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

FromJSON Resample

Defined in Statistics.Resampling

Methods

parseJSON :: Value -> Parser Resample

parseJSONList :: Value -> Parser [Resample]

ToJSON Resample

Defined in Statistics.Resampling

Methods

toJSON :: Resample -> Value

toEncoding :: Resample -> Encoding

toJSONList :: [Resample] -> Value

toEncodingList :: [Resample] -> Encoding

Data Resample

Defined in Statistics.Resampling

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 :: forall r r'. (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

Generic Resample

Defined in Statistics.Resampling

Associated Types

type Rep Resample :: Type -> Type

Methods

from :: Resample -> Rep Resample x

to :: Rep Resample x -> Resample

Read Resample

Defined in Statistics.Resampling

Methods

readsPrec :: Int -> ReadS Resample

readList :: ReadS [Resample]

readPrec :: ReadPrec Resample

readListPrec :: ReadPrec [Resample]

Show Resample

Defined in Statistics.Resampling

Methods

showsPrec :: Int -> Resample -> ShowS

show :: Resample -> String

showList :: [Resample] -> ShowS

Binary Resample

Defined in Statistics.Resampling

Methods

put :: Resample -> Put

get :: Get Resample

putList :: [Resample] -> Put

Eq Resample

Defined in Statistics.Resampling

Methods

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

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

type Rep Resample

Defined in Statistics.Resampling

type Rep Resample = D1 ('MetaData "Resample" "Statistics.Resampling" "statistics-0.16.2.1-34qObKIlIVGJpKYv9daW0Y" 'True) (C1 ('MetaCons "Resample" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromResample") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector Double))))

data Bootstrap v a

Constructors

Bootstrap

Fields

• fullSample :: !a
• resamples :: v a

Instances

Foldable v => Foldable (Bootstrap v)

Defined in Statistics.Resampling

Methods

fold :: Monoid m => Bootstrap v m -> m

foldMap :: Monoid m => (a -> m) -> Bootstrap v a -> 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)

Defined in Statistics.Resampling

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)

Functor v => Functor (Bootstrap v)

Defined in Statistics.Resampling

Methods

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

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

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

Defined in Statistics.Resampling

Methods

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

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

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

Defined in Statistics.Resampling

Methods

toJSON :: Bootstrap v a -> Value

toEncoding :: Bootstrap v a -> Encoding

toJSONList :: [Bootstrap v a] -> Value

toEncodingList :: [Bootstrap v a] -> Encoding

(Typeable v, Data a, Data (v a)) => Data (Bootstrap v a)

Defined in Statistics.Resampling

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 :: forall r r'. (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)

Generic (Bootstrap v a)

Defined in Statistics.Resampling

Associated Types

type Rep (Bootstrap v a) :: Type -> Type

Methods

from :: Bootstrap v a -> Rep (Bootstrap v a) x

to :: Rep (Bootstrap v a) x -> Bootstrap v a

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

Defined in Statistics.Resampling

Methods

readsPrec :: Int -> ReadS (Bootstrap v a)

readList :: ReadS [Bootstrap v a]

readPrec :: ReadPrec (Bootstrap v a)

readListPrec :: ReadPrec [Bootstrap v a]

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

Defined in Statistics.Resampling

Methods

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

show :: Bootstrap v a -> String

showList :: [Bootstrap v a] -> ShowS

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

Defined in Statistics.Resampling

Methods

put :: Bootstrap v a -> Put

get :: Get (Bootstrap v a)

putList :: [Bootstrap v a] -> Put

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

Defined in Statistics.Resampling

Methods

(==) :: Bootstrap v a -> Bootstrap v a -> Bool

(/=) :: Bootstrap v a -> Bootstrap v a -> Bool

type Rep (Bootstrap v a)

Defined in Statistics.Resampling

type Rep (Bootstrap v a) = D1 ('MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.16.2.1-34qObKIlIVGJpKYv9daW0Y" 'False) (C1 ('MetaCons "Bootstrap" 'PrefixI 'True) (S1 ('MetaSel ('Just "fullSample") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Just "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.