statistics-0.15.2.0: A library of statistical types, data, and functions

Copyright(c) 2015 Mihai Maruseac
LicenseBSD3
Maintainermihai.maruseac@maruseac.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

Statistics.Distribution.Laplace

Contents

Description

The Laplace distribution. This is the continuous probability defined as the difference of two iid exponential random variables or a Brownian motion evaluated as exponentially distributed times. It is used in differential privacy (Laplace Method), speech recognition and least absolute deviations method (Laplace's first law of errors, giving a robust regression method)

Synopsis

Documentation

data LaplaceDistribution Source #

Instances
Eq LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Data LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> LaplaceDistribution -> c LaplaceDistribution

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c LaplaceDistribution

toConstr :: LaplaceDistribution -> Constr

dataTypeOf :: LaplaceDistribution -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c LaplaceDistribution)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c LaplaceDistribution)

gmapT :: (forall b. Data b => b -> b) -> LaplaceDistribution -> LaplaceDistribution

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> LaplaceDistribution -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> LaplaceDistribution -> r

gmapQ :: (forall d. Data d => d -> u) -> LaplaceDistribution -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> LaplaceDistribution -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> LaplaceDistribution -> m LaplaceDistribution

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> LaplaceDistribution -> m LaplaceDistribution

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> LaplaceDistribution -> m LaplaceDistribution

Read LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Show LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

showsPrec :: Int -> LaplaceDistribution -> ShowS

show :: LaplaceDistribution -> String

showList :: [LaplaceDistribution] -> ShowS

Generic LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Associated Types

type Rep LaplaceDistribution :: Type -> Type

Binary LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

FromJSON LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

Methods

parseJSON :: Value -> Parser LaplaceDistribution

parseJSONList :: Value -> Parser [LaplaceDistribution]

ToJSON LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

ContGen LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

Methods

genContVar :: PrimMonad m => LaplaceDistribution -> Gen (PrimState m) -> m Double Source #

Entropy LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

Methods

entropy :: LaplaceDistribution -> Double Source #

MaybeEntropy LaplaceDistribution Source # 
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Methods

maybeEntropy :: LaplaceDistribution -> Maybe Double Source #

Variance LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

MaybeVariance LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

maybeVariance :: LaplaceDistribution -> Maybe Double Source #

maybeStdDev :: LaplaceDistribution -> Maybe Double Source #

Mean LaplaceDistribution Source # 
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Methods

mean :: LaplaceDistribution -> Double Source #

MaybeMean LaplaceDistribution Source # 
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Defined in Statistics.Distribution.Laplace

Methods

maybeMean :: LaplaceDistribution -> Maybe Double Source #

ContDistr LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

density :: LaplaceDistribution -> Double -> Double Source #

quantile :: LaplaceDistribution -> Double -> Double Source #

complQuantile :: LaplaceDistribution -> Double -> Double Source #

logDensity :: LaplaceDistribution -> Double -> Double Source #

Distribution LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

cumulative :: LaplaceDistribution -> Double -> Double Source #

complCumulative :: LaplaceDistribution -> Double -> Double Source #

FromSample LaplaceDistribution Double Source #

Create Laplace distribution from sample. No tests are made to check whether it truly is Laplace. Location of distribution estimated as median of sample.

Instance details

Defined in Statistics.Distribution.Laplace

Methods

fromSample :: Vector v Double => v Double -> Maybe LaplaceDistribution Source #

type Rep LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

type Rep LaplaceDistribution = D1 (MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.15.2.0-FobexxUIuAfbpoQyeDMuJ" False) (C1 (MetaCons "LD" PrefixI True) (S1 (MetaSel (Just "ldLocation") SourceUnpack SourceStrict DecidedStrict) (Rec0 Double) :*: S1 (MetaSel (Just "ldScale") SourceUnpack SourceStrict DecidedStrict) (Rec0 Double)))

Constructors

laplace Source #

Arguments

:: Double

Location

-> Double

Scale

-> LaplaceDistribution 

Create an Laplace distribution.

laplaceE Source #

Arguments

:: Double

Location

-> Double

Scale

-> Maybe LaplaceDistribution 

Create an Laplace distribution.

Accessors

ldLocation :: LaplaceDistribution -> Double Source #

Location.

ldScale :: LaplaceDistribution -> Double Source #

Scale.