Proper Interpretation of Heaps' and Zipf's Laws

Abstract

We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a ``superposition'' model, which leads to an asymptotic power-law distribution of the number of occurrences (or frequency) of words, that is, Zipf's law. The model is well consistent with observations.