A Novel Accelerated Failure Time Model with Risk Analysis under Actuarial Data, Censored and Uncensored Application

This paper proposes a novel Accelerated Failure Time (AFT) model based on the Weighted Topp-Leone (WTLE) exponential distribution, designed for robust survival analysis under censored and uncensored actuarial and biomedical data. The AFT-WTLE model introduces flexible hazard rate shapes, validated through goodness-of-fit tests and real-world applications, including electric insulating fluid failure times and body fat percentage datasets. Parameter estimation employs maximum likelihood (MLE), Cram´er-von Mises (CVM), Anderson-Darling (ADE), and their modified variants (RTADE, AD2LE), 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 are 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 confirms the AFT-WTLE’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 illustrate its practical utility in actuarial, healthcare, and engineering domains. Computational efficiency is achieved via the BB algorithm for parameter optimization. Simulation results emphasize improved estimation consistency with increasing sample sizes, particularly for RTADE in high-quantile risk metrics. This work bridges gaps in survival modeling by integrating flexible baseline hazards with advanced risk quantification tools, offering a versatile framework for analyzing complex survival data across disciplines.