Vord length distribution

[Anton]

Thanks... yes I get the same counts over your sample.

It turns out this is not the process which leads us to normal distribution.  

Indeed, with random generators which produce uniformly distributed results the word type frequency distribution will be uniform.

To get what we want (binomial/normal) we can act in the success/failure fashion, kinda what Stolfi discussed.

Here's the word generation process.

Suppose there are N targets, let's say thirteen, and we are shooting those targets in succession. Let's say the chance to hit the target is 50%. Those targets which we manage to hit, we fill with letters, one letter per target. Does not matter which letters, let's say we pick them randomly. (This will ensure that we mostly generate new word each time, and not repeat words already generated). If we hit 5/13, this would be a 5-character word. If we hit 11/13, this is 11-character word. And so on. If we hit zero targets (which will not happen very often, but is a realistic case), we don't record the word at all.

And then we clear all 13 targets and repeat this process again to generate the next word. And this way we generate a vocabulary of words.

Then the word length distribution will be binomial.