Decouple rand and eltype

[devmotion]

One of my take-aways from issues such as #1252, #1902, #894, #1783, #1041, and #1071 is that eltype is not only quite inconsistently implemented and unclearly documented currently but more generally it might be a bad design decision to use it for pre-allocating containers of samples: Setting it to a fixed type (historically Float64 for continuous and Int for discrete distributions) is too limiting, but trying to infer it from parameters is challenging and doomed to fail for more challenging scenarios that are not as clear as e.g. Normal.

This PR tries to decouple rand and eltype, to make it easier to possibly eventually deprecate and remove eltype.

Fixes #1041.
Fixes #1071.
Fixes #1082.
Fixes #1252.
Fixes #1783.
Fixes #1884.
Fixes #1902.
Fixes #1907.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 98.18182% with 2 lines in your changes missing coverage. Please review.

Project coverage is 85.60%. Comparing base (a1010e4) to head (17154a2).

Files with missing lines	Patch %	Lines
src/multivariate/mvtdist.jl	83.33%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1905      +/-   ##
==========================================
- Coverage   86.08%   85.60%   -0.49%     
==========================================
  Files         144      144              
  Lines        8696     8758      +62     
==========================================
+ Hits         7486     7497      +11     
- Misses       1210     1261      +51     

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[andreasnoack]

Given that, according to the docstring

Distributions.jl/src/common.jl

Lines 96 to 102 in a1010e4

	"""
	eltype(::Type{Sampleable})
	The default element type of a sample. This is the type of elements of the samples generated
	by the `rand` method. However, one can provide an array of different element types to
	store the samples using `rand!`.
	"""

the sole purpose of eltype is to return the type of rand, which I agree isn't really feasible, should we also deprecate the methods here as part of this PR?

[quildtide]

#1907 is related.

[devmotion]

#1907 is related.

17154a2 fixes it.

[quildtide]

My personal opinion:
rand(d::Distribution) should remain a valid method (I don't think anyone is trying to change this), and its return type should be predictable by knowing what d is. It would also be useful to have a method that tells you what type rand(d::Distribution) returns without running rand(d::Distribution). eltype(d::Distribution) is logical for this.

This is orthogonal to the fact that Distributions should probably support rand(d::Distribution, T::Type).

In an ideal situation, I think we would define rand(d::Distribution, T::Type) for distributions (to allow for potential type-specific optimizations and evade unnecessary typecasts) and then dispatch rand(d::Distribution) = rand(d, eltype(d)).

[devmotion]

its return type should be predictable by knowing what d is

I became convinced that in general this is not possible. It basically means trying to manually figure out type inference, a task that even the Julia compiler can fail at. Of course, for some number types and distributions it can be done (as also the compiler will succeed in many instances). But in general it's far from trivial. As in the initial stages of Distributions, one could be restrictive and limit samples to Int and Float but that's IMO not desirable either. Therefore I think it's best to remove eltype (which IMO has also been a weird name since I don't view distributions as containers or collections) from the API. IMO it's just too brittle and currently to inconsistent. Of course, that doesn't prevent users from trying to figure out the (element) type of samples with eg the help of the compiler, it's just not an official feature anymore.