In the past few years a detailed quantitative model for automatic indexing based on some statistical assumptions about the distribution of words in text has been worked out by Bookstein, Swanson, and Harter[29, 30, 31].
The difference between the terms word-type and word-token is crucial to the understanding of their model.
A token instantiates a type, so that it is possible to refer to the occurrence of a word-type WAR; then a particular occurrence at one point in the text of a document (or abstract) will be a word-token.
Hence 'the frequency of occurrence of word w in a document' means the number of word-tokens occurring in that document corresponding to a unique word-type.
The type/token qualification of a word will be dropped whenever the context makes it clear what is meant when I simply refer to a 'word'.
In their model they consider the difference in the distributional behaviour of words as a guide to whether a word should be assigned as an index term.
Their starting point has been the much earlier work by Stone and Rubinoff, Damerau, and Dennis who showed that the statistical behaviour of 'speciality' words was different from that of 'function' words.
They found that function words were closely modelled by a Poisson distribution over all documents whereas specialty words did not follow a Poisson distribution.
Specifically, if one is looking at the distribution of a function word w over a set of texts then the probability, f(n), that a text will have n occurrences of the function word w is given by
In general the parameter x will vary from word to word, and for a given word should be proportional to the length of the text.
We also interpret x as the mean number of occurrences of the w in the set of texts.
The Bookstein-Swanson-Harter model assumes that specialty words are 'content-bearing' whereas function words are not.
What this means is that a word randomly distributed according to a Poisson distribution is not informative about the document in which it occurs.
At the same time the fact that a word does not follow a Poisson distribution is assumed to indicate that it conveys information as to what a document is about.
This is not an unreasonable view: knowing that the specialty word WAR occurs in the collection one would expect it to occur only in the relatively few documents that are about WAR.
On the other hand, one would expect a typical function word such as FOR to be randomly distributed.