Copyright	(c) 2009 2010 Bryan O'Sullivan
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

Statistics.Resampling

Contents

Data types
Resampling
Jackknife
Helper functions

Description

Resampling statistics.

Synopsis

Data types

newtype Resample Source #

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.

Constructors

Resample
Fields fromResample :: Vector Double

Instances

Eq Resample Source #
Methods (==) :: Resample -> Resample -> Bool # (/=) :: Resample -> Resample -> Bool #
Data Resample Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Resample -> c Resample # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Resample # toConstr :: Resample -> Constr # dataTypeOf :: Resample -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c Resample) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Resample) # gmapT :: (forall b. Data b => b -> b) -> Resample -> Resample # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Resample -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Resample -> r # gmapQ :: (forall d. Data d => d -> u) -> Resample -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Resample -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Resample -> m Resample # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Resample -> m Resample # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Resample -> m Resample #
Read Resample Source #
Methods readsPrec :: Int -> ReadS Resample # readList :: ReadS [Resample] # readPrec :: ReadPrec Resample # readListPrec :: ReadPrec [Resample] #
Show Resample Source #
Methods showsPrec :: Int -> Resample -> ShowS # show :: Resample -> String # showList :: [Resample] -> ShowS #
Generic Resample Source #
Associated Types type Rep Resample :: * -> * # Methods from :: Resample -> Rep Resample x # to :: Rep Resample x -> Resample #
ToJSON Resample Source #
Methods toJSON :: Resample -> Value # toEncoding :: Resample -> Encoding # toJSONList :: [Resample] -> Value # toEncodingList :: [Resample] -> Encoding #
FromJSON Resample Source #
Methods parseJSON :: Value -> Parser Resample # parseJSONList :: Value -> Parser [Resample] #
Binary Resample Source #
Methods put :: Resample -> Put # get :: Get Resample # putList :: [Resample] -> Put #
type Rep Resample Source #
type Rep Resample = D1 (MetaData "Resample" "Statistics.Resampling" "statistics-0.14.0.2-9wDz1lVU92ZDJSrAe5uHzb" True) (C1 (MetaCons "Resample" PrefixI True) (S1 (MetaSel (Just Symbol "fromResample") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector Double))))

data Bootstrap v a Source #

Constructors

Bootstrap
Fields fullSample :: !a resamples :: v a

Instances

Functor v => Functor (Bootstrap v) Source #
Methods fmap :: (a -> b) -> Bootstrap v a -> Bootstrap v b # (<$) :: a -> Bootstrap v b -> Bootstrap v a #
Foldable v => Foldable (Bootstrap v) Source #
Methods fold :: Monoid m => Bootstrap v m -> m # foldMap :: Monoid m => (a -> m) -> Bootstrap v a -> m # foldr :: (a -> b -> b) -> b -> Bootstrap v a -> b # foldr' :: (a -> b -> b) -> b -> Bootstrap v a -> b # foldl :: (b -> a -> b) -> b -> Bootstrap v a -> b # foldl' :: (b -> a -> b) -> b -> Bootstrap v a -> b # foldr1 :: (a -> a -> a) -> Bootstrap v a -> a # foldl1 :: (a -> a -> a) -> Bootstrap v a -> a # toList :: Bootstrap v a -> [a] # null :: Bootstrap v a -> Bool # length :: Bootstrap v a -> Int # elem :: Eq a => a -> Bootstrap v a -> Bool # maximum :: Ord a => Bootstrap v a -> a # minimum :: Ord a => Bootstrap v a -> a # sum :: Num a => Bootstrap v a -> a # product :: Num a => Bootstrap v a -> a #
Traversable v => Traversable (Bootstrap v) Source #
Methods traverse :: Applicative f => (a -> f b) -> Bootstrap v a -> f (Bootstrap v b) # sequenceA :: Applicative f => Bootstrap v (f a) -> f (Bootstrap v a) # mapM :: Monad m => (a -> m b) -> Bootstrap v a -> m (Bootstrap v b) # sequence :: Monad m => Bootstrap v (m a) -> m (Bootstrap v a) #
(Eq (v a), Eq a) => Eq (Bootstrap v a) Source #
Methods (==) :: Bootstrap v a -> Bootstrap v a -> Bool # (/=) :: Bootstrap v a -> Bootstrap v a -> Bool #
(Data (v a), Data a, Typeable (* -> *) v) => Data (Bootstrap v a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bootstrap v a -> c (Bootstrap v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Bootstrap v a) # toConstr :: Bootstrap v a -> Constr # dataTypeOf :: Bootstrap v a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Bootstrap v a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Bootstrap v a)) # gmapT :: (forall b. Data b => b -> b) -> Bootstrap v a -> Bootstrap v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bootstrap v a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bootstrap v a -> r # gmapQ :: (forall d. Data d => d -> u) -> Bootstrap v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bootstrap v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) #
(Read (v a), Read a) => Read (Bootstrap v a) Source #
Methods readsPrec :: Int -> ReadS (Bootstrap v a) # readList :: ReadS [Bootstrap v a] # readPrec :: ReadPrec (Bootstrap v a) # readListPrec :: ReadPrec [Bootstrap v a] #
(Show (v a), Show a) => Show (Bootstrap v a) Source #
Methods showsPrec :: Int -> Bootstrap v a -> ShowS # show :: Bootstrap v a -> String # showList :: [Bootstrap v a] -> ShowS #
Generic (Bootstrap v a) Source #
Associated Types type Rep (Bootstrap v a) :: * -> * # Methods from :: Bootstrap v a -> Rep (Bootstrap v a) x # to :: Rep (Bootstrap v a) x -> Bootstrap v a #
(ToJSON a, ToJSON (v a)) => ToJSON (Bootstrap v a) Source #
Methods toJSON :: Bootstrap v a -> Value # toEncoding :: Bootstrap v a -> Encoding # toJSONList :: [Bootstrap v a] -> Value # toEncodingList :: [Bootstrap v a] -> Encoding #
(FromJSON a, FromJSON (v a)) => FromJSON (Bootstrap v a) Source #
Methods parseJSON :: Value -> Parser (Bootstrap v a) # parseJSONList :: Value -> Parser [Bootstrap v a] #
(Binary a, Binary (v a)) => Binary (Bootstrap v a) Source #
Methods put :: Bootstrap v a -> Put # get :: Get (Bootstrap v a) # putList :: [Bootstrap v a] -> Put #
type Rep (Bootstrap v a) Source #
type Rep (Bootstrap v a) = D1 (MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.14.0.2-9wDz1lVU92ZDJSrAe5uHzb" False) (C1 (MetaCons "Bootstrap" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "fullSample") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Just Symbol "resamples") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (v a)))))

data Estimator Source #

An estimator of a property of a sample, such as its mean.

The use of an algebraic data type here allows functions such as jackknife and bootstrapBCA to use more efficient algorithms when possible.

Constructors

Mean
Variance
VarianceUnbiased
StdDev
Function (Sample -> Double)

estimate :: Estimator -> Sample -> Double Source #

Run an Estimator over a sample.

Resampling

resampleST Source #

Arguments

:: PrimMonad m
=> Gen (PrimState m)
-> [Estimator]	Estimation functions.
-> Int	Number of resamples to compute.
-> Vector Double	Original sample.
-> m [Bootstrap Vector Double]

Single threaded and deterministic version of resample.

resample Source #

Arguments

:: GenIO
-> [Estimator]	Estimation functions.
-> Int	Number of resamples to compute.
-> Vector Double	Original sample.
-> IO [(Estimator, Bootstrap Vector Double)]

O(e*r*s) Resample a data set repeatedly, with replacement, computing each estimate over the resampled data.

This function is expensive; it has to do work proportional to e*r*s, where e is the number of estimation functions, r is the number of resamples to compute, and s is the number of original samples.

To improve performance, this function will make use of all available CPUs. At least with GHC 7.0, parallel performance seems best if the parallel garbage collector is disabled (RTS option -qg).

resampleVector :: (PrimMonad m, Vector v a) => Gen (PrimState m) -> v a -> m (v a) Source #

Create vector using resamples

Jackknife

jackknife :: Estimator -> Sample -> Vector Double Source #

O(n) or O(n^2) Compute a statistical estimate repeatedly over a sample, each time omitting a successive element.

jackknifeMean :: Sample -> Vector Double Source #

O(n) Compute the jackknife mean of a sample.

jackknifeVariance :: Sample -> Vector Double Source #

O(n) Compute the jackknife variance of a sample.

jackknifeVarianceUnb :: Sample -> Vector Double Source #

O(n) Compute the unbiased jackknife variance of a sample.

jackknifeStdDev :: Sample -> Vector Double Source #

O(n) Compute the jackknife standard deviation of a sample.

Helper functions

splitGen :: Int -> GenIO -> IO [GenIO] Source #

Split a generator into several that can run independently.