Replace broadcasting over distributions with broadcasting with partially applied functions

[devmotion]

Broadcasting treats UnivariateDistributions as scalars due to

Distributions.jl/src/common.jl

Line 175 in 9e72f1f

Broadcast.broadcastable(d::UnivariateDistribution) = Ref(d)

. However, such Refs are suboptimal since

• they may affect the broadcasting style and/or break broadcasting (see, e.g., rand! with Uniform distribution does not work with CUDA arrays #1815 and Remove special-casing of Ref in broadcast. JuliaGPU/GPUArrays.jl#510 (comment))
• tuples tend to infer better (see, e.g., Remove special-casing of Ref in broadcast. JuliaGPU/GPUArrays.jl#510 (comment) and https://discourse.julialang.org/t/add-scalar-macro-to-base/50255/4)

Unfortunately, replacing

Distributions.jl/src/common.jl

Line 175 in 9e72f1f

Broadcast.broadcastable(d::UnivariateDistribution) = Ref(d)

with broadcastable(d::UnivariateDistribution) = (d,) is not an option since broadcasting with tuples is not identical to broadcasting with Refs (see, e.g., https://discourse.julialang.org/t/add-scalar-macro-to-base/50255/5).

However, broadcasting over distributions is actually not needed as one can just broadcast with a partially applied function that captures the distribution instead. Therefore this PR changes all broadcasts over distributions in Distributions.jl to broadcasts with such partially applied functions (and quite often this implies that broadcasting is not needed anymore and a simple map would be sufficient).

Fixes #1815.

---

As a side note, IMO it would be more convenient for users and downstream packages that would like to follow the same pattern if we would define pdf(d::Distribution) = Base.Fix1(pdf, d) etc. (similar to ==(x) etc. in Base) (ref #966). Unfortunately, pdf(d::DiscreteUnivariateDistribution) is already defined in a different way:

Distributions.jl/src/deprecates.jl

Line 43 in 9e72f1f

@deprecate pdf(d::DiscreteUnivariateDistribution) pdf.(Ref(d), support(d))

[codecov-commenter]

Codecov Report

Attention: 5 lines in your changes are missing coverage. Please review.

Comparison is base (9e72f1f) 85.93% compared to head (b48ca27) 85.93%.
Report is 1 commits behind head on master.

Files	Patch %	Lines
src/univariate/discrete/betabinomial.jl	50.00%	3 Missing ⚠️
src/mixtures/mixturemodel.jl	50.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1818      +/-   ##
==========================================
- Coverage   85.93%   85.93%   -0.01%     
==========================================
  Files         144      144              
  Lines        8655     8658       +3     
==========================================
+ Hits         7438     7440       +2     
- Misses       1217     1218       +1     

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[theogf]

Unfortunately, pdf(d::DiscreteUnivariateDistribution) is already defined in a different way

I find your proposal for the use of the single argument pdf to be far more useful.
Since it's already deprecated, does that mean we could introduce the new definition in the next breaking release?