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I'm interested in relationships among distributions. Like 'Sum of exponential random variables is a gamma random variable. Certain conditional distribution is another distribution etc.' I searched wikipedia and google but there are just summaries of them, not specifically proved or explained. I want to know about distribution's relationships and detailed proof or explanation. Either web sites or books would be OK.

Xi'an
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C.Hawk
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    What about Page 47 of http://www.math.wm.edu/~leemis/2008amstat.pdf ? – Henry Sep 14 '16 at 08:01
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    with an almost interactive version at http://www.math.wm.edu/~leemis/chart/UDR/UDR.html – Henry Sep 14 '16 at 08:12
  • Thank you for your answer, but i already read that and there are no specific explanation or proofs... i can't fully understand relationships among distributions by given summaries... so sad. – C.Hawk Sep 14 '16 at 08:17
  • Related: [Comprehensive list of distributions?](http://stats.stackexchange.com/q/110235/22228); [Reference with distributions with various properties](http://stats.stackexchange.com/q/26073/22228) – Silverfish Sep 14 '16 at 12:18

2 Answers2

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Those books are massive references on all connections between distributions:

N.L. Johnson, S. Kotz, & N. Balakrishnan (1994) Continuous Univariate Distributions, Vol. 1. J. Wiley

N.L. Johnson, S. Kotz, & N. Balakrishnan (1995) Continuous Univariate Distributions, Vol. 2. J. Wiley

N.L. Johnson, S. Kotz, & A.W. Kemp (1993) Univariate Discrete Distributions. J. Wiley

that cover all the links found on the Wikipedia graph. If not all possible relationships, of course!

Xi'an
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Check the following papers:

Leemis, L. M. (1986). Relationships among common univariate distributions. The American Statistician, 40(2), 143-146.

Leemis, L. M., & McQueston, J. T. (2008). Univariate distribution relationships. The American Statistician, 62(1), 45-53.

You can find such information also in Wikipedia articles about probability distributions since in most cases they have Related distributions section that describes such relations.

Tim
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