Article,
Can simple models explain Zipf's law for all exponents?
Glottometrics, (2005)
Abstract
H. Simon proposed a simple stochastic process for explaining Zipf’s law for word
frequencies. Here we introduce two similar generalizations of Simon’s model that cover the same
range of exponents as the standard Simon model. The mathematical approach followed minimizes the
amount of mathematical background needed for deriving the exponent, compared to previous
approaches to the standard Simon’s model. Reviewing what is known from other simple explanations
of Zipf’s law, we conclude there is no single radically simple explanation covering the whole range of
variation of the exponent of Zipf’s law in humans. The meaningfulness of Zipf’s law for word
frequencies remains an open question.
