Table 1. Comparison of the estimators ML* and ML_CSN on empirical data sets that were used in [23].

These include the frequency of surnames, intensity of wars, populations of cities, earthquake intensity, numbers of religious followers, citations of scientific papers, counts of words, wealth of the Forbes 500 firms, numbers of papers authored, solar flare intensity, terrorist attack severity, numbers of links to websites, and forest fire sizes. We added the word frequencies in the novel “A tale of two cities” (C. Dickens). The second column states if α or λ were estimated. The exponents reported in [23] are found in column CSN₁, those reproduced by us applying their algorithm to data [23, 34–37] is shown in column CSN₂. The latter correspond well with the new ML* algorithm. For values λ < 1.5, CSN can not be used. We list the corresponding values for Kolmogorov-Smirnov test for the two estimators, KS_CSN and KS*.

	exp.	CSN1	CSN2	ML*	KSCSN	KS*
blackouts	λ	2.3	2.27	2.25	0.061	0.031
surnames	α	2.5	2.49	2.66	0.041	0.019
int. wars	λ	1.7	1.73	1.83	0.078	0.076
city pop.	λ	2.37	2.36	2.31	0.019	0.016
quake int.	λ	1.64	1.64	1.88	0.092	0.085
relig. fol.	λ	1.8	1.79	1.61	0.091	0.095
citations	λ	3.16	3.16	3.10	0.010	0.018
words	α	1.95	1.95	1.99	0.009	0.015
wealth	λ	2.3	2.34	2.30	0.063	0.066
papers	λ	4.3	4.32	3.89	0.079	0.082
sol. flares	λ	1.79	1.79	1.81	0.009	0.021
terr. attacks	λ	2.4	2.37	2.36	0.018	0.017
websites	λ	2.336	2.12	1.72	0.025	0.056
forest fires	λ	2.2	2.16	2.46	0.036	0.034
Dickens novel	λ	-	-	1.04	-	0.017