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I'd like to review published papers or book chapters (so I could formally refer to them) that graphically illustrate the parametric relationships between univariate distribution families. The papers by Lawrence M. Leemis are well-known, see e.g. here for 1986 and 2008 versions. This paper presents two more diagrams and mentions two more sources for previously published graphical summaries:

Nakagawa, T. and Yoda, H. (1977) Relationships among distributions. IEEE Transactions on Reliability, 26(5), 352–353.

Kotz, S. and Jogn Rene van Dorp (2004) Beyond Beta—Other Continuous families of Distributions with Bounded Support and Applications, World Scientific, NJ, p. 251.

Here is another link to a paper with presumably original contribution.

Are there any useful omissions in the above list? Is there a paper that reviews various graphical summaries of the known relationships between univariate distributions?

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    $\begingroup$ Not a paper, but I highly recommend this blog post by @JohnD.Cook: Clickable diagram of probability distribution relationships. $\endgroup$ Feb 8 '14 at 3:13
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    $\begingroup$ Thanks, I think it would be okay to make an exception for contributions to well-known blogs by statisticians, provided the contributions are original. $\endgroup$ Feb 8 '14 at 3:32
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    $\begingroup$ If you click through the link to the 'clickable version' you get the information: "The chart above is adapted from the chart originally published by Lawrence Leemis in 1986 (Relationships Among Common Univariate Distributions, American Statistician 40:143-146.) Leemis published a larger chart in 2008 which is available online." $\endgroup$
    – Glen_b
    Feb 8 '14 at 3:50
  • $\begingroup$ @Glen_b, good point. Presumably I knew that in the past when I first spent time w/ that post, but now I simply remembered it, found the link & pasted it here w/o rereading the blurb. $\endgroup$ Feb 8 '14 at 3:54
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    $\begingroup$ @gung That wasn't intended as criticism in any sense; just trying to make sure Hibernating was aware that a reference to the original paper was there, since that's what was asked for. $\endgroup$
    – Glen_b
    Feb 8 '14 at 5:39
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Not a paper, but I highly recommend this blog post by @JohnD.Cook: Clickable diagram of probability distribution relationships

-gung

If you click through the link to the 'clickable version' you get the information: "The chart above is adapted from the chart originally published by Lawrence Leemis in 1986 (Relationships Among Common Univariate Distributions, American Statistician 40:143-146.) Leemis published a larger chart in 2008 which is available online."

-Glen_b

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  • $\begingroup$ I've copied these comments as a community wiki answer because they are, more or less, answers to this question. We have a dramatic gap between answers and questions. At least part of the problem is that some questions are answered in comments: if comments which answered the question were answers instead, we would have fewer unanswered questions. – $\endgroup$
    – mkt
    Sep 11 '19 at 12:00

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