Power-Law Behavior in the Inter-Event Times of Word Occurrences

In this paper, we investigate the inter-event times of frequent words observed in 17 academic books, where the inter-event time is defined as the number of sentences between two successive appearances of a given word. Our results show that the distributions of inter-event times for frequent words can be classified into three types: the exponential distribution, the q-exponential distribution, and the power-law distribution. To examine the generative mechanisms underlying these three types, we conducted text generation simulations and found that combining two mechanisms for word selection—priority-based selection and randomized selection—is sufficient to reproduce the observed three distribution types. In particular, the priority-based selection mechanism, in which words for a constructed sentence are chosen mechanically according to predefined priorities assigned to each word, is identified as the underlying mechanism of the power-law distribution of inter-event times. We also discuss in detail the relationship between the priority-based selection mechanism and the multivariate Hawkes process, which effectively captures mutual correlations among occurrences of important words.