The Modified Fréchet-Exponentiated Exponential Distribution: Novel Model for Reliability and Survival Analysis

This study introduces a novel statistical model called the modified Fréchet-exponentiated exponential (MFrEE) distribution. The existing exponentiated exponential (EE) distribution, while useful for lifetime and reliability data, has limited flexibility in capturing diverse hazard shapes and may not adequately model extreme events or tail behavior. To address these limitations, the MFrEE distribution applies a modified Fréchet generator to the EE baseline, enhancing the model’s flexibility and robustness. Its survival and hazard functions, cumulative distribution function, and probability density function are derived, presented, and illustrated with plots for various parameter values. The study provides a comprehensive mathematical analysis of the distribution, deriving its moments, mean, variance, quantiles, and moment-generating function. Methodologically, the model is simulated using an accept–reject algorithm, and its parameters are estimated via maximum likelihood estimation (MLE). The performance of the estimators is assessed through Monte Carlo simulations using bias, mean squared error, and coverage probability (CP), with the CP results showing values close to the nominal 95% level across different parameter settings. Furthermore, the robustness and performance of the proposed method are evaluated using AIC, BIC, and AICc, demonstrating superior performance compared to baseline methods across three publicly available datasets. The study concludes by proposing this model as a significant contribution to probability theory and suggests two avenues for future research: applying the model to more real-world problems and using machine learning methods for parameter estimation to compare with the MLE approach used in this study.