Arguments typed as `Number`

[dmbates]

In many method definitions arguments are typed as Number. For example, in src/distrs/chisq.jl

# pdf for numbers with generic types
function chisqpdf(k::Real, x::Number)
  hk = k / 2  # half k
  1 / (2^(hk) * gamma(hk)) * x^(hk - 1) * exp(-x / 2)
end

# logpdf for numbers with generic types
function chisqlogpdf(k::Real, x::Number)
  hk = k / 2  # half k
  -hk * log(oftype(hk, 2)) - lgamma(hk) + (hk - 1) * log(x) - x / 2
end

It appears that the only difference between Number and Real is that Number includes Complex

julia> subtypes(Number)
2-element Array{Union{DataType, UnionAll},1}:
 Complex
 Real   

I don't see the purpose in allowing complex numbers in these cases. Any objection to my changing these to Real?

[ararslan]

For negative complex x do the values correspond to the generalized chi squared distribution?

[andreasnoack]

I think many of these were relaxed at a time when we discussed the proper location in the type tree for dual numbers. Initially, they were not Real so to allow for autodiff, we relaxed the methods here to Number. Eventually, it was concluded that it was easier to make dual numbers Real so we can probably restrict most of the signatures again. However, I there might be a few specificity issues. In https://github.com/JuliaStats/StatsFuns.jl/pull/35/files we actually defined the promotion method for Number to avoid ambiguity issues.

[dmbates]

@andreasnoack I suspected that the use of Number was related to autodiff. I will change those in the promotions branch that I am working on.