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 tasks and researchers treat those forms as different concepts. In this paper, we are curious to know whether there are some common characteristics connecting 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 properties behind those diverse entities. We find from twelve datasets about different types of entities and eighteen datasets about different languages of entities that although these entities are dramatically diverse from each in many aspects, their length-frequencies can be well characterized by Marshall-Olkin power-law (MOPL) distributions, and these distributions possess defined means and finite variances. Our experiments show that while not all the entities are drawn from the same underlying population, those entities under same types tend to be drawn from the same distribution. Our experiments also show that Marshall-Olkin power-law models characterize the length-frequencies of entities much better than pure power-law models and log-normal models.