  Some authors have recently argued that a finite-size scaling law for the
text-length dependence of word-frequency distributions cannot be conceptually
valid. Here we give solid quantitative evidence for the validity of such
scaling law, both using careful statistical tests and analytical arguments
based on the generalized central-limit theorem applied to the moments of the
distribution (and obtaining a novel derivation of Heaps' law as a by-product).
We also find that the picture of word-frequency distributions with power-law
exponents that decrease with text length [Yan and Minnhagen, Physica A 444, 828
(2016)] does not stand with rigorous statistical analysis. Instead, we show
that the distributions are perfectly described by power-law tails with stable
exponents, whose values are close to 2, in agreement with the classical Zipf's
law. Some misconceptions about scaling are also clarified.
