A flexible accelerated Weibull distribution for actuarial risk analysis: Theoretical and empirical evaluation with real claims data

This paper proposed a novel accelerated failure time (AFT) model based on the weighted Topp-Leone Weibull (WTLW) distribution, designed for robust survival analysis under censored and uncensored actuarial and biomedical data. The AFT-WTLW model introduced flexible hazard rate shapes, validated through goodness-of-fit tests and real applications, including electric insulating fluid failure times and body fat percentage datasets. Parameter estimation employed maximum likelihood (MLE), Cramér -von Mises (CVM), Anderson-Darling (ADE), right tail Anderson-Darling (RTADE) and left tail Anderson-Darling (LTADE), with simulation studies demonstrating RTADE's superior accuracy in bias and root mean squared error (RMSE) for small-to-moderate samples. The model's risk assessment capabilities were highlighted via value-at-risk (VaR), tail VaR (TVaR), and tail mean-variance metrics, revealing RTADE and ADE as optimal for capturing extreme tail risks. A modified Nikulin-Rao-Robson (NRR) chi-square test confirmed the AFT-WTLW's validity for censored data, with empirical rejection levels aligning closely with theoretical thresholds. Applications to motor failure data and Johnson's body fat dataset illustrated its practical utility in actuarial, healthcare, and engineering domains. Computational efficiency was achieved via the Barzilai–Borwein optimization (BBO) algorithm for parameter optimization. Simulation results emphasized improved estimation consistency with increasing sample sizes, particularly for RTADE in high-quantile risk metrics.