# Statistical laws in linguistics

arXiv: https://arxiv.org/abs/1502.03296 · HTML: https://mlsanity.com/paper/1502.03296/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2015.

## Built on by (most cited first, 13 of 13)

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- [Complete asymptotic type-token relationship for growing complex systems with inverse power-law count rankings](https://mlsanity.com/paper/2511.02069/) (2025)
- [A Zipf-preserving, long-range correlated surrogate for written language and other symbolic sequences](https://mlsanity.com/paper/2603.02213/) (2026)
- [Detecting Historical Turning Points in Italian Media: A Complex Systems Approach to a Diachronic News Corpus](https://mlsanity.com/paper/2606.14348/) (2026)
- [A scaling law of contextual persistence in human language](https://mlsanity.com/paper/2607.25184/) (2026)
- [A Generative Grammar Underlying the Voynich Manuscript, the Pastiche Hypothesis: Evidence from Large Language Models](https://mlsanity.com/paper/2609.20835/) (2026)

## Abstract (arXiv)

Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern availability of large databases of written text allows for tests with an unprecedent statistical accuracy and also a characterization of the fluctuations around the typical behavior. We find that fluctuations are usually much larger than expected based on simplifying statistical assumptions (e.g., independence and lack of correlations between observations).These simplifications appear also in usual statistical tests so that the large fluctuations can be erroneously interpreted as a falsification of the law. Instead, here we argue that linguistic laws are only meaningful (falsifiable) if accompanied by a model for which the fluctuations can be computed (e.g., a generative model of the text). The large fluctuations we report show that the constraints imposed by linguistic laws on the creativity process of text generation are not as tight as one could expect.