributions. By integrating the Bell-G mechanism with classical baseline distributions, including the Weibull, Burr XII, log-logistic, and lognormal, we develop flexible survival models capable of capturing complex hazard dynamics and tail behavior. The proposed models naturally accommodate a cured fraction while offering enhanced flexibility in representing diverse distributional shapes. Parameter estimation is carried out using the maximum-likelihood method, and the finite-sample performance of the estimators is assessed via Monte Carlo simulations in terms of bias, root-mean-squared error and estimated cure proportions. Covariate effects on the cure fraction are incorporated via a logistic link function. An extensive empirical analysis using real credit risk datasets demonstrates that the proposed Bell-G cure rate models provide improved goodness-of-fit, as measured by standard information criteria and likelihood-based metrics, relative to conventional cure and non-cure survival models. Overall, the results highlight the practical utility of the proposed framework in capturing latent heterogeneity and enhancing risk quantification in credit risk applications.