Rank diversity of languages: Generic behavior in computational linguistics

TL;DR

This study introduces rank diversity as a new measure of how word ranks change over time in languages, revealing universal patterns and categorizing words into stable, general, and context-specific regimes across six European languages.

Contribution

It presents the concept of rank diversity, demonstrates its universal lognormal distribution, and proposes a Gaussian random walk model to explain word rank variations over time.

Findings

Rank diversity follows a universal lognormal distribution.

Languages have similar core sizes of basic communication words.

A Gaussian random walk model reproduces observed rank variations.

Abstract

Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: "heads" consist of words which almost do not change their rank in time, "bodies" are words of general use, while "tails" are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.