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Table 1 Exponents of Zipf’s Law and Heaps’ Law. Column 1 displays \(\beta = 1+ \alpha \); the PDF exponent of Zipf’s Law with corresponding standard deviation displayed in column 2 for each of the four continents. Values were calculated by fitting a line to the PDF of city sizes X for each continent, starting from a minimum population of \(X = 10^{5}\) (see Fig. 2(a)). Column 3 displays γ; the exponent of Heaps’ Law with corresponding standard deviation displayed in column 4 for each of the four continents. Values of γ and the error were obtained by fitting a line to the logarithm of Heaps’ Law; \(\log (C) = \gamma \log (N)\), for each continent (see Figs. 2(b)–(c) and (e)–(f)). Exponents β and γ were fit to the data using non-linear least squares

From: Testing Heaps’ law for cities using administrative and gridded population data sets

Continent

β

\(\sigma _{\beta }\)

γ

\(\sigma _{\gamma }\)

Africa

1.77

0.05

0.78

0.09

Asia

1.94

0.04

0.85

0.05

America

1.96

0.04

0.97

0.07

Europe

2.02

0.05

1.01

0.06