statistics-0.16.2.1: A library of statistical types, data, and functions
Copyright(c) 2015 Mihai Maruseac
LicenseBSD3
Maintainermihai.maruseac@maruseac.com
Stabilityexperimental
Portabilityportable
Safe HaskellSafe-Inferred
LanguageHaskell2010

Statistics.Distribution.Laplace

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 #

Instances

Instances details
FromJSON LaplaceDistribution # 
Instance details

Defined in Statistics.Distribution.Laplace

ToJSON LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Data LaplaceDistribution # 
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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 :: forall r r'. (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

Generic LaplaceDistribution # 
Instance details

Defined in Statistics.Distribution.Laplace

Associated Types

type Rep LaplaceDistribution :: Type -> Type

Read LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Show LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

showsPrec :: Int -> LaplaceDistribution -> ShowS

show :: LaplaceDistribution -> String

showList :: [LaplaceDistribution] -> ShowS

Binary LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Eq LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

ContDistr LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

density :: LaplaceDistribution -> Double -> Double #

logDensity :: LaplaceDistribution -> Double -> Double #

quantile :: LaplaceDistribution -> Double -> Double #

complQuantile :: LaplaceDistribution -> Double -> Double #

ContGen LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

genContVar :: StatefulGen g m => LaplaceDistribution -> g -> m Double #

Distribution LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

cumulative :: LaplaceDistribution -> Double -> Double #

complCumulative :: LaplaceDistribution -> Double -> Double #

Entropy LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

entropy :: LaplaceDistribution -> Double #

MaybeEntropy LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

maybeEntropy :: LaplaceDistribution -> Maybe Double #

MaybeMean LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

maybeMean :: LaplaceDistribution -> Maybe Double #

MaybeVariance LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

maybeVariance :: LaplaceDistribution -> Maybe Double #

maybeStdDev :: LaplaceDistribution -> Maybe Double #

Mean LaplaceDistribution # 
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Defined in Statistics.Distribution.Laplace

Methods

mean :: LaplaceDistribution -> Double #

Variance LaplaceDistribution # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

variance :: LaplaceDistribution -> Double #

stdDev :: LaplaceDistribution -> Double #

FromSample LaplaceDistribution Double #

Create Laplace distribution from sample. The location is estimated as the median of the sample, and the scale as the mean absolute deviation of the median.

Instance details

Defined in Statistics.Distribution.Laplace

Methods

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

type Rep LaplaceDistribution # 
Instance details

Defined in Statistics.Distribution.Laplace

type Rep LaplaceDistribution = D1 ('MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.16.2.1-98mJfW1HOHt8aIUJHLREex" '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 #

Arguments

:: Double

Location

-> Double

Scale

-> LaplaceDistribution 

Create an Laplace distribution.

laplaceE #

Arguments

:: Double

Location

-> Double

Scale

-> Maybe LaplaceDistribution 

Create an Laplace distribution.

Accessors

ldLocation :: LaplaceDistribution -> Double #

Location.

ldScale :: LaplaceDistribution -> Double #

Scale.