Uniform's pretty much the go to distribution for stuff like that--or having a non-random piece and a small random component. That's how Pokemon determined Catch

Uniform's pretty much the go to distribution for stuff like that--or having a non-random piece and a small random component. That's how Pokemon determined Catch Rates[1]. The problem with a lot of these distributions is that while you may have a closed form expressed for the PDF, it doesn't always give you an easy way to generate samples from that distribution. There's a huge amount of research that goes into efficient ways to generate samples from these distributions, and they are often quite complex once you are unable to use the inverse probability transform [2]. There's a reason that the Metropolis-Hastings Algorithm was such a big breakthrough, and that's because sampling is often quite difficult. In the multivariate setting, sometimes you may have to throw away 10,000 random numbers before you finally get one that could come from your target distribution. For most of the univariate distributions, it's not tremendously difficult to sample, though, so you may be okay. [1]: http://bulbapedia.bulbagarden.net/wiki/Catch_rate http://bulbapedia.bulbagarden.net/wiki/Catch_rate (this article is total nerdvana, by the way) [2]: http://en.wikipedia.org/wiki/Inverse_transform_sampling http://en.wikipedia.org/wiki/Inverse_transform_sampling