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 HaskellNone
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 Source #

Instances

Instances details
FromJSON LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

ToJSON 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 :: 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 Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Associated Types

type Rep LaplaceDistribution 
Instance details

Defined in Statistics.Distribution.Laplace

type Rep LaplaceDistribution = D1 ('MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.16.2.1-GC0UmpORwJ8SU4BdSiJEf" 'False) (C1 ('MetaCons "LD" 'PrefixI 'True) (S1 ('MetaSel ('Just "ldLocation") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "ldScale") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double)))
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

Binary LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Eq LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

ContDistr LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

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

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

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

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

ContGen LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

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

Distribution LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

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

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

Entropy LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

entropy :: LaplaceDistribution -> Double Source #

MaybeEntropy LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

maybeEntropy :: LaplaceDistribution -> Maybe Double Source #

MaybeMean LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

maybeMean :: LaplaceDistribution -> Maybe Double Source #

MaybeVariance LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

maybeVariance :: LaplaceDistribution -> Maybe Double Source #

maybeStdDev :: LaplaceDistribution -> Maybe Double Source #

Mean LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

Methods

mean :: LaplaceDistribution -> Double Source #

Variance LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

FromSample LaplaceDistribution Double Source #

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 Source #

type Rep LaplaceDistribution Source # 
Instance details

Defined in Statistics.Distribution.Laplace

type Rep LaplaceDistribution = D1 ('MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.16.2.1-GC0UmpORwJ8SU4BdSiJEf" '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.