Development of odd Rayleigh-Frechet distribution: properties and applications

Abstract

Accurate modelling of rainfall patterns is crucial for hydrological forecasting, water resource management, and climate analysis. In this study, we propose the Odd Rayleigh Fréchet Distribution (ORFD) as a novel probability model for analysing rainfall at the Piracicaba River and the average annual rainfall across Nigeria. The performance of ORFD is assessed against two competing models: Fréchet Distribution (FD) and Weibull Distribution (WD) using log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) across five months (May-September). The results show that ORFD consistently provides the best fit, exhibiting the lowest AIC and BIC values, whereas FD and WD perform less effectively and indicating numerical instability. A simulation study is conducted to evaluate the Bias and Root Mean Square Error (RMSE) of the parameter estimates for ORFD. The results demonstrate that bias and RMSE decrease as the sample size increases, confirming the consistency and efficiency of the proposed model. These findings highlight the potential of ORFD as a robust statistical tool for modelling heavy-tailed rainfall data, thereby improving hydrological predictions and decision-making processes.