Simple stochastic processes behind Menzerath's Law

TL;DR

This paper demonstrates that simple stochastic processes, modeled by bivariate log-normal distributions and Gaussian copulas, can effectively explain Menzerath's Law in language, aligning well with empirical data.

Contribution

It introduces a new stochastic model based on multiplicative changes and Gaussian copulas that better fits Menzerath's Law data than previous models.

Findings

Bivariate log-normal distribution models word length changes.

Gaussian copula improves model accuracy.

Models align well with empirical linguistic data.

Abstract

This paper revisits Menzerath's Law, also known as the Menzerath-Altmann Law, which models a relationship between the length of a linguistic construct and the average length of its constituents. Recent findings indicate that simple stochastic processes can display Menzerathian behaviour, though existing models fail to accurately reflect real-world data. If we adopt the basic principle that a word can change its length in both syllables and phonemes, where the correlation between these variables is not perfect and these changes are of a multiplicative nature, we get bivariate log-normal distribution. The present paper shows, that from this very simple principle, we obtain the classic Altmann model of the Menzerath-Altmann Law. If we model the joint distribution separately and independently from the marginal distributions, we can obtain an even more accurate model by using a Gaussian copula. The models are confronted with empirical data, and alternative approaches are discussed.