move stats functions from Base to StatsBase, move StatsBase to stdlib?

[JeffBezanson]

It doesn't seem ideal to have a tiny number of stats functions in Base, and also have a StatsBase package. These could be consolidated and moved to the stdlib, possibly as Statistics.jl.

[nalimilan]

I've made that proposal before, so +1. A few things to discuss, some of which make the situation more complex:

• Which functions should be moved to stdlib? I guess cor, cov, var, std and quantile, but probably not mean nor middle?
• StatsBase currently depends on SortingAlgorithms (for radix sort), which would also have to be moved to the stdlib. I think that's a good idea anyway. There's also a dependency on DataStructures, but it's only used in one function (for heaps), so maybe we can work around it.
• We plan to have (actually, update) a Stats.jl meta-package which will load all packages providing what people generally expect to have available by default for a statistical environment. So StatsBase is a better name than Statistics to avoid confusion; or we should call the meta-package AllStats, StatsEnvironment or something like that.
• I'm not sure we are completely happy with all the APIs provided in StatsBase. I know stdlib isn't guaranteed to remain completely stable, but we could also move only parts of StatsBase to the stdlib, and keep the StatsBase package in parallel for some time.

EDIT: see also #27152 (comment)

[JeffBezanson]

I think we should move everything listed under statistics in export.jl, which includes mean. Anything else seems too arbitrary.

[ViralBShah]

I would think that mean is more generally used and it could perhaps continue to be in Base as a reducer.

[fredrikekre]

Seems a bit iffy to to have a *Base library as a stdlib. Why can't we just move them out completely to a package, like we did with e.g. FFTW, SpecialFunctions, QuadGK etc?