diff --git a/online.cabal b/online.cabal
--- a/online.cabal
+++ b/online.cabal
@@ -1,6 +1,6 @@
-cabal-version: 2.0
+cabal-version: 3.0
 name:           online
-version:        0.4.0.0
+version:        0.5.0
 synopsis:       online statistics
 description:    transformation of statistics to online algorithms
 category:       statistics
@@ -9,7 +9,7 @@
 author:         Tony Day
 maintainer:     tonyday567@gmail.com
 copyright:      Tony Day
-license:        BSD3
+license:        BSD-3-Clause
 license-file:   LICENSE
 build-type:     Simple
 
@@ -21,6 +21,7 @@
   exposed-modules:
       Online
       Online.Averages
+      Online.AveragesB
       Online.Medians
       Online.Quantiles
   hs-source-dirs:
@@ -32,6 +33,7 @@
     , tdigest
     , vector
     , vector-algorithms
+    , backprop
   default-language: Haskell2010
 
 test-suite test
diff --git a/src/Online.hs b/src/Online.hs
--- a/src/Online.hs
+++ b/src/Online.hs
@@ -1,10 +1,12 @@
 -- | online library
 module Online
   ( module Online.Averages
+  , module Online.AveragesB
   , module Online.Medians
   , module Online.Quantiles
   ) where
 
 import Online.Quantiles
 import Online.Averages
+import Online.AveragesB
 import Online.Medians
diff --git a/src/Online/AveragesB.hs b/src/Online/AveragesB.hs
new file mode 100644
--- /dev/null
+++ b/src/Online/AveragesB.hs
@@ -0,0 +1,64 @@
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE CPP #-}
+{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}
+
+-- | online statistics based on a moving average
+module Online.AveragesB
+  ( foldB,
+    foldB',
+    maB,
+    absmaB,
+    sqmaB,
+    stdB,
+    std'
+  ) where
+
+import Prelude
+import Numeric.Backprop as B
+import qualified Prelude.Backprop as PB
+import Control.Foldl (Fold(..))
+
+foldB' :: (Backprop a, Backprop b, Reifies s W, Fractional b) => (BVar s a -> BVar s b) -> BVar s b -> BVar s [a] -> BVar s b
+foldB' f r xs = divide (PB.foldl' (step' f r) (T2 0 0) xs) where
+  step' f' r' (T2 s c) a = uncurry T2 ((r'*) $ s + f' a, (r'*) $ c + 1)  
+  divide (T2 s c) = s / c
+
+
+online :: (Reifies s W, Fractional b) => (BVar s a -> BVar s b) -> (BVar s b -> BVar s b) -> Fold (BVar s a) (BVar s b)
+online f g = Fold step begin extract
+  where
+    begin = (0, 0)
+    step (s, c) a = (g $ s + f a, g $ c + 1)
+    extract (s, c) = s / c
+
+ma' :: (Reifies s W, Fractional b) => BVar s b -> Fold (BVar s b) (BVar s b)
+ma' r = online id (*r)
+
+sqma' :: (Reifies s W, Fractional b) => BVar s b -> Fold (BVar s b) (BVar s b)
+sqma' r = online (\x -> x * x) (*r)
+
+std' :: (Reifies s W, Floating b) => BVar s b -> Fold (BVar s b) (BVar s b)
+std' r = (\s ss -> sqrt (ss - s ** 2)) <$> ma' r <*> sqma' r
+
+-- coerceVar
+
+foldB :: (Reifies s W) => (BVar s Double -> BVar s Double) -> BVar s Double -> BVar s [Double] -> BVar s Double
+foldB f r xs = divide (PB.foldl' (step' f r) (T2 0 0) xs) where
+  step' f' r' (T2 s c) a = uncurry T2 ((r*) $ s + f' a, (r'*) $ c + 1)  
+  divide (T2 s c) = s / c
+
+stdB :: Reifies s W => BVar s Double -> BVar s [Double] -> BVar s Double
+stdB r xs = (\ss s -> sqrt (ss - s ** 2)) (foldB id r xs) (foldB (\x -> x * x) r xs)
+
+-- stdB' :: Reifies s W => BVar s Double -> BVar s [Double] -> BVar s Double
+-- stdB' r xs = (\(T2 ss s) -> sqrt (ss - s ** 2)) (foldB' (\x -> (T2 x (x*x))) (T2 r r) xs)
+
+maB :: Reifies s W => BVar s Double -> BVar s [Double] -> BVar s Double
+maB r = foldB id r
+
+absmaB :: Reifies s W => BVar s Double -> BVar s [Double] -> BVar s Double
+absmaB r = foldB abs r
+
+sqmaB :: Reifies s W => BVar s Double -> BVar s [Double] -> BVar s Double
+sqmaB r = foldB (\x -> x * x) r
+