# Distribution of number of files in folders on personal computers?

At a company I work for, we're trying to simulate running software on an enterprise-scale system. We would like to put files in folders, to simulate a customer environment. At the moment, we uniformly distribute files into folders, so that each folder has the same number of files (roughly 5).

We'd like to make a more realistic setup. To that end, I have a question:

• What distribution do the number of files in a folder on a typical personal computer tend to?

We guessed that a power law (with $0<\alpha<1)$ might be sensible, although it's mildly problematic since it's not discrete (and the number of files per folder is always integer), and it's singular at the origin, which makes no sense (since we'd expect a finite nonzero number of folders to be empty).

What sort of discrete distribution would be most realistic?

• There are discrete power laws (see the zeta and the closely related Zipf's law), but for something like that I'd start by considering some kind of stochastic process (maybe a Chinese restaurant process, for example). I bet this particular modelling problem has been dealt with in the computing literature (rather than the stats or ML literature). – Glen_b Mar 26 '15 at 5:07
• Interesting question, but without any empirical data, how would anyone judge the realisticness of a particular answer? – rolando2 Mar 26 '15 at 11:40