Marshall–Olkin power-law distributions in length-frequency of entities

Entities involve important concepts with concrete meanings and play important roles in numerous linguistic tasks. Entities have different forms in different linguistic tasks and researchers treat those different forms as different concepts. In this paper, we are curious to know whether there are some common characteristics that connect those different forms of entities. Specifically, we investigate the underlying distributions of entities from different types and different languages, trying to figure out some common characteristics behind those diverse entities. After analyzing twelve datasets about different types of entities and eighteen datasets about entities in different languages, we find that while these entities are dramatically diverse from each other in many aspects, their length-frequencies can be well characterized by a family of Marshall–Olkin power-law (MOPL) distributions. We conduct experiments on those thirty datasets about entities in different types and different languages, and experimental results demonstrate that MOPL models characterize the length-frequencies of entities much better than two state-of-the-art power-law models and an alternative log-normal model. Experimental results also demonstrate that MOPL models are scalable to the length-frequency of entities in large-scale real-world datasets.