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A reference that not just enlist the formulas of continuous (multivariate) distributions but goes in details about them and maybe treat the relations between them (e.g. derivation/proofs, intuition and applications).

Of course the normal distribution is not the problem, but, for example, the following are hardly touched in many books:

  • Gamma, Beta
  • Chi-square
  • Student's t
  • Multivariate Student's t

I found these references/books so far:

  • statlect.com: contains all the mentioned distributions above but still feels like just a database of formulas.
  • Introduction to Probability, Second Edition By Joseph K. Blitzstein, Jessica Hwang : this book touches on non-multivariate continuous distribution, and a good gamma, beta reference.
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  • $\begingroup$ Because most of the distribution names you have listed apply only to univariate distributions, could you please be more specific about what you mean by "multivariate"? $\endgroup$
    – whuber ♦
    Commented Jun 8, 2019 at 21:15
  • $\begingroup$ @whuber Any distribution over random vectors (if it exists). Of course there are more continuous distributions. But, those felt related (including the normal distribution), thus I guess maybe there's a reference that treat them as such. $\endgroup$
    – one1
    Commented Jun 9, 2019 at 0:27
  • $\begingroup$ The series of volumes by Johnson, Kotz, and Balakrishnan is extremely thorough. (See this Google image search as an illustration ... $\endgroup$
    – Ben Bolker
    Commented Jul 1, 2019 at 11:31

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One reference that goes into much detail about some of this distribution, like the Wishart distribution, which is a matrix analogy of the chi-square distributions. So it appears in theory of manova. That is Robb Muirhead's Aspects of Multivariate Statistical Theory.

Another good book going even more into the mathemathical theory behind the calculations is R. H. Farrell's Techniques of Multivariate Calculation (Lecture Notes in Mathematics) . If you want something more basic, you can say so in a comment.

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    $\begingroup$ Thanks a lot. I didn't try to read them yet, but if you could enlist more basic resources for me and future viewers, it would be nice. $\endgroup$
    – one1
    Commented Jul 7, 2019 at 9:01

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