Statistics.Resampling

Resampling statistics.

Data types

newtype Resample

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

Methods

(==) :: Resample -> Resample -> Bool

(/=) :: Resample -> Resample -> Bool

Data Resample

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

Methods

readsPrec :: Int -> ReadS Resample

readList :: ReadS [Resample]

readPrec :: ReadPrec Resample

readListPrec :: ReadPrec [Resample]

Show Resample

Methods

showsPrec :: Int -> Resample -> ShowS

show :: Resample -> String

showList :: [Resample] -> ShowS

Generic Resample

Associated Types

type Rep Resample :: * -> *

Methods

from :: Resample -> Rep Resample x

to :: Rep Resample x -> Resample

ToJSON Resample

Methods

toJSON :: Resample -> Value

toEncoding :: Resample -> Encoding

toJSONList :: [Resample] -> Value

toEncodingList :: [Resample] -> Encoding

FromJSON Resample

Methods

parseJSON :: Value -> Parser Resample

parseJSONList :: Value -> Parser [Resample]

Binary Resample

Methods

put :: Resample -> Put

get :: Get Resample

putList :: [Resample] -> Put

type Rep Resample

type Rep Resample = D1 (MetaData "Resample" "Statistics.Resampling" "statistics-0.14.0.0-9xPMo3QbnR7BEP0FkvUcUB" True) (C1 (MetaCons "Resample" PrefixI True) (S1 (MetaSel (Just Symbol "fromResample") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector Double))))

data Bootstrap v a

Constructors

Bootstrap

Fields

• fullSample :: !a
• resamples :: v a

Instances

Functor v => Functor (Bootstrap v)

Methods

fmap :: (a -> b) -> Bootstrap v a -> Bootstrap v b

(<$) :: a -> Bootstrap v b -> Bootstrap v a

Foldable v => Foldable (Bootstrap v)

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)

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)

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)

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)

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)

Methods

showsPrec :: Int -> Bootstrap v a -> ShowS

show :: Bootstrap v a -> String

showList :: [Bootstrap v a] -> ShowS

Generic (Bootstrap v a)

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)

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)

Methods

parseJSON :: Value -> Parser (Bootstrap v a)

parseJSONList :: Value -> Parser [Bootstrap v a]

(Binary a, Binary (v a)) => Binary (Bootstrap v a)

Methods

put :: Bootstrap v a -> Put

get :: Get (Bootstrap v a)

putList :: [Bootstrap v a] -> Put

type Rep (Bootstrap v a)

type Rep (Bootstrap v a) = D1 (MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.14.0.0-9xPMo3QbnR7BEP0FkvUcUB" 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

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

Run an Estimator over a sample.

Resampling

resampleST

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

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)

Create vector using resamples

Jackknife

jackknife :: Estimator -> Sample -> Vector Double

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

jackknifeMean :: Sample -> Vector Double

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

jackknifeVariance :: Sample -> Vector Double

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

jackknifeVarianceUnb :: Sample -> Vector Double

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

jackknifeStdDev :: Sample -> Vector Double

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

Helper functions

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

Split a generator into several that can run independently.