The frequency spectrum of finite samples from the intermittent silence process

It has been argued that the actual distribution of word frequencies could be reproduced or explained by generating a random sequence of letters and spaces according to the so-called intermittent silence process. The same kind of process could reproduce or explain the counts of other kinds of units from a wide range of disciplines. Taking the linguistic metaphor, we focus on the frequency spectrum, i.e., the number of words with a certain frequency, and the vocabulary size, i.e., the number of different words of text generated by an intermittent silence process. We derive and explain how to calculate accurately and efficiently the expected frequency spectrum and the expected vocabulary size as a function of the text size.