(a) Zipf's Law: word counts are globally distributed according to a power law

. The maximum likelihood estimates of the characteristic exponent

are 1.83 for Wikipedia, 1.78 for IS, and 1.88 for ODP. A Kolmogorov-Smirnov goodness-of-fit test comparing the original data against 2500 synthetic datasets gives p-values for the maximum likelihood fits of 1 for Wikipedia and IS and 0.56 for ODP, all well above a conservative threshold of 0.1. This ensures that the power-law distribution is a plausible and indeed very good model candidate for the real distributions. (b) Heaps' law: as the number of words

*n* in a document grows, the average vocabulary size (i.e. the number of distinct words)

*w(n)* grows sublinearly with

*n*. (c) Burstiness: fraction of documents

*P(f*_{d}) containing

*f*_{d} occurrences of common or rare terms. For each dataset, we label as “common” those terms that account for 71% of total word occurrences in the collection, while rare terms account for 8%. (d) Similarity: distribution of cosine similarity

*s* across all pairs of documents, each represented as a term frequency vector. Also shown are

*w(n)*, the distributions of

*f*_{d}, and the distribution of

*s* according to the Zipf null model (see text) corresponding to the IS dataset.