Simplifying Distributions type hierarchy

[Tamas_Papp]

I think that the current approach comes from the early days of Julia when users were still exploring the language — most importantly, before traits were widely used. I have said this before in a previous discussion we had:

Distributions.jl interop for probprog

The first official release of Distributions.jl was in 2013, 6 years ago, before the actual release of Julia 0.3. IMO a lot of its design reflects that, eg it is full of ostensibly performance-enhancing checks and conversions which may not needed anymore, as the compiler got way smarter, the idiomatic Julia style for writing generic code has matured a lot since these days, using traits instead of elaborate type hierarchies, and duck typing where one can get away with it. This is natural …

I agree with @mohamed82008 that a rewrite would be best to demo a simpler setup. I would recommend much less inheritance and parameterization at the API level, and suggest traits instead (inheritance and type parameters could still be used to implement a lot of functionality where they make sense). This could start as a PR, and depending on the reception it could either be merged or become Distributions2.