Zipf's Law Leads to Heaps' Law

Lü, Zhang, & Zhou. (2010). Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems. PLoS ONE.

Type

Journal article

Intellectual base

Primary research

Year

2010

DOI

10.1371/journal.pone.0014139

DOI registrant

Public Library of Science

Link

https://doi.org/10.1371/journal.pone.0014139

Cited by

1 citation across 1 artifact.

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Domain-specific

• Heaps' Law
  • The mechanism behind the regularity is the Zipfian rank-frequency distribution of words: when the r-th most common word has frequency proportional to 1/r^α with α > 1, the expected type count at sample size N grows asymptotically as N^(1/α), so β = 1/α in the large-sample limit and the two laws are analytically coupled

    This sourceLü, Zhang & Zhou (2010) establish that β=1/α is an asymptotic, large-size-limit relation that degenerates to β=1 for α≤1; the two-regime core-lexicon/rare-tail account of natural-language Zipf exponents used here to reconcile that coupling with observed β≈0.4–0.6 is not this paper's finding and needs a separate source (e.g., empirical work on the two-piece structure of word-frequency rank curves).

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