An Investigation of Stretched Exponential Function in Quantifying Long-Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

Figure 1

(a) Illustration of maxima series in the GEV model, where represents the interval size (here  days) and represents the maximum value of the th interval. (b) Definition of the return interval in time series for the threshold value . The return interval is the distance between two adjacent events that exceed the threshold . The black dotted line in (b) represents the next unknown events that exceed the threshold at the moment of “NOW”; is the elapsed time since the last event; and is the residual waiting time to the next extreme event.

(a)

(b)