A New Generalized Gamma-Weibull Distribution with Applications to Time-to-event Data

In this research, a new class of probability distributions referred to as Generalized Gamma Weibull (GGW) distributions was introduced within the context of parametric survival analysis. This distribution represents a modification of the gamma Weibull distribution and offers valuable insights, particularly when dealing with highly skewed lifetime data. The study extensively examined the mathematical characteristics of these distributions, encompassing hazard functions, moments, quantile functions, and order statistics. Furthermore, the research delved into parameter estimation methods for these newly proposed distributions, employing the maximum likelihood technique, Fisher Information (FI), and deriving asymptotic confidence intervals for both censored and uncensored scenarios. To illustrate the practical utility of these proposed distributions, the study applied them to analyze two sets of real-life survival data and two sets of real-life data, resulting in a total of four distinct datasets. To gauge the effectiveness of the GGW distributions in comparison to existing methods such as Generalized Weibull and Generalized gamma (G-Weibull and G-Gamma) distributions, the research employed statistical indices including the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), and Bayesian Information Criterion (BIC). The outcomes of this comparative analysis demonstrated the superior performance of the newly introduced GGW distributions (AIC=338.6313, BIC=346.2794, and CAIC=339.5202) when contrasted with the existing methods (G-Weibull: AIC=376.1946, BIC=381.9307, and CAIC=376.5424) across all three criteria, thereby highlighting the enhanced suitability of GGW distributions for modeling and analyzing skewed lifetime data. ### Competing Interest Statement The authors have declared no competing interest.