# Reference with distributions with various properties

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?

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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.

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You should find all of them on Google books for a peek. –  Momo Apr 8 '12 at 16:27
(+1) These are the classical references and a great place to start. I'm also a big fan of the poster, especially when printed at actual poster size. I've seen a few different incarnations of it. –  cardinal Apr 8 '12 at 18:24
The poster looks awesome. :-). The books look...intimidating. –  Ari B. Friedman Apr 9 '12 at 12:56
@gsk3: The books are desk references. They're intended to be (somewhat) comprehensive. –  cardinal Apr 9 '12 at 13:07
I think if you got the univar book, drilled a hole through it, mounted it to one end of a pole, and did the same with the multivar book on the other side, you'd have a nice zombie sledgehammer. –  Ari B. Friedman Apr 9 '12 at 15:36
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Merran Evans, Nicholas Hastings, Brian Peacock - Statistical distributions - John Wiley and Sons

I have the second edition and the distributions are in simple alphabetical order (from Bernoulli to Wishart central distribution).

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