Abstract: Let Vn be the number of word types in a text of n words. If the arrival of the ith word type is governed by a Poisson process with rate λi, we show that the growth rate of the series Σλi determines the asymptotic behavior of Vn. Specific conditions are given for Vn→∞ its rate of divergence, as well as its asymptotic rate of convergence to a distribution. The cases that λn=n-p, p>1 and λn =αn, 0<α<1 , are fully discussed, and they agree with two well known classical species-area models. Finally, for certain finite vocabulary cases, a correction factor is introduced.
Key words and phrases: Linguistics, Poisson process, regular variation, slow variation, species-area.