Parametric Distribution Fitting and Extreme Value Inference for Rainfall in Maiduguri
DOI:
https://doi.org/10.70882/josrar.2025.v2i6.143Keywords:
Extreme Value Theory (EVT), Rainfall Modelling, Gamma Distribution, Probability Distribution Fitting, Gumbel Distribution, Flood Risk Assessment, Return Level EstimationAbstract
The paper takes a stringent approach of statistical characterization and existence of extreme values of monthly rainfall in Maiduguri capital city of Borno State, Nigeria and applies a 4-decade dataset (1981-2023). Descriptive statistics show that there is a highly skewed, discontinuous rainfall regimen as indicated by the wide gap between the value of mean (53.86 mm) and the median (1.60 mm). As this aims to determine the best probabilistic model that describes the non-zero monthly rainfall, Gamma, Weibull, and Lognormal distributions were both fit using Maximum Likelihood Estimation (MLE) and compared using Akaike (AIC) and Bayesian (BIC) Information Criteria. The Gamma distribution proved to be the best model to choose since it gave the smallest AIC (3007.99) and BIC (3018.78) values and its estimation value was strong though in the lower and middle quantile ranges. To select the Gumbel distribution (as opposed to the Generalized Extreme Value (GEV) distribution) to model annual maxima, the shape parameter closes to zero and the principle of parsimony were used. The estimation of the level at returns describes the large flood events indicating a 469.44 mm and 516.21 mm of the significant floods 50-year and 100-year returns respectively. The results offer crucially designed site values critical to improving the urban drainage-related infrastructure and flood resilience mechanisms of the semi-arid Sudano-Sahelian region.
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