Well, the first thing that manifests itself in these graphs is that in many cases the actual reduplication count is tremendously higher than the expected. I don't know how to explain that except shuffling.

And even if text being shuffled, why it would lead to such curious result.
Next, supposing there's no shuffling,
aiin is outstanding in that it never reduplicates, while that is something what would be expected, if the words were independent. Given that the pattern "aiin any aiin any" is exhibited more often than "expected", this, I'd say, would strongly suggest aiin being some specific word. Like all other words are function, while
aiin is not, or
aiin is function while others are not, don't know.
aiin is not like others. Same thing about
shey, although here the expected count is probably too low to make conclusions.