The UG-EM Lifetime Model: Analysis and Application to Symmetric and Asymmetric Survival Data

This paper introduces the UG-EM (Unconditional Gamma-Exponential Model) as a new compound lifetime model designed to enhance flexibility in tail behavior compared to traditional distributions. The UG-EM model provides a unified framework for analyzing deviations from symmetry in survival data, effectively capturing right-skewed patterns, which are commonly observed in real-world lifetime phenomena. The main analytical properties are derived, including the probability density, cumulative distribution, hazard and reversed-hazard functions, mean residual life, and several measures of dispersion and uncertainty. The effects of the UG-EM parameters (α and λ) are examined, showing that increasing either parameter can cause a temporary reduction in entropy H(T) at early times followed by a long-term increase; in some cases, the influence of α is stronger than that of λ. Parameter estimation is carried out using the maximum likelihood method and assessed through Monte Carlo simulations to evaluate estimator bias and variability, highlighting the significant role of sample size in estimation accuracy. The proposed model is applied to three survival datasets (Lung, Veteran, and Kidney) and compared with classical alternatives such as Exponential, Weibull, and Log-normal distributions using standard goodness-of-fit criteria. Results indicate that the UG-EM model offers superior flexibility and can capture patterns that simpler models fail to represent, although the empirical results do not demonstrate a clear, consistent superiority over standard competitors across all tested datasets. The paper also discusses identifiability issues, estimation challenges, and practical implications for reliability and medical survival analysis. Recommendations for further theoretical development and broader model comparison are provided.