  The article introduces corrections to Zipf's and Heaps' laws based on
systematic models of the proportion of hapaxes, i.e., words that occur once.
The derivation rests on two assumptions: The first one is the standard urn
model which predicts that marginal frequency distributions for shorter texts
look as if word tokens were sampled blindly from a given longer text. The
second assumption posits that the hapax rate is a simple function of the text
length. Four such functions are discussed: the constant model, the Davis model,
the linear model, and the logistic model. It is shown that the logistic model
yields the best fit.
