Table 2. The parameters for fitting CDFs shown in Figs. 2 and 3 (S&P500 Index in the US stock market) with R or R′ ranging from “Minimum” to “Maximum”.

CDF	Minimum	Maximum	α	Std. Dev.	r 2
Fig. 2(a) : R	1	100	2.28	0.01	0.99
Fig. 2(b) : R′	1	100	2.05	0.01	0.99
Fig. 3(a): Rfor Δt = 1	2	62	1.41	0.01	0.99
Fig. 3(a): Rfor Δt = 10	2	28	3.28	0.02	0.99
Fig. 3(a): Rfor Δt = 50	2	50	2.52	0.01	0.99
Fig. 3(a): Rfor Δt = 100	2	62	1.86	0.01	0.99
Fig. 3(b): R′for Δt = 1	3	58	1.39	0.01	0.99
Fig. 3(b): R′for Δt = 10	3	27	3.15	0.03	0.99
Fig. 3(b): R′for Δt = 50	3	53	2.52	0.01	0.99
Fig. 3(b): R′for Δt = 100	3	58	1.87	0.01	0.99

α is the exponent (scaling parameter); “Std. Dev.” is the standard deviation for α, indicating the fitting error; and r ² is the regression coefficient that represents the degree of fitting with the power law: the perfect fitting corresponds to r ² = 1 [30].