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?
The most comprehensive collection of distributions and their properties that I know of are
Johnson, Kotz, Balakrishnan: Continuous Univariate Distributions Volume 1 and 2;
Kotz, Johnson, Balakrishnan: Continuous Multivariate Distributions;
Johnson, Kemp, Kotz: Univariate Discrete Distributions;
Johnson, Kotz, Balakrishnan: Multivariate Discrete Distributions;
The books have a broad subject index. All books are from Wiley.
Edit: Oh yes and then there also is the nice poster displaying properties and relationships between univariate distributions. http://www.math.wm.edu/~leemis/2008amstat.pdf This might be of further interest.