On the relation between types and tokens in literary text

The ratio of the number X n of different words (types) in a text of length n (token) words to n has received considerable attention in the literature of statistical linguistics. The present note contains two stochastic models for X n based on an inhomogeneous discrete Markov process of the pure birth type where the transition probabilities take certain forms depending only upon n. These models are then tested against data obtained from the plays of William Shakespeare.