Language Learning, Power Laws, and Sexual Selection

A diagnostic of a power law distribution is that a log-log plot of frequency against rank yields a (nearly) straight line. For instance, Zipf (1935) plotted word token counts in a variety of texts against the inverse rank of each distinct word type and showed that typically such plots approximate a straight line. The characteristic ‘Zipf curve’ of word frequency against rank deviates from this line because the relative frequency of very common word types, such as the English determiners the and a, tend to be more similar than the power law predicts, as also does the relative frequency of very rare words in the tail of the distribution. Zipf’s ‘law’ is often expressed as: c(w) ∝ 1 r(w)B (1)