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).

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) )