Gumbel Distribution Adjustment Improvement for Accurate Extreme Values Prediction

Abstract

In this paper, we focus on using the Extreme Value Theory (EVT), especially the Gumbel Distribution (GD) for Extreme values prediction in a time series. GD is used to model the distribution of extreme values in a time series. Furthermore, if a time series formed by extreme values follows (can be adjusted to) the Gumbel distribution, the GD parameters can be estimated on the basis of the observed data, then these parameters are used to predict future extreme values/events. However, in the literature, most studies rely on a visual adjustment method to prove that the time series formed by extreme values follows the Gumbel Distribution. In this paper, our main contribution consists on studying different adjustment methods, compare them and use an automated mathematical adjustment method to demonstrate the adjustment of the studied time series to the Gumbel Distribution.