```-- |
-- Module    : Statistics.Resampling
-- Copyright : (c) 2009, 2010 Bryan O'Sullivan
--
-- Maintainer  : bos@serpentine.com
-- Stability   : experimental
-- Portability : portable
--
-- Resampling statistics.

module Statistics.Resampling
(
Resample(..)
, jackknife
, resample
) where

import Data.Vector.Algorithms.Intro (sort)
import Data.Vector.Generic (unsafeFreeze)
import Data.Vector.Unboxed ((!))
import Statistics.Function (create, indexed, indices)
import Statistics.Types (Estimator, Sample)
import System.Random.MWC (Gen, uniform)
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as MU

-- | A resample drawn randomly, with replacement, from a set of data
-- points.  Distinct from a normal array to make it harder for your
-- humble author's brain to go wrong.
newtype Resample = Resample {
fromResample :: U.Vector Double
} deriving (Eq, Show)

-- | Resample a data set repeatedly, with replacement, computing each
-- estimate over the resampled data.
resample :: (PrimMonad m) => Gen (PrimState m) -> [Estimator] -> Int -> Sample -> m [Resample]
resample gen ests numResamples samples = do
results <- mapM (const (MU.new numResamples)) \$ ests
loop 0 (zip ests results)
mapM_ sort results
mapM (liftM Resample . unsafeFreeze) results
where
loop k ers | k >= numResamples = return ()
| otherwise = do
re <- create n \$ \_ -> do
r <- uniform gen
return (samples ! (abs r `mod` n))
forM_ ers \$ \(est,arr) ->
MU.write arr k . est \$ re
loop (k+1) ers
n = U.length samples
{-# INLINE resample #-}

-- | Compute a statistical estimate repeatedly over a sample, each
-- time omitting a successive element.
jackknife :: Estimator -> Sample -> U.Vector Double
jackknife est sample = U.map f . indices \$ sample
where f i = est (dropAt i sample)
{-# INLINE jackknife #-}

-- | Drop the /k/th element of a vector.
dropAt :: U.Unbox e => Int -> U.Vector e -> U.Vector e
dropAt n = U.map snd . U.filter notN . indexed
where notN (i , _) = i /= n
```