We have $nA_{N} = s_{1} + \cdots + s_{n}$ and $(n + 1)A_{n + 1} = s_{1} + \cdots + s_{n + 1}$ so $s_{n + 1} = (n + 1)A_{n + 1} - nA_{n}$ from which we observe $A_{n + 1} = \frac{s_{n + 1} + nA_{n}}{n + 1} = A_{n} + \frac{s_{n + 1} + nA_{n}}{n + 1} - A_{n} = A_{n} + \frac{s_{n + 1} - A_{n}}{n + 1}$.

OCaml:

let cumulative_moving_average (l : float list) : float = let f (s, i) x = let k = i + 1 in let s = (s +. (x -. s)/. (float_of_int k)) in (s, k) in fst @@ List.fold_left f (0., 0) l

Felix:

fun cumulative_moving_average (l : list[double]) : double = { var f = fun (s : double, var i : int) (x : double) : double * int = { ++i; return (s + ((x - s) / (double)i), i); }; return (fold_left f (0.0, 0) l) .0 ; }

C++03:

#include <numeric> #include <utility> namespace detail { typedef std::pair<double, int> acc_t; inline acc_t cumulative_moving_average (acc_t const& p, double x) { double s = p.first; int k = p.second + 1; return std::make_pair (s + (x - s) / k, k); } }//namespace detail template <class ItT> double cumulative_moving_average (ItT begin, ItT end) { return ( std::accumulate ( begin, end, std::make_pair (0.0, 0), detail::cumulative_moving_average) ).first; }

C++11:

template <class T> auto cumulative_moving_average(T c) { return accumulate ( std::begin (c), std::end (c), std::make_pair (0.0, 0), [](auto p, auto x) { ++std::get<1> (p); return std::make_pair ( std::get<0> (p) + (x - std::get<0> (p)) / std::get<1> (p), std::get<1> (p)); }).first; }(credit : Juan Alday)