A Gauss Hypergeometric-Type Model for Heavy-Tailed Survival Times in Biomedical Research

In this study, we introduced and analyzed the Slash–Log–Logistic (SlaLL) distribution, a novel statistical model developed by applying the slash methodology to log–logistic and beta distributions. The SlaLL distribution is particularly suited for modeling datasets characterized by heavy tails and extreme values, frequently encountered in survival time analyses. We derived the mathematical representation of the distribution involving Gauss hypergeometric and beta functions, explicitly established the probability density function, cumulative distribution function, hazard rate function, and reliability function, and provided clear definitions of its moments. Through comprehensive simulation studies, the accuracy and robustness of maximum likelihood and Bayesian methods for parameter estimation were validated. Comparative empirical analyses demonstrated the SlaLL distribution’s superior fitting performance over well-known slash-based models, emphasizing its practical utility in accurately capturing the complexities of real-world survival time data.