  The dependence with text length of the statistical properties of word
occurrences has long been considered a severe limitation quantitative
linguistics. We propose a simple scaling form for the distribution of absolute
word frequencies which uncovers the robustness of this distribution as text
grows. In this way, the shape of the distribution is always the same and it is
only a scale parameter which increases linearly with text length. By analyzing
very long novels we show that this behavior holds both for raw, unlemmatized
texts and for lemmatized texts. For the latter case, the word-frequency
distribution is well fit by a double power law, maintaining the Zipf's exponent
value $\gamma\simeq 2$ for large frequencies but yielding a smaller exponent in
the low frequency regime. The growth of the distribution with text length
allows us to estimate the size of the vocabulary at each step and to propose an
alternative to Heaps' law, which turns out to be intimately connected to Zipf's
law, thanks to the scaling behavior.
