Where can I find a study on the amount of different word frequencies in a corpus?
What you're asking directly refers to Information Retrieval. Information Retrieval directly creates models for such things as frequency of words in a corpus and so on.

In a corpus, different indicators are estimated in order to create a score. Two indicators are predominant in those models :


Inverse document frequency (idf)


This model aims at attenuating words that appear too often and considered irrelevant to judge the score of a word.

$ idf_{t} = log\frac{N}{df_{t}}$ where $N$ stands for the total of document in a collection and $df_{t}$  the number of documents in a collector that contain the term $t$


Term frequency (tf)


This is the most basic way to modelize word frequency in a corpus. It can be computed by saying that:

$tf_{t,d} = \frac{t_{occ}}{N}$ where $t_{occ}$ is the occurence of the term divided by the number of words in the document.

More information on this subject can be found here :

Scoring, term weighting and the
vector space model