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The dependence with text length of the statistical properties of wordoccurrences has long been considered a severe limitation quantitativelinguistics. We propose a simple scaling form for the distribution of absoluteword frequencies which uncovers the robustness of this distribution as textgrows. In this way, the shape of the distribution is always the same and it isonly a scale parameter which increases linearly with text length. By analyzingvery long novels we show that this behavior holds both for raw, unlemmatizedtexts and for lemmatized texts. For the latter case, the word-frequencydistribution is well fit by a double power law, maintaining the Zipf's exponentvalue $\gamma\simeq 2$ for large frequencies but yielding a smaller exponent inthe low frequency regime. The growth of the distribution with text lengthallows us to estimate the size of the vocabulary at each step and to propose analternative to Heaps' law, which turns out to be intimately connected to Zipf'slaw, thanks to the scaling behavior.

A scaling law beyond Zipf's law and its relation to Heaps' law