Modeling Fréchet Distribution Using Novel Statistical Family: Mathematical Properties, Simulation Study and Applications in Epidemiological and Environmental Data

Abstract

In this study, we introduce a novel and highly flexible probability model, called the Novel Exponentiated G-family distribution (NEGFD), which serves as a general framework for generating new probability models. We apply this framework to the Fréchet distribution, resulting in the Novel Exponentiated G-family Fréchet distribution (NEGFFD), which extends the classical Fréchet model by incorporating greater flexibility in modeling skewness and tail behavior. Rooted in the broader class of exponentiated G-families, this approach enhances modeling flexibility, making it particularly effective for capturing skewed and heavy-tailed patterns commonly observed in empirical data. Theoretical aspects of the model are rigorously developed, including derivations of its moments, incomplete moments and hazard rate function. To evaluate the performance of parameter estimation, a detailed Monte Carlo simulation study is conducted using the method of maximum likelihood estimation (MLE) under various sample sizes. The simulation
fiindings demonstrate the consistency, efficiency, and robustness of the maximum likelihood estimates (MLEs) across different scenarios. The practical usefulness of the proposed distribution is illustrated through its application to real-world dataset;  epidemiological data and environmental data. In both domains, the model exhibits superior performance compared to the classical Fréchet and related competing models, as evidenced by lower values of standard model selection criteria. Additional graphical diagnostics and non-parametric goodness-of-fit assessments further support the proposed model’s effectiveness and flexibility in real data modeling contexts.