Functions sum, mean, maximum etc. accept a function as first argument
mean(f::Function, v)
Apply the function f to each element of v and take the mean.
julia> mean(√, [1, 2, 3])
1.3820881233139908
Functions std, var, median, extrema does not. Is there any particular reason for this behaviour?
I think that mean(::Function, ...) predates the nice broadcasting syntax (like so many similar convenience forms). This would be a good time to deprecate, then remove it.
As for the other statistics, you can always do std(f.(x)) and similar, or use a generator. Note that centered moments take two passes (unless you provide the mean), so the choice depends on whether f is expensive. For large amounts of data, there is always
I don’t think broadcasting replaces these methods, since it (currently) allocates a new vector before computing the reduction. On the other hand, generators should be fine (though slightly more verbose).
I frequently wish for a function like
lazymap(f, xs) = (f(x) for x in xs)
Or an annotation that makes broadcast forms return generators.
Does this package help?
I’ll add that (on master) OnlineStats has a new type that filters and transforms a data stream without allocating new arrays.
julia> s = series(Mean(); transform = abs, filter = !isnan);
julia> fit!(s, [-1, NaN, -3])
▦ AugmentedSeries{0} | EqualWeight | nobs = 2
▦ filter = Base.#57 | transform = abs
└── Mean(2.0)
@map from Query.jl is a lazy map that should work in these situations.
Generator works exactly like lazymap. I wish it was exported.
Thanks for all the answers! I think the generators solve my use case for now (and they are not that verbose compared to what I came up with without generators std(cat(3,[fun(i) for i = 1:N]...), 3) 
)
Perhaps you could make a one line PR? This would be a great feature.
Apparently, generators are not quite like map:
I could its worth thinking through though. Maybe there’s a better name than Generator?
MappedArrays is a thing too. Hmm
FWIW, I like Generator.
What about Iterators.map?