Modeling extreme temperature events: a comparative analysis of the generalized pareto and lindley exponentiated gumbel distributions

Abstract

Extreme heat events pose increasing risks to public health, energy systems, and urban sustainability, particularly in rapidly urbanizing regions of sub Saharan Africa. This study applies Extreme Value Theory (EVT) to model daily maximum temperature extremes for Lagos, Abuja, and Kano, Nigeria, using satellite derived data spanning 1981 to 2023. A Peaks Over Threshold (POT) framework is adopted to extract extreme temperature exceedances. The classical Generalized Pareto Distribution (GPD), which arises as the asymptotic limit model under EVT, is compared with the recently proposed Lindley Exponentiated Gumbel (LEG) distribution, introduced as a flexible parametric alternative for empirical tail modeling. Model parameters are estimated via maximum likelihood, and uncertainty is quantified using nonparametric bootstrap resampling. Model performance is evaluated using Akaike and Bayesian Information Criteria alongside graphical diagnostics. Results reveal pronounced spatial heterogeneity in heat extremes, with Kano exhibiting the most intense extremes and Lagos the least. While GPD shape parameters are negative across all cities, indicating physically bounded temperature tails, the LEG distribution consistently provides superior statistical fit, particularly in the upper tail. Although return level estimates from both models are numerically similar, the LEG model demonstrates improved tail alignment and greater robustness for risk assessment over long return periods. These findings highlight the value of flexible tail models for climate risk analysis in regions where classical EVT assumptions may be restrictive.