Authors: Faweya. O, OYELAKIN O.P, Odukoya E.A, Aladejana A.E
Abstract: This research estimates the parameters of the Fréchet distribution for extreme rainfall data using two widely recognized statistical approaches: Maximum Likelihood Estimation (MLE) and Least Squares Estimation (LSE). The objectives include estimating the Fréchet distribution parameters using both methods, conducting a comparative evaluation of their performance, and identifying the more accurate and reliable technique. The comparative analysis demonstrated that the Maximum Likelihood Estimation method outperformed the Least Squares Estimation method. MLE produced parameter estimates with lower standard errors and biases, indicating greater precision and reduced variability. The model evaluation criteria, used include the Negative Log-Likelihood (NLLH), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), further supported the preference for MLE over LSE. The MLE method yielded an NLLH of 98.7, AIC of 71.08, and BIC of 74.06, indicating a better overall fit than LSE ,As a result, the study concludes that MLE is the more robust and dependable method for modeling extreme rainfall data using the Fréchet distribution. These findings highlight the importance of selecting appropriate estimation techniques for extreme value analysis, particularly in environmental and disaster risk management applications. By utilizing the strengths of the Fréchet distribution and the MLE approach, this study contributes to the expanding field of extreme value theory and its practical applications in hydrology and climatology. The findings have significant implications for enhancing predictive models, refining flood risk assessments, and strengthening resilience against climate-induced extreme weather events.
