Comparative Analysis of Fréchet Distribution Variants: Parameter Estimation and Model Performance Evaluation.

Abstract:

This study presents a comparative analysis of six Fréchet distribution variants: Kumaraswamy Fréchet (KF), Exponentiated Fréchet (EF), Beta Fréchet (BF), Gamma Extended Fréchet (GExF), Odd Lomax Fréchet (OLxF), and the standard Fréchet (F) focusing on their structural properties, parameter estimation, and model performance. These distributions, characterized by varying levels of complexity and flexibility, are particularly effective for modelling extreme values and heavy tails, crucial in fields like econometrics and reliability analysis. Differences in Probability Density Functions (PDFs) reveal the enhanced adaptability of BF and GExF variants, attributed to their additional beta and gamma components. The models were applied to three datasets: Jobs made of Iron Sheets, Airborne Communication Transceiver Repairs, and Tax Revenue. The performance of the distributions under study was evaluated using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The finding showed that the standard Fréchet distribution consistently outperformed its variants, achieving the lowest AIC and BIC values across datasets, indicating a superior balance of simplicity and adaptability. EF and KF variants demonstrated competitive performance but lacked the robustness of the standard Fréchet model, while OLxF and GExF showed higher AIC and BIC values due to potential over-parameterization. This study underscores the importance of aligning model complexity with dataset characteristics and highlights the standard Fréchet distribution as a versatile choice for analyzing extreme data.