Large-Scale Analysis of Zipf's Law in English Texts

PloS One
Isabel Moreno-SánchezÁlvaro Corral

Abstract

Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been confronted to a representatively large number of texts. So, we can summarize the current support of Zipf's law in texts as anecdotic. We try to solve these issues by studying three different versions of Zipf's law and fitting them to all available English texts in the Project Gutenberg database (consisting of more than 30 000 texts). To do so we use state-of-the art tools in fitting and goodness-of-fit tests, carefully tailored to the peculiarities of text statistics. Remarkably, one of the three versions of Zipf's law, consisting of a pure power-law form in the complementary cumulative distribution function of word frequencies, is able to fit more than 40% of the texts in the database (at the 0.05 significance level), for the whole domain of frequencies (from 1 to the maximum value), and with only one free parameter (the exponent).

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Citations

Mar 9, 2017·Scientific Reports·Iván González TorreAntoni Hernández-Fernández
Feb 5, 2019·PloS One·Carlos Velarde, Alberto Robledo
Apr 18, 2020·Journal of Speech, Language, and Hearing Research : JSLHR·Adam C LammertThomas F Quatieri
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Sep 28, 2017·Physical Review. E·Álvaro Corral, Francesc Font-Clos
May 11, 2019·Physical Review Letters·Martin Gerlach, Eduardo G Altmann
Jan 23, 2020·Physical Review. E·Víctor Navas-PortellaÁlvaro Corral
Dec 9, 2020·PloS One·Adrian Patrick Kennedy, Sheung Chi Phillip Yam
Dec 9, 2020·Entropy·Álvaro Corral, Montserrat García Del Muro
Jan 1, 2021·Proceedings of the National Academy of Sciences of the United States of America·Matteo SerafinoGuido Caldarelli
Aug 21, 2021·PloS One·Iván G TorreAntoni Hernández-Fernández
Aug 29, 2021·Scientific Reports·Charlie Pilgrim, Thomas T Hills

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