# Simple stochastic processes behind Menzerath's Law

arXiv: https://arxiv.org/abs/2409.00279 · HTML: https://mlsanity.com/paper/2409.00279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2024.

## Abstract (arXiv)

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.