Beyond Zipf’s law: Exploring the discrete generalized beta distribution in open-source repositories

Rank-size distributions, such as Zipf’s Law, have been instrumental in providing insights into the emergence of hierarchies across diverse systems, from linguistic corpuses to urban structures. However, the application of Zipf’s Law reveals limitations, particularly in its focus on distribution tails, sometimes overlooking a large proportion of the data which might play a pivotal role in system dynamics. Yet, fitting rank-size distributions other than a straight line on the log–log scale requires caution. In this study, we re-evaluate the utility of rank-size distributions by contrasting the traditional Zipf’s Law with the Discrete Generalized Beta Distribution (DGBD). We show the need of cautious fitting techniques for rank distributions, including the use of binning to prevent overfitting to data tails. Through both analytical derivation and empirical validation on commit data of open-source repositories, we show that DGBD consistently improves over Zipf distribution for concave rank distributions of large datasets (N≥100). This approach contributes to the advancement of methodologies for analyzing hierarchical systems.