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Is there a comprehensive list of distributions, e.g. gamma, Poisson, Gaussian, and when you should use each somewhere? My internet searching has been fruitless.

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It is impossible to come up with a comprehensive list of distributions, simply because the space of probability distributions is an infinite dimensional space.

There are many sources where you can find the popular ones:

Wikipedia: http://en.wikipedia.org/wiki/List_of_probability_distributions

The books by Kotz: http://www.amazon.com/s/ref=ntt_athr_dp_sr_2/187-8807448-8621258?_encoding=UTF8&field-author=Samuel%20Kotz&search-alias=books&sort=relevancerank

Among many, many, many other compilations.

Even more, there is new journal about newly developed distributions:

http://www.jsdajournal.com/

In these compilations you will find basic features of the distributions, such as whether they are discrete or continuous, symmetric or asymmetric, heavy-tailed or light-tailed. However, the final choice is up to the user, and this is usually based on their experience, intuition, and etcetera. This idea is summarised in the popular saying "Modelling is an art".

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  • $\begingroup$ I'm more interested in a consolidated table or logic tree of information on when to use each. $\endgroup$ – timothy.s.lau Aug 3 '14 at 5:41
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As @Glen_b points out, the question is just too broad. I believe these links provide some helpful references. I believe it would help to know what you are particularly interested in, so that someone can point to actually relevant distributions.

Still, I love this table. It covers most common distributions, and provides with the relationships with their resp. conjugate priors. A more comprehensive diagram is this one. Notice that this diagrams are interactive, so that you can click on each element, and you jump to a description of the distribution.

See also the related entries and references.

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  • $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. $\endgroup$ – Andy Aug 1 '14 at 10:44
  • $\begingroup$ you're right Andy. In this case this links are very interesting because they provide an interactive chart I cannot embed in here. Plus they provide some further valuable links. $\endgroup$ – jpmuc Aug 1 '14 at 11:24
  • $\begingroup$ Can you get any ofthe relevant info here? If not, it might be better as a comment. $\endgroup$ – gung - Reinstate Monica Aug 1 '14 at 11:53

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