Weibull -Fréchet Distribution for Modeling Annual Maximum Rainfall of India

Accurate modelling of extreme rainfall is fundamental to hydrological risk assessment and climate‑impact studies. Although several flexible distributional families have been developed to capture complex tail behaviour, their empirical performance for rainfall extremes requires rigorous evaluation. This study provides a comprehensive empirical assessment of the Weibull–Fréchet distribution for modelling annual maximum rainfall in India. Long‑term gridded monthly rainfall records spanning 1900–2016 were used to construct annual maximum rainfall series for the All‑India and Peninsular regions. Model parameters were estimated using maximum likelihood method, and the performance of the Weibull–Fréchet distribution was systematically evaluated against the classical Fréchet and Weibull distribution using standard goodness‑of‑fit criteria and graphical diagnostics. The results demonstrate that the Weibull–Fréchet distribution offers a superior empirical fit, particularly in the upper tail, and yields balanced and physically plausible return‑level estimates. These findings highlight the practical relevance of the Weibull–Fréchet distribution for modelling rainfall extremes across distinct climatic regions.