A HYBRID EXPONENTIAL-GENERALIZED GAMMA DISTRIBUTION WITH MEAN BASES MIXING PROPORTION: THEORY AND APPLICATIONS

Abstract

In our study, we propose the Exponential-Generalized Gamma Distribution (EGGD) with Mean-Based Mixing Proportion. A new hybrid survival distribution developed to overcome the limitations of existing parametric models in modeling complex hazard functions and structures. The EGGD combines the simplicity of the exponential distribution with the flexibility of the generalized gamma distribution. The analytical calculations of the distribution’s important statistical properties, namely moments, skewness, kurtosis, survival, and hazard functions, have been derived to provide further insights into the distribution’s behavior. The EGGD parameter estimation is conducted using maximum likelihood estimation (MLE). The performance of the maximum likelihood estimates was rigorously examined through a Monte Carlo simulation study. The performance measures used in the study were bias and MSE. The practicality of the Model was examined through its application to real-world lifetime data. Its performance was compared with that of other existing three-parameter and two-parameter lifetime distributions. The model adequacy is assessed using information criteria, including AIC, AICc, HQIC, and BIC. Across three datasets, the EGGD consistently exhibits superior goodness-of-fit compared to the other considered models, highlighting its flexibility and robustness as a tool for survival and reliability analysis.