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This paper introduces a novel two-parameter G-family of distributions derived through a mixing approach, where a mixture of the exponentiated G-family with parameter α follows gamma distribution. Within this new family, we focus on the mixture of gamma-exponentiated exponential distribution (MGExED) as a key sub-model. The study thoroughly investigates by determining some of the MGExED statistical properties, such as quantile function, moments, and order statistics. The MGExED's parameters are estimated using different estimation methods. Due to the complexity of obtaining explicit forms for MGExED's estimators, the accuracy of these estimates is assessed through Monte Carlo simulations. To illustrate the practical utility of the MGExED, we apply it to two distinct real datasets, demonstrating its superior flexibility and fit compared to several established distributions in the literature. This comprehensive evaluation underscores the MGExED's potential for broader statistical modeling and analysis application., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)