Table 1.
Zipf–Mandelbrot parameters.
| Dataset | N. of galaxies | N. of groups | N. of clusters | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Q | Qmin | γ | Q | Qmin | γ | Q | Qmin | γ | |
| Liivamagi (2012a) | 1.68 | 2.21 × 10−5 | 0.79 | 1.48 | 2.34 × 10−6 | 0.70 | − | − | − |
| Liivamagi (2012b) | 2.16 × 10−6 | 8.28 × 10−8 | 0.51 | 1.54 × 10−5 | 7.73 × 10−8 | 0.46 | − | − | − |
| Einasto (2007) | 3.12 × 10−5 | 4.41 × 10−8 | 0.76 | 0.42 | 1.23 × 10−7 | 0.77 | 1.10 | 6.71 × 10−5 | 0.73 |
| Einasto (2006) | 1.12 | 5.91 × 10−7 | 0.78 | 1.46 | 3.56 × 10−6 | 0.70 | 0.03 | 1.09 × 10−7 | 0.51 |
| Einasto (2001) | − | − | − | − | − | − | 0.51 | 8.18 × 10−7 | 0.53 |
| Chow Martinez (2014a) | − | − | − | − | − | − | 0.99 | 1.44 × 10−6 | 0.51 |
| Chow Martinez (2014b) | − | − | − | − | − | − | 0.84 | 1.12 × 10−5 | 0.60 |
Notes. Values of the deviation parameter Q and the Zipf’s exponent γ for all the rank-size plots shown in Fig. 1. We also report the minimum value of Q, denoted by Qmin, at 95% confidence. Since all Qmin are very close to zero, all samples are compatible with a power law with an intrinsic upper cutoff much larger than the observed maximum.
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