From 4b7bf60e85d82a5d86199f173989c2bf360026af Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 05:23:00 +0530
Subject: [PATCH 1/7] Update nix flake

---
 flake.lock | 10 +++++-----
 flake.nix  |  2 +-
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/flake.lock b/flake.lock
index 05f06b6..114d59a 100644
--- a/flake.lock
+++ b/flake.lock
@@ -7,16 +7,16 @@
         "nixpkgs-darwin": "nixpkgs-darwin"
       },
       "locked": {
-        "lastModified": 1776376313,
-        "narHash": "sha256-lfL+xfAZVM4nYLEggaRo3nBNxTHKgjdxJTcEHkM8P7Q=",
+        "lastModified": 1776414440,
+        "narHash": "sha256-Be67u+Qea2sEuI+3BVjkc+o4fYgRT/fOANGNAp2OuFk=",
         "ref": "refs/heads/master",
-        "rev": "187bde6bd362eced707ed96198ddc193af66ff42",
-        "revCount": 123,
+        "rev": "69728978adc44f53b3dd907acb2eb5bd2415fd60",
+        "revCount": 125,
         "type": "git",
         "url": "ssh://git@github.com/composewell/streamly-packages"
       },
       "original": {
-        "rev": "187bde6bd362eced707ed96198ddc193af66ff42",
+        "rev": "69728978adc44f53b3dd907acb2eb5bd2415fd60",
         "type": "git",
         "url": "ssh://git@github.com/composewell/streamly-packages"
       }
diff --git a/flake.nix b/flake.nix
index 6a50244..5629dc5 100644
--- a/flake.nix
+++ b/flake.nix
@@ -2,7 +2,7 @@
   description = "streamly-statistics";
 
   inputs = {
-    basepkgs.url = "git+ssh://git@github.com/composewell/streamly-packages?rev=187bde6bd362eced707ed96198ddc193af66ff42";
+    basepkgs.url = "git+ssh://git@github.com/composewell/streamly-packages?rev=69728978adc44f53b3dd907acb2eb5bd2415fd60";
     nixpkgs.follows = "basepkgs/nixpkgs";
     nixpkgs-darwin.follows = "basepkgs/nixpkgs-darwin";
   };

From 632e04cc7fc5524f36fdbf3187905d9ece5efd74 Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 05:23:26 +0530
Subject: [PATCH 2/7] Allow streamly development version

---
 streamly-statistics.cabal | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/streamly-statistics.cabal b/streamly-statistics.cabal
index 09c7042..f9e70ce 100644
--- a/streamly-statistics.cabal
+++ b/streamly-statistics.cabal
@@ -113,7 +113,7 @@ library
         Streamly.Statistics
       , Streamly.Statistics.Scanl
     build-depends:       base     >= 4.9 && < 5
-                       , streamly-core >= 0.3.0 && < 0.4.0
+                       , streamly-core >= 0.3.0 && < 0.5
                        , containers  >= 0.5   && < 0.9
                        , random >= 1.2 && < 1.4
                        , mwc-random >= 0.15 && < 0.16

From b2a2b308183444ebcfd165e8deb2981b53ca9f91 Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 06:18:33 +0530
Subject: [PATCH 3/7] Deprecate incremental folds in favor of Scans

---
 src/Streamly/Statistics.hs       | 142 +++++++++++++------------------
 src/Streamly/Statistics/Scanl.hs |  22 ++---
 2 files changed, 69 insertions(+), 95 deletions(-)

diff --git a/src/Streamly/Statistics.hs b/src/Streamly/Statistics.hs
index cda3630..e16eabd 100644
--- a/src/Streamly/Statistics.hs
+++ b/src/Streamly/Statistics.hs
@@ -71,110 +71,67 @@
 {-# LANGUAGE ScopedTypeVariables #-}
 module Streamly.Statistics
     (
-    -- * Incremental Folds
-    -- | Folds of type @Fold m (a, Maybe a) b@ are incremental sliding window
-    -- folds. An input of type @(a, Nothing)@ indicates that the input element
-    -- @a@ is being inserted in the window without ejecting an old value
-    -- increasing the window size by 1. An input of type @(a, Just a)@
-    -- indicates that the first element is being inserted in the window and the
-    -- second element is being removed from the window, the window size remains
-    -- the same. The window size can only increase and never decrease.
-    --
-    -- You can compute the statistics over the entire stream using sliding
-    -- window folds by keeping the second element of the input tuple as
-    -- @Nothing@.
-    --
-      lmap
-    , Window.cumulative
+    -- ** Weighted Means
+    -- | Exponential Smoothing.
+      ewmaAfterMean
+
+    -- ** Resampling
+    , resample
+    , foldResamples
+    , jackKnifeMean
+    , jackKnifeVariance
+    , jackKnifeStdDev
 
-    -- * Summary Statistics
-    -- | See https://en.wikipedia.org/wiki/Summary_statistics .
+    -- ** Probability Distribution
+    , frequency'
+    , mode
 
-    -- ** Sums
+    -- Histograms
+    , HistBin (..)
+    , binOffsetSize
+    , binFromSizeN
+    , binFromToN
+    , binBoundaries
+    , histogram
+
+    -- * Transforms
+    , fft
+
+    -- * Deprecated
+    -- | Incremental Folds in this module have been deprecated in favor of the
+    -- incremental scans in the Scanl module.
+
+    , ewma
+    , ewmaRampUpSmoothing
+    , lmap
+    , Window.cumulative
     , length
     , sum
     , sumInt
     , powerSum
-
-    -- ** Location
-    -- | See https://en.wikipedia.org/wiki/Location_parameter .
-    --
-    -- See https://en.wikipedia.org/wiki/Central_tendency .
     , minimum
     , maximum
     , rawMoment
     , rawMomentFrac
-
-    -- Pythagorean means (https://en.wikipedia.org/wiki/Pythagorean_means)
     , mean
     , welfordMean
     , geometricMean
     , harmonicMean
-
     , quadraticMean
-
-    -- Generalized mean
     , powerMean
     , powerMeanFrac
-
-    -- ** Weighted Means
-    -- | Exponential Smoothing.
-    , ewma
-    , ewmaAfterMean
-    , ewmaRampUpSmoothing
-
-    -- ** Spread
-    -- | Second order central moment is a statistical measure of dispersion.
-    -- The \(k\)th moment about the mean (or \(k\)th central moment) is defined
-    -- as:
-    --
-    -- \(\mu_k = \frac{1}{n}\sum_{i=1}^n {(x_{i}-\mu)}^k\)
-    --
-    -- See https://mathworld.wolfram.com/CentralMoment.html .
-    --
-    -- See https://en.wikipedia.org/wiki/Statistical_dispersion .
     , range
     , md
     , variance
     , stdDev
-
-    -- ** Shape
-    -- | Third and fourth order central moments are a measure of shape.
-    --
-    -- See https://en.wikipedia.org/wiki/Shape_parameter .
-    --
-    -- See https://en.wikipedia.org/wiki/Standardized_moment .
     , skewness
     , kurtosis
-
-    -- XXX Move to Statistics.Sample or Statistics.Estimation module?
-    -- ** Estimation
     , sampleVariance
     , sampleStdDev
     , stdErrMean
-
-    -- ** Resampling
-    , resample
-    , foldResamples
-    , jackKnifeMean
-    , jackKnifeVariance
-    , jackKnifeStdDev
-
-    -- ** Probability Distribution
     , frequency
-    , frequency'
-    , mode
 
-    -- Histograms
-    , HistBin (..)
-    , binOffsetSize
-    , binFromSizeN
-    , binFromToN
-    , binBoundaries
-    , histogram
 
-    -- * Transforms
-    , fft
     )
 where
 
@@ -222,25 +179,23 @@ import Prelude hiding (length, sum, minimum, maximum)
 -- Re-exports
 -------------------------------------------------------------------------------
 
--- XXX Deprecate these once the streamly functions are released.
-
--- {-# DEPRECATED lmap "Use Streamly.Data.Fold.windowLmap instead" #-}
+{-# DEPRECATED lmap "Use Streamly.Internal.Data.Scanl.incrRollingMap instead" #-}
 lmap :: (c -> a) -> Fold m (a, Maybe a) b -> Fold m (c, Maybe c) b
 lmap = Window.windowLmap
 
--- {-# DEPRECATED length "Use Streamly.Data.Fold.windowLength instead" #-}
+{-# DEPRECATED length "Use Streamly.Internal.Data.Scanl.incrCount instead" #-}
 length :: (Monad m, Num b) => Fold m (a, Maybe a) b
 length = Window.windowLength
 
--- {-# DEPRECATED sum "Use Streamly.Data.Fold.windowSum instead" #-}
+{-# DEPRECATED sum "Use Streamly.Internal.Data.Scanl.incrSum instead" #-}
 sum :: (Monad m, Num a) => Fold m (a, Maybe a) a
 sum = Window.windowSum
 
--- {-# DEPRECATED sumInt "Use Streamly.Data.Fold.windowSumInt instead" #-}
+{-# DEPRECATED sumInt "Use Streamly.Internal.Data.Scanl.incrSumInt instead" #-}
 sumInt :: (Monad m, Integral a) => Fold m (a, Maybe a) a
 sumInt = Window.windowSumInt
 
--- {-# DEPRECATED powerSum "Use Streamly.Data.Fold.windowPowerSum instead" #-}
+{-# DEPRECATED powerSum "Use Streamly.Internal.Data.Scanl.incrPowerSum instead" #-}
 powerSum :: (Monad m, Num a) => Int -> Fold m (a, Maybe a) a
 powerSum = Window.windowPowerSum
 
@@ -369,6 +324,7 @@ fft marr
 -- /Time/: \(\mathcal{O}(n*w)\) where \(w\) is the window size.
 --
 {-# INLINE minimum #-}
+{-# DEPRECATED minimum "Use Streamly.Statistics.Scanl.incrMinimum instead" #-}
 minimum :: (Monad m, Ord a) => Fold m (a, Maybe a) a
 minimum = Fold step initial extract extract
 
@@ -429,6 +385,7 @@ minimum = Fold step initial extract extract
 -- /Time/: \(\mathcal{O}(n*w)\) where \(w\) is the window size.
 --
 {-# INLINE maximum #-}
+{-# DEPRECATED maximum "Use Streamly.Statistics.Scanl.incrMaximum instead" #-}
 maximum :: (Monad m, Ord a) => Fold m (a, Maybe a) a
 maximum = Fold step initial extract extract
 
@@ -501,6 +458,7 @@ maximum = Fold step initial extract extract
 --
 -- /Time/: \(\mathcal{O}(n)\)
 {-# INLINE mean #-}
+{-# DEPRECATED mean "Use Streamly.Internal.Data.Scanl.incrMean instead" #-}
 mean :: forall m a. (Monad m, Fractional a) => Fold m (a, Maybe a) a
 mean = Window.windowMean
 
@@ -543,6 +501,7 @@ meanReplace n oldMean oldItem newItem =
 --
 -- /Internal/
 {-# INLINE welfordMean #-}
+{-# DEPRECATED welfordMean "Use Streamly.Statistics.Scanl.incrWelfordMean instead" #-}
 welfordMean :: forall m a. (Monad m, Fractional a) => Fold m (a, Maybe a) a
 welfordMean = Fold step initial extract extract
 
@@ -584,6 +543,7 @@ welfordMean = Fold step initial extract extract
 --
 -- /Time/: \(\mathcal{O}(n)\)
 {-# INLINE rawMoment #-}
+{-# DEPRECATED rawMoment "Use Streamly.Statistics.Scanl.incrRawMoment instead" #-}
 rawMoment :: (Monad m, Fractional a) => Int -> Fold m (a, Maybe a) a
 rawMoment k = Fold.teeWith (/) (Window.windowPowerSum k) Window.windowLength
 
@@ -593,6 +553,7 @@ rawMoment k = Fold.teeWith (/) (Window.windowPowerSum k) Window.windowLength
 -- >>> rawMomentFrac p = Fold.teeWith (/) (Fold.windowPowerSumFrac p) Fold.windowLength
 --
 {-# INLINE rawMomentFrac #-}
+{-# DEPRECATED rawMomentFrac "Use Streamly.Statistics.Scanl.incrRawMomentFrac instead" #-}
 rawMomentFrac :: (Monad m, Floating a) => a -> Fold m (a, Maybe a) a
 rawMomentFrac k =
     Fold.teeWith (/) (Window.windowPowerSumFrac k) Window.windowLength
@@ -616,6 +577,7 @@ rawMomentFrac k =
 -- See https://en.wikipedia.org/wiki/Generalized_mean
 --
 {-# INLINE powerMean #-}
+{-# DEPRECATED powerMean "Use Streamly.Statistics.Scanl.incrPowerMean instead" #-}
 powerMean :: (Monad m, Floating a) => Int -> Fold m (a, Maybe a) a
 powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
 
@@ -625,6 +587,7 @@ powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
 -- >>> powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
 --
 {-# INLINE powerMeanFrac #-}
+{-# DEPRECATED powerMeanFrac "Use Streamly.Statistics.Scanl.incrPowerMeanFrac instead" #-}
 powerMeanFrac :: (Monad m, Floating a) => a -> Fold m (a, Maybe a) a
 powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
 
@@ -641,6 +604,7 @@ powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
 -- See https://en.wikipedia.org/wiki/Harmonic_mean .
 --
 {-# INLINE harmonicMean #-}
+{-# DEPRECATED harmonicMean "Use Streamly.Statistics.Scanl.incrHarmonicMean instead" #-}
 harmonicMean :: (Monad m, Fractional a) => Fold m (a, Maybe a) a
 harmonicMean =
     Fold.teeWith (/)
@@ -660,6 +624,7 @@ harmonicMean =
 --
 -- See https://en.wikipedia.org/wiki/Geometric_mean .
 {-# INLINE geometricMean #-}
+{-# DEPRECATED geometricMean "Use Streamly.Statistics.Scanl.incrGeometricMean instead" #-}
 geometricMean :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 geometricMean = exp <$> Window.windowLmap log mean
 
@@ -673,6 +638,7 @@ geometricMean = exp <$> Window.windowLmap log mean
 -- See https://en.wikipedia.org/wiki/Root_mean_square .
 --
 {-# INLINE quadraticMean #-}
+{-# DEPRECATED quadraticMean "Use Streamly.Statistics.Scanl.incrQuadraticMean instead" #-}
 quadraticMean :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 quadraticMean = powerMean 2
 
@@ -712,6 +678,7 @@ ewmaStep k x0 x1 = (1 - k) * x0 + k * x1
 -- See https://en.wikipedia.org/wiki/Exponential_smoothing
 --
 {-# INLINE ewma #-}
+{-# DEPRECATED ewma "Use Streamly.Statistics.Scanl.ewma instead" #-}
 ewma :: Monad m => Double -> Fold m Double Double
 ewma k = extract <$> Fold.foldl' step (Tuple' 0 1)
 
@@ -743,6 +710,7 @@ ewmaAfterMean n k =
 -- This is significantly faster than 'ewmaAfterMean'.
 --
 {-# INLINE ewmaRampUpSmoothing #-}
+{-# DEPRECATED ewmaRampUpSmoothing "Use Streamly.Statistics.Scanl.ewmaRampUpSmoothing instead" #-}
 ewmaRampUpSmoothing :: Monad m => Double -> Double -> Fold m Double Double
 ewmaRampUpSmoothing n k1 = extract <$> Fold.foldl' step initial
 
@@ -773,6 +741,7 @@ ewmaRampUpSmoothing n k1 = extract <$> Fold.foldl' step initial
 -- /Time/: \(\mathcal{O}(n*w)\) where \(w\) is the window size.
 --
 {-# INLINE range #-}
+{-# DEPRECATED range "Use Streamly.Statistics.Scanl.incrRange instead" #-}
 range :: (Monad m, Num a, Ord a) => Fold m (a, Maybe a) a
 range = Fold.teeWith (-) maximum minimum
 
@@ -793,6 +762,7 @@ range = Fold.teeWith (-) maximum minimum
 --
 -- /Pre-release/
 {-# INLINE md #-}
+{-# DEPRECATED md "Use Streamly.Statistics.Scanl.incrMd instead" #-}
 md ::  MonadIO m => Fold m ((Double, Maybe Double), m (MA.MutArray Double)) Double
 md =
     Fold.rmapM computeMD
@@ -828,6 +798,7 @@ md =
 --
 -- /Time/: \(\mathcal{O}(n)\)
 {-# INLINE variance #-}
+{-# DEPRECATED variance "Use Streamly.Statistics.Scanl.incrVariance instead" #-}
 variance :: (Monad m, Fractional a) => Fold m (a, Maybe a) a
 variance = Fold.teeWith (\p2 m -> p2 - m ^ (2 :: Int)) (rawMoment 2) mean
 
@@ -844,6 +815,7 @@ variance = Fold.teeWith (\p2 m -> p2 - m ^ (2 :: Int)) (rawMoment 2) mean
 --
 -- /Time/: \(\mathcal{O}(n)\)
 {-# INLINE stdDev #-}
+{-# DEPRECATED stdDev "Use Streamly.Statistics.Scanl.incrStdDev instead" #-}
 stdDev :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 stdDev = sqrt <$> variance
 
@@ -870,6 +842,7 @@ stdDev = sqrt <$> variance
 -- See https://en.wikipedia.org/wiki/Skewness .
 --
 {-# INLINE skewness #-}
+{-# DEPRECATED skewness "Use Streamly.Statistics.Scanl.incrSkewness instead" #-}
 skewness :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 skewness =
     unTee
@@ -906,6 +879,7 @@ skewness =
 -- See https://en.wikipedia.org/wiki/Kurtosis .
 --
 {-# INLINE kurtosis #-}
+{-# DEPRECATED kurtosis "Use Streamly.Statistics.Scanl.incrKurtosis instead" #-}
 kurtosis :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 kurtosis =
     unTee
@@ -934,6 +908,7 @@ kurtosis =
 -- See https://en.wikipedia.org/wiki/Bessel%27s_correction.
 --
 {-# INLINE sampleVariance #-}
+{-# DEPRECATED sampleVariance "Use Streamly.Statistics.Scanl.incrSampleVariance instead" #-}
 sampleVariance :: (Monad m, Fractional a) => Fold m (a, Maybe a) a
 sampleVariance =
     Fold.teeWith (\n s2 -> n * s2 / (n - 1)) Window.windowLength variance
@@ -948,6 +923,7 @@ sampleVariance =
 -- .
 --
 {-# INLINE sampleStdDev #-}
+{-# DEPRECATED sampleStdDev "Use Streamly.Statistics.Scanl.incrSampleStdDev instead" #-}
 sampleStdDev :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 sampleStdDev = sqrt <$> sampleVariance
 
@@ -961,6 +937,7 @@ sampleStdDev = sqrt <$> sampleVariance
 --
 -- /Time/: \(\mathcal{O}(n)\)
 {-# INLINE stdErrMean #-}
+{-# DEPRECATED stdErrMean "Use Streamly.Statistics.Scanl.incrStdErrMean instead" #-}
 stdErrMean :: (Monad m, Floating a) => Fold m (a, Maybe a) a
 stdErrMean =
     Fold.teeWith (\sd n -> sd / sqrt n) sampleStdDev Window.windowLength
@@ -1064,6 +1041,7 @@ foldResamples n arr fld =
 -- fromList [(1,1),(3,1),(4,2)]
 --
 {-# INLINE frequency #-}
+{-# DEPRECATED frequency "Use Streamly.Statistics.Scanl.incrFrequency instead" #-}
 frequency :: (Monad m, Ord a) => Fold m (a, Maybe a) (Map a Int)
 frequency = Fold.foldl' step Map.empty
 
diff --git a/src/Streamly/Statistics/Scanl.hs b/src/Streamly/Statistics/Scanl.hs
index 10983ba..3698403 100644
--- a/src/Streamly/Statistics/Scanl.hs
+++ b/src/Streamly/Statistics/Scanl.hs
@@ -7,25 +7,21 @@
 -- Portability : GHC
 --
 -- See "Streamly.Statistics" for general information. This module provides
--- scans instead of folds.
+-- composable incremental scans which can be used to efficiently compute online
+-- statistics in rolling or sliding windows, or cumulative statistics over the
+-- entire stream as well.
 
 {-# LANGUAGE ScopedTypeVariables #-}
 module Streamly.Statistics.Scanl
     (
     -- * Incremental Scans
-    -- | Scans of type @Scanl m (a, Maybe a) b@ are incremental sliding window
-    -- scans. An input of type @(a, Nothing)@ indicates that the input element
-    -- @a@ is being inserted in the window without ejecting an old value
-    -- increasing the window size by 1. An input of type @(a, Just a)@
-    -- indicates that the first element is being inserted in the window and the
-    -- second element is being removed from the window, the window size remains
-    -- the same. The window size can only increase and never decrease.
+    -- | Scans of type @Scanl m (Incr a) b@ are incremental sliding window
+    -- scans.
     --
-    -- You can compute the statistics over the entire stream using sliding
-    -- window folds by keeping the second element of the input tuple as
-    -- @Nothing@.
-    --
-    -- Also see "Streamly.Data.Scanl" for some basic window scans.
+    -- See "Streamly.Internal.Data.Scanl" for more details, especially the
+    -- documentation of 'Incr' type and 'incrScan' and 'cumulativeScan'
+    -- functions. Additional incremental scans can also be found in that
+    -- module.
 
     -- * Summary Statistics
     -- | See https://en.wikipedia.org/wiki/Summary_statistics .

From 1af66d436e255026309da20bd5c6acf855e3742b Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 17:16:55 +0530
Subject: [PATCH 4/7] Remove deprecated fold benchmarks

---
 benchmark/Main.hs          | 162 +++----------------------------------
 src/Streamly/Statistics.hs |   3 +
 streamly-statistics.cabal  |   1 -
 3 files changed, 12 insertions(+), 154 deletions(-)

diff --git a/benchmark/Main.hs b/benchmark/Main.hs
index 176ba33..8a23416 100644
--- a/benchmark/Main.hs
+++ b/benchmark/Main.hs
@@ -7,7 +7,6 @@ import Streamly.Data.Stream (Stream)
 import System.Random (randomRIO)
 
 import qualified Streamly.Data.Fold as Fold
-import qualified Streamly.Internal.Data.RingArray as Ring
 import qualified Streamly.Internal.Data.Scanl as Scanl
 import qualified Streamly.Data.Stream as Stream
 import qualified Streamly.Data.Array as Array
@@ -46,10 +45,6 @@ benchWith src len name f =
 benchWithFold :: Int -> String -> Fold IO Double Double -> Benchmark
 benchWithFold len name f = benchWith source len name f
 
-{-# INLINE benchWithFoldInt #-}
-benchWithFoldInt :: Int -> String -> Fold IO Int Int -> Benchmark
-benchWithFoldInt len name f = benchWith source len name f
-
 {-# INLINE benchWithScanSrc #-}
 benchWithScanSrc :: (Num a) =>
     (Int -> a -> Stream IO a) -> Int -> String -> Scanl IO a a -> Benchmark
@@ -84,152 +79,13 @@ benchWithFoldResamples len name f = bench name $ nfIO $ do
 numElements :: Int
 numElements = 100000
 
-mkBenchmarks ::
+mkFolds ::
        (Int -> String -> Fold IO Double Double -> Benchmark)
     -> [Benchmark]
-mkBenchmarks mkBench =
+mkFolds mkBench =
     [
-      mkBench numElements "minimum (window size 100)"
-        (Ring.slidingWindow 100 Statistics.minimum)
-    , mkBench numElements "minimum (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.minimum)
-    , benchWith sourceDescendingInt numElements
-        "minimum descending (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.minimum)
-
-    , mkBench numElements "maximum (window size 100)"
-        (Ring.slidingWindow 100 Statistics.maximum)
-    , mkBench numElements "maximum (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.maximum)
-    , benchWith sourceDescendingInt numElements
-        "maximum descending (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.maximum)
-
-    , mkBench numElements "range (window size 100)"
-        (Ring.slidingWindow 100 Statistics.range)
-    , mkBench numElements "range (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.range)
-
-    , mkBench numElements "sum (window size 100)"
-        (Ring.slidingWindow 100 Statistics.sum)
-    , mkBench numElements "sum (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.sum)
-    , mkBench numElements "sum (entire stream)"
-        (Statistics.cumulative Statistics.sum)
-    , mkBench numElements "sum (Data.Fold)" Fold.sum
-
-    , mkBench numElements "mean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.mean)
-    , mkBench numElements "mean (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.mean)
-    , mkBench numElements "mean (entire stream)"
-        (Statistics.cumulative Statistics.mean)
-    , mkBench numElements "mean (Data.Fold)" Fold.mean
-
-    , mkBench numElements "welfordMean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.welfordMean)
-    , mkBench numElements "welfordMean (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.welfordMean)
-    , mkBench numElements "welfordMean (entire stream)"
-        (Statistics.cumulative Statistics.welfordMean)
-
-    , mkBench numElements "geometricMean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.geometricMean)
-    , mkBench numElements "geometricMean (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.geometricMean)
-    , mkBench numElements "geometricMean (entire stream)"
-        (Statistics.cumulative Statistics.geometricMean)
-
-    , mkBench numElements "harmonicMean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.harmonicMean)
-    , mkBench numElements "harmonicMean (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.harmonicMean)
-    , mkBench numElements "harmonicMean (entire stream)"
-        (Statistics.cumulative Statistics.harmonicMean)
-
-    , mkBench numElements "quadraticMean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.quadraticMean)
-    , mkBench numElements "quadraticMean (window size 1000)"
-        (Ring.slidingWindow 1000 Statistics.quadraticMean)
-    , mkBench numElements "quadraticMean (entire stream)"
-        (Statistics.cumulative Statistics.quadraticMean)
-
-    , mkBench numElements "powerSum 2 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerSum 2))
-    , mkBench numElements "powerSum 2 (entire stream)"
-        (Statistics.cumulative (Statistics.powerSum 2))
-
-    , mkBench numElements "rawMoment 2 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerSum 2))
-    , mkBench numElements "rawMoment 2 (entire stream)"
-        (Statistics.cumulative (Statistics.rawMoment 2))
-
-    , mkBench numElements "powerMean 1 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMean 1))
-    , mkBench numElements "powerMean 2 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMean 2))
-    , mkBench numElements "powerMean 10 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMean 10))
-
-    , mkBench numElements "powerMeanFrac (-1) (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMeanFrac (-1)))
-    , mkBench numElements "powerMeanFrac 1 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMeanFrac 1))
-    , mkBench numElements "powerMeanFrac 2 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMeanFrac 2))
-    , mkBench numElements "powerMeanFrac 10 (window size 100)"
-        (Ring.slidingWindow 100 (Statistics.powerMeanFrac 10))
-
-    , mkBench numElements "ewma (entire stream)"
-        (Statistics.ewma 0.5)
-    , mkBench numElements "ewmaAfterMean (entire stream)"
+      mkBench numElements "ewmaAfterMean (entire stream)"
          (Statistics.ewmaAfterMean 10 0.5)
-    , mkBench numElements "ewmaRampUpSmoothing (entire stream)"
-        (Statistics.ewmaRampUpSmoothing 0.5 0.5)
-
-    , mkBench numElements "variance (window size 100)"
-        (Ring.slidingWindow 100 Statistics.variance)
-    , mkBench numElements "variance (entire stream)"
-        (Statistics.cumulative Statistics.variance)
-    -- , mkBench numElements "variance (Data.Fold)" Fold.variance
-
-    , mkBench numElements "sampleVariance (window size 100)"
-        (Ring.slidingWindow 100 Statistics.sampleVariance)
-    , mkBench numElements "sampleVariance (entire stream)"
-        (Statistics.cumulative Statistics.sampleVariance)
-
-    , mkBench numElements "stdDev (window size 100)"
-        (Ring.slidingWindow 100 Statistics.stdDev)
-    , mkBench numElements "stdDev (entire stream)"
-        (Statistics.cumulative Statistics.stdDev)
-    -- , mkBench numElements "stdDev (Data.Fold)" Fold.stdDev
-
-    , mkBench numElements "sampleStdDev (window size 100)"
-        (Ring.slidingWindow 100 Statistics.sampleStdDev)
-    , mkBench numElements "sampleStdDev (entire stream)"
-        (Statistics.cumulative Statistics.sampleStdDev)
-
-    , mkBench numElements "stdErrMean (window size 100)"
-        (Ring.slidingWindow 100 Statistics.stdErrMean)
-    , mkBench numElements "stdErrMean (entire stream)"
-        (Statistics.cumulative Statistics.stdErrMean)
-
--- These benchmarks take a lot of time/memory with fusion-plugin possibly
--- because of the use of Tee.
-#ifndef FUSION_PLUGIN
-    , mkBench numElements "skewness (window size 100)"
-        (Ring.slidingWindow 100 Statistics.skewness)
-    , mkBench numElements "skewness (entire stream)"
-        (Statistics.cumulative Statistics.skewness)
-
-    , mkBench numElements "kurtosis (window size 100)"
-        (Ring.slidingWindow 100 Statistics.kurtosis)
-    , mkBench numElements "kurtosis (entire stream)"
-        (Statistics.cumulative Statistics.kurtosis)
-#endif
-    , mkBench numElements "md (window size 100)"
-        (Ring.slidingWindowWith 100 Statistics.md)
-
     ]
 
 mkScans ::
@@ -382,12 +238,12 @@ main :: IO ()
 main =
   defaultMain
     [
-      bgroup "fold" $ mkBenchmarks benchWithFold
-    , bgroup "fold_Int"
-        [ benchWithFoldInt numElements "sumInt (window size 100)"
-            (Ring.slidingWindow 100 Statistics.sumInt)
-        , benchWithFoldInt numElements "sum for Int (window size 100)"
-            (Ring.slidingWindow 100 Statistics.sum)
+      bgroup "fold" $ mkFolds benchWithFold
+    , bgroup "scan_Int"
+        [ benchWithScanSrc source numElements "sumInt (window size 100)"
+            (Scanl.incrScan 100 Scanl.incrSumInt :: Scanl IO Int Int)
+        , benchWithScanSrc source numElements "sum for Int (window size 100)"
+            (Scanl.incrScan 100 Scanl.incrSum :: Scanl IO Int Int)
         ]
     , bgroup "scan" $ mkScans benchWithPostscan
     -- XXX These benchmarks measure the cost of creating the array as well,
diff --git a/src/Streamly/Statistics.hs b/src/Streamly/Statistics.hs
index e16eabd..b41fac0 100644
--- a/src/Streamly/Statistics.hs
+++ b/src/Streamly/Statistics.hs
@@ -1,3 +1,6 @@
+-- We are re-exporting some deprecated functions.
+{-# OPTIONS_GHC -Wno-deprecations #-}
+
 -- |
 -- Module      : Streamly.Statistics
 -- Copyright   : (c) 2020 Composewell Technologies
diff --git a/streamly-statistics.cabal b/streamly-statistics.cabal
index f9e70ce..29d8002 100644
--- a/streamly-statistics.cabal
+++ b/streamly-statistics.cabal
@@ -94,7 +94,6 @@ common compile-options
                  -Wincomplete-uni-patterns
                  -Wredundant-constraints
                  -Wnoncanonical-monad-instances
-                 -Wno-deprecations
                  -Rghc-timing
 
 common optimization-options

From 31b4528f936480903388a8c6ecaa3f58b2c537ff Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 17:34:50 +0530
Subject: [PATCH 5/7] Fix deprecation warnings in tests

---
 test/Main.hs | 34 ++++++++++++++++------------------
 1 file changed, 16 insertions(+), 18 deletions(-)

diff --git a/test/Main.hs b/test/Main.hs
index 95ef8cb..9e52483 100644
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -1,5 +1,3 @@
-{-# LANGUAGE TupleSections #-}
-
 import Control.Monad.IO.Class (liftIO)
 import Data.Complex (Complex ((:+)))
 import Data.Functor.Classes (liftEq2)
@@ -18,7 +16,7 @@ import qualified Data.Vector as V
 import qualified Statistics.Sample.Powers as STAT
 import qualified Statistics.Transform as STAT
 import qualified Streamly.Data.Array as Array
-import qualified Streamly.Data.Fold as Fold
+import qualified Streamly.Internal.Data.Fold as Fold
 import qualified Streamly.Data.MutArray as MA
 import qualified Streamly.Internal.Data.RingArray as Ring
 import qualified Streamly.Data.Stream as Stream
@@ -61,7 +59,7 @@ jackStdDevRes =
 
 testDistributions
     :: (STAT.Powers -> Double)
-    -> Fold.Fold IO (Double, Maybe Double) Double
+    -> Scanl.Scanl IO (Incr Double) Double
     -> Property
 testDistributions func fld =
     forAll (chooseInt (1, 1000)) $ \list_length ->
@@ -71,22 +69,22 @@ testDistributions func fld =
                 let var2 = func . STAT.powers 2 $ V.fromList ls
                     strm = S.fromList ls
                 var1 <-
-                    liftIO $ S.fold (Ring.slidingWindow list_length fld) strm
+                    liftIO $ S.fold (Fold.fromScanl (Scanl.incrScan list_length fld)) strm
                 assert (validate $ abs (var1 - var2))
 
 testVariance :: Property
-testVariance = testDistributions STAT.variance variance
+testVariance = testDistributions STAT.variance Stat.incrVariance
 
 testStdDev :: Property
-testStdDev = testDistributions STAT.stdDev stdDev
+testStdDev = testDistributions STAT.stdDev Stat.incrStdDev
 
 testFuncMD ::
-    Fold.Fold IO ((Double, Maybe Double), IO (MA.MutArray Double)) Double -> Spec
+    Scanl.Scanl IO (Incr Double, Ring.RingArray Double) Double -> Spec
 testFuncMD f = do
                 let c = S.fromList [10.0, 11.0, 12.0, 14.0]
-                a1 <- runIO $ S.fold (Ring.slidingWindowWith 2 f) c
-                a2 <- runIO $ S.fold (Ring.slidingWindowWith 3 f) c
-                a3 <- runIO $ S.fold (Ring.slidingWindowWith 4 f) c
+                a1 <- runIO $ S.fold (Fold.fromScanl (Scanl.incrScanWith 2 f)) c
+                a2 <- runIO $ S.fold (Fold.fromScanl (Scanl.incrScanWith 3 f)) c
+                a3 <- runIO $ S.fold (Fold.fromScanl (Scanl.incrScanWith 4 f)) c
                 it ("MD should be 1.0 , 1.1111111111111114 , 1.25 but actual is "
                     ++ show a1 ++ " " ++ show a2 ++ " " ++ show a3)
                     (  validate (abs (a1 - 1.0))
@@ -98,7 +96,7 @@ testFuncKurt :: Spec
 testFuncKurt = do
     let c = S.fromList
             [21.3 :: Double, 38.4, 12.7, 41.6]
-    krt <- runIO $ S.fold (Ring.slidingWindow 4 kurtosis) c
+    krt <- runIO $ S.fold (Fold.fromScanl (Scanl.incrScan 4 Stat.incrKurtosis)) c
     it ( "kurtosis should be 1.2762447351370185 Actual is " ++
         show krt
         )
@@ -219,8 +217,8 @@ main = hspec $ do
             deviationLimit = 1
             testFunc f = do
                 let c = S.fromList input
-                a <- runIO $ S.fold (Ring.slidingWindow winSize f) c
-                b <- runIO $ S.fold f $ S.take winSize $ fmap (, Nothing) c
+                a <- runIO $ S.fold (Fold.fromScanl (Scanl.incrScan winSize f)) c
+                b <- runIO $ S.fold (Fold.fromScanl f) $ S.take winSize $ fmap Insert c
                 let c1 = a - b
                 it ("deviation " ++ show c1 ++ " should not be more than "
                     ++ show deviationLimit
@@ -229,9 +227,9 @@ main = hspec $ do
                     )
                     $ c1 >= -1 * deviationLimit && c1 <= deviationLimit
 
-        describe "Sum" $ testFunc sum
-        describe "mean" $ testFunc mean
-        describe "welfordMean" $ testFunc welfordMean
+        describe "Sum" $ testFunc Scanl.incrSum
+        describe "mean" $ testFunc Scanl.incrMean
+        describe "welfordMean" $ testFunc Stat.incrWelfordMean
 
     describe "Correctness" $ do
         let winSize = 3
@@ -266,7 +264,7 @@ main = hspec $ do
             testFoldResamples 6 sampleList
 
         -- Spread/Mean
-        describe "MD" $ testFuncMD md
+        describe "MD" $ testFuncMD Stat.incrMd
         describe "Kurt" testFuncKurt
         prop "fft" testFFT
         describe "minimum" $ do

From c3fd81e7eb663a5e0e48c69418ba3e4366f629db Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 18:17:15 +0530
Subject: [PATCH 6/7] Fix docspec examples

---
 src/Streamly/Statistics.hs       | 35 ++++++++++++++++++--------------
 src/Streamly/Statistics/Scanl.hs | 30 +++++++++++++++------------
 2 files changed, 37 insertions(+), 28 deletions(-)

diff --git a/src/Streamly/Statistics.hs b/src/Streamly/Statistics.hs
index b41fac0..8feec2a 100644
--- a/src/Streamly/Statistics.hs
+++ b/src/Streamly/Statistics.hs
@@ -169,6 +169,11 @@ import qualified Streamly.Data.Stream as Stream
 
 import Prelude hiding (length, sum, minimum, maximum)
 
+-- $setup
+-- >>> :set -Wno-deprecations
+-- >>> import qualified Streamly.Data.Stream as Stream
+-- >>> import qualified Streamly.Internal.Data.RingArray as Ring
+
 -- TODO: Overflow checks. Would be good if we can directly replace the
 -- operations with overflow checked operations.
 --
@@ -453,9 +458,9 @@ maximum = Fold step initial extract extract
 --
 -- \(\mu = \mu'_1\)
 --
--- >>> mean = rawMoment 1
--- >>> mean = powerMean 1
--- >>> mean = Fold.teeWith (/) sum length
+-- > mean = rawMoment 1
+-- > mean = powerMean 1
+-- > mean = Fold.teeWith (/) sum length
 --
 -- /Space/: \(\mathcal{O}(1)\)
 --
@@ -538,7 +543,7 @@ welfordMean = Fold step initial extract extract
 --
 -- \(\mu'_k = \frac{\sum_{i=1}^n x_{i}^k}{n}\)
 --
--- >>> rawMoment k = Fold.teeWith (/) (Fold.windowPowerSum p) Fold.windowLength
+-- > rawMoment k = Fold.teeWith (/) (Fold.windowPowerSum p) Fold.windowLength
 --
 -- See https://en.wikipedia.org/wiki/Moment_(mathematics) .
 --
@@ -553,7 +558,7 @@ rawMoment k = Fold.teeWith (/) (Window.windowPowerSum k) Window.windowLength
 -- | Like 'rawMoment' but powers can be negative or fractional. This is
 -- slower than 'rawMoment' for positive intergal powers.
 --
--- >>> rawMomentFrac p = Fold.teeWith (/) (Fold.windowPowerSumFrac p) Fold.windowLength
+-- > rawMomentFrac p = Fold.teeWith (/) (Fold.windowPowerSumFrac p) Fold.windowLength
 --
 {-# INLINE rawMomentFrac #-}
 {-# DEPRECATED rawMomentFrac "Use Streamly.Statistics.Scanl.incrRawMomentFrac instead" #-}
@@ -572,7 +577,7 @@ rawMomentFrac k =
 --
 -- \(powerMean(k) = (rawMoment(k))^\frac{1}{k}\)
 --
--- >>> powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
+-- > powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
 --
 -- All other means can be expressed in terms of power mean. It is also known as
 -- the generalized mean.
@@ -587,7 +592,7 @@ powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
 -- | Like 'powerMean' but powers can be negative or fractional. This is
 -- slower than 'powerMean' for positive intergal powers.
 --
--- >>> powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
+-- > powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
 --
 {-# INLINE powerMeanFrac #-}
 {-# DEPRECATED powerMeanFrac "Use Streamly.Statistics.Scanl.incrPowerMeanFrac instead" #-}
@@ -601,8 +606,8 @@ powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
 --
 -- \(HM = \left(\frac{\sum\limits_{i=1}^n x_i^{-1}}{n}\right)^{-1}\)
 --
--- >>> harmonicMean = Fold.teeWith (/) length (lmap recip sum)
--- >>> harmonicMean = powerMeanFrac (-1)
+-- > harmonicMean = Fold.teeWith (/) length (lmap recip sum)
+-- > harmonicMean = powerMeanFrac (-1)
 --
 -- See https://en.wikipedia.org/wiki/Harmonic_mean .
 --
@@ -623,7 +628,7 @@ harmonicMean =
 --
 -- \(GM = e ^{{\frac{\sum_{i=1}^{n}\ln a_i}{n}}}\)
 --
--- >>> geometricMean = exp <$> lmap log mean
+-- > geometricMean = exp <$> lmap log mean
 --
 -- See https://en.wikipedia.org/wiki/Geometric_mean .
 {-# INLINE geometricMean #-}
@@ -636,7 +641,7 @@ geometricMean = exp <$> Window.windowLmap log mean
 --
 -- \(RMS = \sqrt{ \frac{1}{n} \left( x_1^2 + x_2^2 + \cdots + x_n^2 \right) }.\)
 --
--- >>> quadraticMean = powerMean 2
+-- > quadraticMean = powerMean 2
 --
 -- See https://en.wikipedia.org/wiki/Root_mean_square .
 --
@@ -734,7 +739,7 @@ ewmaRampUpSmoothing n k1 = extract <$> Fold.foldl' step initial
 
 -- | The difference between the maximum and minimum elements of a rolling window.
 --
--- >>> range = Fold.teeWith (-) maximum minimum
+-- > range = Fold.teeWith (-) maximum minimum
 --
 -- If you want to compute the range of the entire stream @Fold.teeWith (-)
 -- Fold.maximum Fold.minimum@ from the streamly package would be much faster.
@@ -810,7 +815,7 @@ variance = Fold.teeWith (\p2 m -> p2 - m ^ (2 :: Int)) (rawMoment 2) mean
 -- This is the population standard deviation or uncorrected sample standard
 -- deviation.
 --
--- >>> stdDev = sqrt <$> variance
+-- > stdDev = sqrt <$> variance
 --
 -- See https://en.wikipedia.org/wiki/Standard_deviation .
 --
@@ -920,7 +925,7 @@ sampleVariance =
 --
 -- \(s = \sqrt{sampleVariance}\)
 --
--- >>> sampleStdDev = sqrt <$> sampleVariance
+-- > sampleStdDev = sqrt <$> sampleVariance
 --
 -- See https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
 -- .
@@ -1039,7 +1044,7 @@ foldResamples n arr fld =
 -- | Count the frequency of elements in a sliding window.
 --
 -- >>> input = Stream.fromList [1,1,3,4,4::Int]
--- >>> f = Ring.slidingWindow 4 Statistics.frequency
+-- >>> f = Ring.slidingWindow 4 frequency
 -- >>> Stream.fold f input
 -- fromList [(1,1),(3,1),(4,2)]
 --
diff --git a/src/Streamly/Statistics/Scanl.hs b/src/Streamly/Statistics/Scanl.hs
index 3698403..4ade184 100644
--- a/src/Streamly/Statistics/Scanl.hs
+++ b/src/Streamly/Statistics/Scanl.hs
@@ -106,6 +106,11 @@ import qualified Streamly.Data.Stream as Stream
 
 import Prelude hiding (length, sum, minimum, maximum)
 
+-- $setup
+-- >>> import qualified Streamly.Data.Stream as Stream
+-- >>> import qualified Streamly.Internal.Data.Fold as Fold
+-- >>> import qualified Streamly.Internal.Data.Scanl as Scanl
+
 -- TODO: Overflow checks. Would be good if we can directly replace the
 -- operations with overflow checked operations.
 --
@@ -309,7 +314,7 @@ incrWelfordMean = Scanl step initial extract extract
 --
 -- \(\mu'_k = \frac{\sum_{i=1}^n x_{i}^k}{n}\)
 --
--- >>> rawMoment k = Fold.teeWith (/) (Fold.windowPowerSum p) Fold.windowLength
+-- >>> incrRawMoment k = Scanl.teeWith (/) (Scanl.incrPowerSum k) Scanl.incrCount
 --
 -- See https://en.wikipedia.org/wiki/Moment_(mathematics) .
 --
@@ -324,7 +329,7 @@ incrRawMoment k =
 -- | Like 'rawMoment' but powers can be negative or fractional. This is
 -- slower than 'rawMoment' for positive intergal powers.
 --
--- >>> rawMomentFrac p = Fold.teeWith (/) (Fold.windowPowerSumFrac p) Fold.windowLength
+-- >>> incrRawMomentFrac p = Scanl.teeWith (/) (Scanl.incrPowerSumFrac p) Scanl.incrCount
 --
 {-# INLINE incrRawMomentFrac #-}
 incrRawMomentFrac :: (Monad m, Floating a) => a -> Scanl m (Incr a) a
@@ -342,7 +347,7 @@ incrRawMomentFrac k =
 --
 -- \(powerMean(k) = (rawMoment(k))^\frac{1}{k}\)
 --
--- >>> powerMean k = (** (1 / fromIntegral k)) <$> rawMoment k
+-- >>> incrPowerMean k = (** (1 / fromIntegral k)) <$> incrRawMoment k
 --
 -- All other means can be expressed in terms of power mean. It is also known as
 -- the generalized mean.
@@ -356,7 +361,7 @@ incrPowerMean k = (** (1 / fromIntegral k)) <$> incrRawMoment k
 -- | Like 'powerMean' but powers can be negative or fractional. This is
 -- slower than 'powerMean' for positive intergal powers.
 --
--- >>> powerMeanFrac k = (** (1 / k)) <$> rawMomentFrac k
+-- >>> incrPowerMeanFrac k = (** (1 / k)) <$> incrRawMomentFrac k
 --
 {-# INLINE incrPowerMeanFrac #-}
 incrPowerMeanFrac :: (Monad m, Floating a) => a -> Scanl m (Incr a) a
@@ -369,8 +374,8 @@ incrPowerMeanFrac k = (** (1 / k)) <$> incrRawMomentFrac k
 --
 -- \(HM = \left(\frac{\sum\limits_{i=1}^n x_i^{-1}}{n}\right)^{-1}\)
 --
--- >>> harmonicMean = Fold.teeWith (/) length (lmap recip sum)
--- >>> harmonicMean = powerMeanFrac (-1)
+-- >>> incrHarmonicMean = Scanl.teeWith (/) Scanl.incrCount (Scanl.lmap (fmap recip) Scanl.incrSum)
+-- >>> incrHarmonicMean = incrPowerMeanFrac (-1)
 --
 -- See https://en.wikipedia.org/wiki/Harmonic_mean .
 --
@@ -390,7 +395,7 @@ incrHarmonicMean =
 --
 -- \(GM = e ^{{\frac{\sum_{i=1}^{n}\ln a_i}{n}}}\)
 --
--- >>> geometricMean = exp <$> lmap log mean
+-- >>> incrGeometricMean = exp <$> Scanl.lmap (fmap log) Scanl.incrMean
 --
 -- See https://en.wikipedia.org/wiki/Geometric_mean .
 {-# INLINE incrGeometricMean #-}
@@ -402,7 +407,7 @@ incrGeometricMean = exp <$> Scanl.lmap (fmap log) Scanl.incrMean
 --
 -- \(RMS = \sqrt{ \frac{1}{n} \left( x_1^2 + x_2^2 + \cdots + x_n^2 \right) }.\)
 --
--- >>> quadraticMean = powerMean 2
+-- >>> incrQuadraticMean = incrPowerMean 2
 --
 -- See https://en.wikipedia.org/wiki/Root_mean_square .
 --
@@ -541,7 +546,7 @@ incrEwma w = Scanl step initial extract extract
 
 -- | The difference between the maximum and minimum elements of a rolling window.
 --
--- >>> range = Fold.teeWith (-) maximum minimum
+-- >>> incrRange = Scanl.teeWith (-) incrMaximum incrMinimum
 --
 -- If you want to compute the range of the entire stream @Fold.teeWith (-)
 -- Fold.maximum Fold.minimum@ from the streamly package would be much faster.
@@ -620,7 +625,7 @@ incrVariance =
 -- This is the population standard deviation or uncorrected sample standard
 -- deviation.
 --
--- >>> stdDev = sqrt <$> variance
+-- >>> incrStdDev = sqrt <$> incrVariance
 --
 -- See https://en.wikipedia.org/wiki/Standard_deviation .
 --
@@ -727,7 +732,7 @@ incrSampleVariance =
 --
 -- \(s = \sqrt{sampleVariance}\)
 --
--- >>> sampleStdDev = sqrt <$> sampleVariance
+-- >>> incrSampleStdDev = sqrt <$> incrSampleVariance
 --
 -- See https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
 -- .
@@ -760,8 +765,7 @@ incrStdErrMean =
 -- | Count the frequency of elements in a sliding window.
 --
 -- >>> input = Stream.fromList [1,1,3,4,4::Int]
--- >>> f = Ring.slidingWindow 4 Statistics.frequency
--- >>> Stream.fold f input
+-- >>> Stream.fold (Fold.fromScanl (Scanl.incrScan 4 incrFrequency)) input
 -- fromList [(1,1),(3,1),(4,2)]
 --
 {-# INLINE incrFrequency #-}

From 3b5acba068368a980550317202d162f1f48b15ed Mon Sep 17 00:00:00 2001
From: Harendra Kumar <harendra@composewell.com>
Date: Mon, 15 Jun 2026 18:24:48 +0530
Subject: [PATCH 7/7] Fix hlint warnings

---
 src/Streamly/Statistics.hs       | 15 +++++++--------
 src/Streamly/Statistics/Scanl.hs |  3 +--
 2 files changed, 8 insertions(+), 10 deletions(-)

diff --git a/src/Streamly/Statistics.hs b/src/Streamly/Statistics.hs
index 8feec2a..aa9a17f 100644
--- a/src/Streamly/Statistics.hs
+++ b/src/Streamly/Statistics.hs
@@ -224,7 +224,7 @@ isPower2 n = n .&. (n - 1) == 0
 --
 {-# INLINE _power2 #-}
 _power2 :: Int -> Int
-_power2 n = shiftL 1 n
+_power2 = shiftL 1
 
 -- | Create a bit mask with lower n bits 0 and the rest as 1.
 --
@@ -291,7 +291,7 @@ fft marr
         | l == log2len = return ()
         | otherwise = do
             let !l2 = twice l1
-                !e  = -6.283185307179586/fromIntegral l2
+                !e  = -(6.283185307179586/fromIntegral l2)
                 flight j !a | j == l1   = stage (l + 1) l2
                             | otherwise = do
                     let butterfly i | i >= len  = flight (j + 1) (a + e)
@@ -710,7 +710,7 @@ ewma k = extract <$> Fold.foldl' step (Tuple' 0 1)
 {-# INLINE ewmaAfterMean #-}
 ewmaAfterMean :: Monad m => Int -> Double -> Fold m Double Double
 ewmaAfterMean n k =
-    Fold.concatMap (\i -> (Fold.foldl' (ewmaStep k) i)) (Fold.take n Fold.mean)
+    Fold.concatMap (Fold.foldl' (ewmaStep k)) (Fold.take n Fold.mean)
 
 -- | @ewma n k@ is like 'ewma' but uses 1 as the initial smoothing factor and
 -- then exponentially smooths it to @k@ using @n@ as the smoothing factor.
@@ -783,8 +783,7 @@ md =
             Just action -> do
                 arr <- action
                 Stream.fold Fold.mean
-                    $ fmap (\a -> abs (mn - a))
-                    $ Stream.unfold MA.reader arr
+                    $ (\a -> abs (mn - a)) <$> Stream.unfold MA.reader arr
             Nothing -> return 0.0
 
 -- | The variance \(\sigma^2\) of a population of \(n\) equally likely values
@@ -970,7 +969,7 @@ jackKnifeMean :: (Monad m, Fractional a, Unbox a) => Array a -> Stream m a
 jackKnifeMean arr = do
     let len = fromIntegral (Array.length arr - 1)
         s = foldArray Fold.sum arr
-     in fmap (\b -> (s - b) / len) $ Array.read arr
+     in (\b -> (s - b) / len) <$> Array.read arr
 
 -- | Given an array of @n@ items, compute variance of @(n - 1)@ items at a time,
 -- producing a stream of all possible variance values omitting a different item
@@ -984,7 +983,7 @@ jackKnifeVariance arr = do
         foldSums (s, s2) x = (s + x, s2 + x ^ (2 :: Int))
         (sum1, sum2) = foldArray (Fold.foldl' foldSums (0.0, 0.0)) arr
         var x = (sum2 - x ^ (2 :: Int)) / len -  ((sum1 - x) / len) ^ (2::Int)
-     in fmap var $ Array.read arr
+     in var <$> Array.read arr
 
 -- | Standard deviation computed from 'jackKnifeVariance'.
 --
@@ -1006,7 +1005,7 @@ resample = Unfold step inject
 
     inject arr = liftIO $ do
         g <- createSystemRandom
-        return $ (g, arr, Array.length arr, 0)
+        return (g, arr, Array.length arr, 0)
 
     chooseOne g arr len = do
         i <- uniformRM (0, len - 1) g
diff --git a/src/Streamly/Statistics/Scanl.hs b/src/Streamly/Statistics/Scanl.hs
index 4ade184..fb6c2a4 100644
--- a/src/Streamly/Statistics/Scanl.hs
+++ b/src/Streamly/Statistics/Scanl.hs
@@ -592,8 +592,7 @@ incrMd =
         case mRng of
             Just rng -> do
                 Stream.fold Fold.mean
-                    $ fmap (\a -> abs (mn - a))
-                    $ Ring.read rng
+                    $ (\a -> abs (mn - a)) <$> Ring.read rng
             Nothing -> return 0.0
 
 -- | The variance \(\sigma^2\) of a population of \(n\) equally likely values