I often find myself asking questions like, "I know this variable $x$ lies in $(0,1)$ and most of the mass lies in $(0,.20)$ and then declines continuously towards 1. What distribution can I use to model it?"
In practice, I wind up using the same few distributions over and over again simply because I know them. Instead, I'd like to look them up in a more systematic way. How do I go about accessing the wealth of work that probabilitists have done developing all of these distributions?
Ideally I'd like a reference organized by properties (region of support, etc.), so I can find distributions by their characteristics and then learn more about each distribution based on the tractability of the pdf/cdf and how closely the theoretical derivation fits the problem I'm working on.
Does such a reference exist, and if not, how do you go about choosing distributions?