The new heavy-tailed Weibull exponentiated half logistic-G family of distributions: Properties, actuarial measures and inference

Abstract

Accurate statistical modeling of complex real-world data, characterized by heavy tails, skewness, and non-monotonic hazard rates, presents a significant challenge that often exceeds the capabilities of traditional distributions. To address this, we introduce the Heavy-Tailed Weibull Exponentiated Half Logistic-G (HT-W-EHL-G) family of distributions, a novel flexible framework that synthesizes extreme-value robustness with versatile hazard rate shapes. This paper derives the fundamental statistical properties of the proposed family and establishes six estimation methods, whose efficiency is verified via Monte Carlo simulation. The model's practical utility is demonstrated by its robustness to censored data, a critical requirement in survival and reliability analysis, and its direct applicability for computing key actuarial risk measures, including Value at Risk (VaR) and Tail Value at Risk (TVaR). Extensive empirical analyses across diverse domains confirm the model's efficacy and statistically significant superiority in goodness-of-fit over established benchmarks.