Theoretical Contributions to Extreme Value Statistics for Modelling Natural Disaster Risk in the Nigerian Niger Delta and Lake Chad Basin

Extreme weather events and natural disasters in the Nigerian Niger Delta and Lake Chad Basin generate hydrological and meteorological extremes whose statistical characterisation requires rigorous extreme value theory that moves beyond descriptive analysis to provide theoretically grounded tail probability estimation and return period quantification. This dissertation makes theoretical contributions to extreme value statistics for natural disaster risk modelling in these two critical Nigerian ecological zones. New results on the consistency of maximum likelihood estimators for the generalised extreme value (GEV) and generalised Pareto distribution (GPD) under non-stationarity induced by climate trend and cyclical variability are derived. A novel threshold selection method for peaks-over-threshold GPD modelling under spatially structured dependence is introduced with theoretical justification. Non-stationary GEV models with time-varying location and scale parameters estimated by penalised likelihood are developed and their theoretical properties characterised. Applications cover 60-year flood peak records at eight Niger Delta gauging stations and Lake Chad water level extremes from satellite altimetry. Non-stationary GEV modelling at Niger Delta stations showed statistically significant increasing trends in flood peak magnitudes (location parameter trend coefficient p < 0.001 at 6 of 8 stations). Return period recalculation using non-stationary GEV revised 100-year flood estimates upward by 18 to 34 percent compared to stationary estimates, with direct implications for flood plain infrastructure design standards. The dissertation contributes extreme value theory applicable to Nigerian disaster risk reduction planning. Keywords: extreme value theory, generalised Pareto distribution, natural disaster risk, Niger Delta, non-stationary GEV