Weibull -Fréchet Distribution for Modeling Annual Maximum Rainfall of India
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Authors
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Manoj Varma
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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K.N. Singh
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Achal Lama
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Satyam Verma
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Keywords:
Weibull–Fréchet distribution; Annual maximum rainfall; Extreme value analysis; Goodness‑of‑fit; Return‑level estimation; Rainfall extremes.Abstract
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.
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