Use Number instead of Real for mgf and cf

[theogf]

As pointed out in #1502 , mgf and cf should be allowed to take Complex numbers and the second argument should be therefore relaxed.
All functions are also made type-stable.
Breaking?, when the argument for the mgf is given outside of the domain definition a DomainError is thrown.

[devmotion]

Thanks!

Unfortunately, there are a bunch of type stability issues. They exist already in the current implementation so it's probably beyond the scope of this PR to fix all them. I think we should just make sure to not introduce any new issues and possibly fix some simple cases where changes are needed anyway (but then we should also test them to make sure we don't reintroduce them accidentally...).

[theogf]

Thanks for the monster review! I tried to address your comments and integrate them. The inference tests should tell us where things go wrong :)

[theogf]

MGF are not necessarily defined on the whole Real/Complex domain, what should be returned when getting a value out of bound? NaN or ArgumentError ?

[devmotion]

MGF are not necessarily defined on the whole Real/Complex domain, what should be returned when getting a value out of bound? NaN or ArgumentError ?

I was wondering the same. I'm a bit unsure, do you have a concrete example? Then it might be easier to see.

[codecov-commenter]

Codecov Report

Merging #1504 (186066a) into master (620a73a) will increase coverage by 0.04%.
The diff coverage is 80.00%.

❗ Current head 186066a differs from pull request most recent head 9a1211d. Consider uploading reports for the commit 9a1211d to get more accurate results

@@            Coverage Diff             @@
##           master    #1504      +/-   ##
==========================================
+ Coverage   84.92%   84.97%   +0.04%     
==========================================
  Files         128      128              
  Lines        7735     7765      +30     
==========================================
+ Hits         6569     6598      +29     
- Misses       1166     1167       +1     

Impacted Files	Coverage Δ
src/Distributions.jl	100.00% <ø> (ø)
src/univariate/continuous/biweight.jl	61.76% <0.00%> (-1.88%)	⬇️
src/univariate/continuous/epanechnikov.jl	60.52% <0.00%> (-1.64%)	⬇️
src/univariate/continuous/triweight.jl	52.38% <0.00%> (-7.08%)	⬇️
src/univariate/continuous/cauchy.jl	85.10% <100.00%> (+0.66%)	⬆️
src/univariate/continuous/chisq.jl	76.66% <100.00%> (+1.66%)	⬆️
src/univariate/continuous/erlang.jl	69.44% <100.00%> (+1.79%)	⬆️
src/univariate/continuous/exponential.jl	94.00% <100.00%> (+0.25%)	⬆️
src/univariate/continuous/gamma.jl	94.38% <100.00%> (+0.12%)	⬆️
src/univariate/continuous/inversegamma.jl	96.00% <100.00%> (ø)
... and 26 more

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[theogf]

This has gone very very stale so I will just close it.