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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?

Hibernating
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    Not a paper, but I highly recommend this blog post by @JohnD.Cook: [Clickable diagram of probability distribution relationships](http://www.johndcook.com/blog/2008/10/12/clickable-diagram-of-probability-distribution-relationships/). – gung - Reinstate Monica Feb 08 '14 at 03:13
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    Thanks, I think it would be okay to make an exception for contributions to well-known blogs by statisticians, provided the contributions are original. – Hibernating Feb 08 '14 at 03:32
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    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 Feb 08 '14 at 03:50
  • @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. – gung - Reinstate Monica Feb 08 '14 at 03:54
  • That I myself is here interested in the original contributions only does not automatically mean that links to something based on them cannot not be useful to others. Some may prefer something clickable to a formal review I am after. – Hibernating Feb 08 '14 at 04:20
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    @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. – Glen_b Feb 08 '14 at 05:39
  • The problem with such attempts is that in order to produce a diagram, one has to represent a distribution as a black box name (say InvertedGamma(a,b) or InverseGamma(a,b) etc), and there are usually multiple competing definitions and parameterisations in common usage ... which can easily get lost or confused in such diagrams. The diagrams can give the pretence of order and structure, when reality is unfortunately quite different, so they need to be used with inordinate care. – wolfies Feb 08 '14 at 14:18

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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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mkt
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  • 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. – – mkt Sep 11 '19 at 12:00