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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 |