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 $f_X(x)$.
Here are two more distribution resources. They are descriptive and present equations, without much proof, application, or even discussion.
From Dr. M.P. McLaughlin: http://www.causascientia.org/math_stat/Dists/Compendium.pdf
Look at the series "Distributions in Statistics" by Johnson and Kotz.
Continuous Univariate Distributions, Vol. 1 (Wiley Series in Probability and Statistics)
Continuous Univariate Distributions, Vol. 2 (Wiley Series in Probability and Statistics)
Univariate Discrete Distributions (Wiley Series in Probability and Statistics)
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