Functions applied to an empty `skipmissing` should return missing.

[pdeffebach]

julia> mean(skipmissing([missing, missing]))
ERROR: MethodError: reduce_empty(::typeof(Base.add_sum), ::Type{Union{}}) is ambiguous. Candidates:
  reduce_empty(::typeof(Base.add_sum), ::Type{T}) where T<:Union{Int16, Int32, Int8} in Base at reduce.jl:231
  reduce_empty(::typeof(Base.add_sum), ::Type{T}) where T<:Union{UInt16, UInt32, UInt8} in Base at reduce.jl:232
Possible fix, define
  reduce_empty(::typeof(Base.add_sum), ::Type{Union{}})
Stacktrace:
 [1] mapreduce_empty(::typeof(identity), ::Function, ::Type) at ./reduce.jl:247
 [2] mapreduce_empty_iter(::Function, ::Function, ::Base.SkipMissing{Array{Missing,1}}, ::Base.HasEltype) at ./reduce.jl:254
 [3] mean(::typeof(identity), ::Base.SkipMissing{Array{Missing,1}}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/Statistics/src/Statistics.jl:60
 [4] mean(::Base.SkipMissing{Array{Missing,1}}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/Statistics/src/Statistics.jl:42
 [5] top-level scope at REPL[110]:1

People use skipmissing to get away from worrying about missings. They shouldn't have to worry about whether or not the vector they are working with is full of missing values.

xref #35050. I would consider this part of a larger set of PRs I have in mind to make working with missings easier.

[pdeffebach]

This would probably be very easy to fix for all functions that use reduce, mapreduce or foldl. But I can't think of anything that would work on functions that just call for i in itr etc. But it's not hopeless:

julia> x = Union{Int, Missing}[missing, missing]
2-element Array{Union{Missing, Int64},1}:
 missing
 missing

julia> std(skipmissing(x))
NaN

julia> std(Int[])
NaN

My above example of [missing, missing] is bad, it's better to write mean(Union{Int, Missing}[missing, missing]) since there is dispatch based on the element type. For instance

julia> mean(skipmissing(x))
NaN

It's not obvious why mean of an empty iterator returns NaN. Imo it should return zero(eltype(itr)) but I guess there are larger concerns I don't undestand. The relevant line is here

        return Base.mapreduce_empty_iter(f, Base.add_sum, itr,
                                         Base.IteratorEltype(itr)) / 0

[pdeffebach]

X-ref #28777. This issue can be closed I think as i think the current behavior is as intended and earlier devs have thought of this.