Two Regimes in the Frequency of Words and the Origins of Complex Lexicons: Zipf’s Law Revisited^∗

It is made evident that word frequency as a function of the rank follows two different exponents, ˜(-)1 for the first regime and ™(-)2 for the second.

Abstract

Zipf's law states that the frequency of a word is a power function of its rank. The exponent of the power is usually accepted to be close to (-)1. Great deviations between the predicted and real number of different words of a text, disagreements between the predicted and real exponent of the probability density function and statistics on a big corpus, make evident that word frequency as a function of the rank follows two different exponents, ~(-)1 for the first regime and ~(-)2 for the second. The implications of the change in exponents for the metrics of texts and for the origins of complex lexicons are analyzed.