Well, we have accumulate, in terms of which cumall is just accumulate(&, A) and cumany is accumulate(|, A), so it doesn’t seem worthwhile adding specific functions for these.
cummean(A) = cumsum(A) ./ (1:length(A)) is slightly more complicated, at least if you want to eliminate the allocation of a temporary array. If it’s a common operation it might make sense in Statistics. However, I can’t seem to find any record of anyone ever asking for this function before, so that doesn’t seem to indicate a big demand?
Transducer(::OnlineStat) is not really for performance. It’s mainly for exposing the super rich set of functionality that exists in OnlineStats.jl to Transducers.jl-based API. OnlineStats are really “just” reducing functions obscured by the implementation detail that uses in-place mutation. So, it’d be such a pity if two libraries cannot talk to each other.