DiscreteNonParametric should be <: ContinuousDistribution

[abraunst]

The documentation at https://github.com/JuliaStats/Distributions.jl/blob/master/docs/src/types.md declares that distributions with domain in the reals should be subtypes of ContinuousDistribution. However, DiscreteNonParameteric in https://github.com/JuliaStats/Distributions.jl/blob/master/src/univariate/discrete/discretenonparametric.jl is declared as subtype of DiscreteDistribution, violating this rule. This seems a bug (see also my comments at the end of #332).

[matbesancon]

Agreed on that.
Sort-of related to #771

[richardreeve]

This also seems to be related to #916 though that PR actually only adds non-real support. It would be good to fix this ValueSupport bug, and I don't see why the Discrete subtype has to have Int elements at all, it just needs to have a finite (countably infinite?) number of whatever its element type is.

[mschauer]

At this point where we need to define Discrete <: Continuous , we become aware that we all want to abolish the type params :-D

[richardreeve]

Well, I have to admit I'm not thinking of going quite that far! I was imagining DiscreteSupport <: DiscontinuousSupport <: ValueSupport and ContinuousSupport <: ValueSupport, and allowing DiscreteSupport to allow support over any countable set, whereas ContinuousSupport is continuous (and therefore uncountable), and DiscontinuousSupport is a statement about having Dirac deltas in the density function (or in the discrete support case, really just having a probability mass function instead).

[DilumAluthge]

Yeah, I would argue that "discrete" doesn't mean "the support is a subset of integers", but rather "the support is a countable set".

[mschauer]

And continuous does not mean "support is a subset of the reals" but should mean perhaps that the distribution has a density (we are not going to model cantor distributions...)

[richardreeve]

Does continuous require that support is a Number though? That would cover a lot of bases (including complex numbers, Unitful numbers, etc.), though we would also need the underlying number type (? I'm not sure there's anything that extracts this at the moment) to be <: AbstractFloat I imagine?

[mschauer]

Just to state it clearly: The type system needs fixing, but DiscreteNonParametric should not be <: ContinuousDistribution

[richardreeve]

The solution I proposed last year (to Dirac and all other distributions like this) in #941, #945 and ultimately #951 was to overhaul the whole system and fix all this, but there after several iterations (and months), there were always new minor issues being raised until I had no more time to work on it and so there was never enough enthusiasm to merge it. It’s a shame how much time was wasted.

[abraunst]

The solution I proposed last year (to Dirac and all other distributions like this) in #941, #945 and ultimately #951 was to overhaul the whole system and fix all this, but there after several iterations (and months), there were always new minor issues being raised until I had no more time to work on it and so there was never enough enthusiasm to merge it. It’s a shame how much time was wasted.

For what is worth, I think that yours is the right way. 👍