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Does anyone know of a good compendium or catalog of compound distributions, or finite mixture representations of those distributions?

I am trying to find out to what extent the common multi-parameter distributions and their generalized forms can be built up from single parameter distributions through compounding. The ones I have found so far cover only 10 or 15 distributions, and I still can not tell if it is possible to build up e.g. most four parameter distributions from one parameter distributions by successive steps of compounding.

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