The Distribution of Phoneme Frequencies across the World's Languages: Macroscopic and Microscopic Information-Theoretic Models

TL;DR

This paper presents a unified information-theoretic framework explaining phoneme frequency distributions across languages at both macro and micro levels, linking inventory size, entropy, and phoneme probabilities.

Contribution

It introduces a macroscopic Dirichlet distribution model and a microscopic Maximum Entropy model to explain phoneme frequency patterns across languages.

Findings

Phoneme rank-frequency distributions follow a Dirichlet order statistic.

Larger phonemic inventories have lower relative entropy.

Maximum Entropy models accurately predict language-specific phoneme probabilities.

Abstract

We demonstrate that the frequency distribution of phonemes across languages can be explained at both macroscopic and microscopic levels. Macroscopically, phoneme rank-frequency distributions closely follow the order statistics of a symmetric Dirichlet distribution whose single concentration parameter scales systematically with phonemic inventory size, revealing a robust compensation effect whereby larger inventories exhibit lower relative entropy. Microscopically, a Maximum Entropy model incorporating constraints from articulatory, phonotactic, and lexical structure accurately predicts language-specific phoneme probabilities. Together, these findings provide a unified information-theoretic account of phoneme frequency structure.