Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words

Eduardo G. Altmann*, Janet B. Pierrehumbert, Adilson E. Motter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

135 Scopus citations


Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well. Methodology/Principal Findings: By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type - a measure of the logicality of each word - and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage. Conclusions/Significance: Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipf's law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics.

Original languageEnglish (US)
Article numbere7678
JournalPloS one
Issue number11
StatePublished - Nov 11 2009

ASJC Scopus subject areas

  • General
  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences


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