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arXiv · 1901.00521

Types, Tokens, and Hapaxes: A New Heap's Law

Victor Davis
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Abstract

Heap's Law states that in a large enough text corpus, the number of types as a function of tokens grows as $N=KM^\beta$ for some free parameters $K,\beta$. Much has been written about how this result and various generalizations can be derived from Zipf's Law. Here we derive from first principles a completely novel expression of the type-token curve and prove its superior accuracy on real text. This expression naturally generalizes to equally accurate estimates for counting hapaxes and higher $n$-legomena.

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Victor Davis. 2018-12-31. Types, Tokens, and Hapaxes: A New Heap's Law. https://arxiv.org/abs/1901.00521

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