Reading the excellent book Statistical Inference from George Casella and Roger L. Berger, I found a reference to an interesting work from Lawrence M. Leemis in 1986 that's worth reading. In fact, this paper has been updated in 2008 and presents a nice graphical model (but not really in the sense we all imagine now: just a graph) of univariate probability distributions and what it takes to go from one to another, like generalizations or specializations. The graph in this paper is really amazing !
Just for fun, the Graph:
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