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My course textbook for statistics is the one by Levine and Smith. However, I find myself interested in the various probability distributions. The author simply states the $f_X(x)$ and derives $F_X(x)$ and gives an application. I was in the hunt of a good online (FREE) resource which talks about probability distributions in a more intuitive setup. For instance, telling me WHY the equation for exponential, Weibull, Normal, Gamma etc. are the way they are. Especially gamma distribution, he simply states that in the calculus class one can learn to prove that the integral is convergent and states $f_X(x)$.

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    $\begingroup$ It's a good question, but could you be a little more specific about what kind of information you are looking for? The answers to "why" can range from a description of how a distribution arises in applications through a mathematical explanation of properties of its PDF, CDF, and related functions. What are you looking to learn about Gamma distributions? $\endgroup$ – whuber Oct 5 '12 at 16:01
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    $\begingroup$ @whuber, just motivation and uses really. I see people say that something is a normal by chi2 by dof and I ask them why did anyone ever try to do such a thing and they have no clue. $\endgroup$ – user8968 Oct 5 '12 at 20:00
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Here are two more distribution resources. They are descriptive and present equations, without much proof, application, or even discussion.

From NIST: http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm

From Dr. M.P. McLaughlin: http://www.causascientia.org/math_stat/Dists/Compendium.pdf

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Look at the series "Distributions in Statistics" by Johnson and Kotz.

  1. Continuous Univariate Distributions, Vol. 1 (Wiley Series in Probability and Statistics)

  2. Continuous Univariate Distributions, Vol. 2 (Wiley Series in Probability and Statistics)

  3. Univariate Discrete Distributions (Wiley Series in Probability and Statistics)

  4. Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition

They have a volume on discrete distributions, two volumes on univariate continuous distributions and one on multivariate continuous distributions. The various statistical encyclopedias are good sources and so is

Kendall's Advanced Theory of Statistics, Distribution Theory (Volume 1)

Free online information can be found in Wikipedia or through Google searches. There is a lot of good stuff out there. Free online information can be found in Wikipedia or through Google searches. There is a lot of good stuff out there. From Google From Wikipedia

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    $\begingroup$ This is a good resource but the OP says I was in the hunt of a good online (FREE) . $\endgroup$ – user10525 Oct 5 '12 at 15:43
  • $\begingroup$ Thanks Procrastinator I missed that. I still like good old fashion bound books written by the masters. $\endgroup$ – Michael Chernick Oct 5 '12 at 15:46
  • $\begingroup$ OK, I have included some links for completeness. (+1) $\endgroup$ – user10525 Oct 5 '12 at 15:51
  • $\begingroup$ @Procrastinator Thanks. While you did that I was adding the google and wikipedia links. Got stopped by your edit . But it is all there now! $\endgroup$ – Michael Chernick Oct 5 '12 at 15:55
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    $\begingroup$ It is noteworthy--and, I'm afraid, not very amusing--that acquiring this short list of (excellent) books would run about $1000 US. Perhaps one reason they are still so expensive is that the usual online resources aren't anywhere near as good or comprehensive. (E.g., yesterday I was looking for information about how inverse Gamma distributions might arise in nature--apart from their use as conjugate priors for Normal variances--and found nothing in the Wikipedia article.) $\endgroup$ – whuber Oct 5 '12 at 15:58

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