Generalized Extreme Value (GEV) Distribution Analysis of Maximum Temperature: A Case Study of Gombe State Nigeria

Abstract

Data ranging for the period of ten years were used to study the problem of modelling extreme temperature. The Generalized Extreme Value distribution is fitted to the maximums of six distinct time periods: daily, weekly, biweekly, monthly, quarterly, and half-yearly. These selection periods are based on the findings, which indicate that only the daily, weekly, and biweekly maximums are substantial enough to suit the GEV model. In agreement with the Mann-Kendall (MK) test, which indicates that there is no significant trend for any of the three selection periods, neither the Augmented Dickey Fuller (ADF) nor the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) stationarity tests found any stochastic trends for maximum temperatures. After evaluating the three models, the model with a location parameter that increases over time was concluded to be the most effective for every selection period. All three selection period maximums converge to the GEV distribution, according to the Anderson-Darling and Kolmogorov-Smirnov goodness of fit tests, with the daily maximums exhibiting the best convergence to the GEV distribution. According to return level estimates, the return temperature that surpasses the observation period's maximum temperature (43.3) begins to show up in the return period of T = 10, 20, 50, and 100 for weekly and biweekly maximums, while it was anticipated to be higher than T = 20, 50, and 100 for daily maximum.