Comment on 'A Scaling law beyond Zipf's law and its relation to Heaps' law' [arXiv:1303.0705]
Xiao-Yong Yan, Petter Minnhagen · arXiv (Cornell University) · 2014
It is shown that the scaling law for the text-length dependence of word-frequency distributions proposed by Font-Clos et al in 2013 [New J. Phys. 15 093033, arXiv:1303.0705] is fundamentally impossible and leads to incorrect conclusions. Instead the text-length-dependence can be connected to the general properties of a random book with consistent agreement. It is pointed out that this finding has strong implications, when deciding between two conceptually different views on word-frequency distributions, i.e. the `Zipf's-view' and the `Randomness-view', as is discussed. It is also noticed that the text-length transformation of a random book does have an exact scaling property precisely for the power-law index $\gamma=1$, as opposed to the Zipf's exponent $\gamma=2$ and the implication of this exact scaling property is discussed. However a real text has $\gamma>1$ and as a consequence $\gamma$ increases when shortening a real text, contrary to the claim by Font-Clos et al in 2013 New J. Phys. 15 093033. The connections to the predictions from the RGF (Random Group Formation) and to the infinite length-limit of a meta-book are also discussed. The difference between `curve-fitting' and `predicting' word-frequency distributions is stressed.