Copyright	(c) 2015 Mihai Maruseac
License	BSD3
Maintainer	mihai.maruseac@maruseac.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Statistics.Distribution.Laplace

Contents

Constructors
Accessors

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

data LaplaceDistribution
laplace :: Double -> Double -> LaplaceDistribution
laplaceE :: Double -> Double -> Maybe LaplaceDistribution
ldLocation :: LaplaceDistribution -> Double
ldScale :: LaplaceDistribution -> Double

Documentation

data LaplaceDistribution Source #

Instances

Instances details

FromJSON LaplaceDistribution Source #
Instance details Defined in Statistics.Distribution.Laplace Methods parseJSON :: Value -> Parser LaplaceDistribution Source # parseJSONList :: Value -> Parser [LaplaceDistribution] Source #
ToJSON LaplaceDistribution Source #
Instance details Defined in Statistics.Distribution.Laplace Methods toJSON :: LaplaceDistribution -> Value Source # toEncoding :: LaplaceDistribution -> Encoding Source # toJSONList :: [LaplaceDistribution] -> Value Source # toEncodingList :: [LaplaceDistribution] -> Encoding Source #
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 :: Type -> Type # Methods from :: LaplaceDistribution -> Rep LaplaceDistribution x # to :: Rep LaplaceDistribution x -> LaplaceDistribution #
Read LaplaceDistribution Source #
Instance details Defined in Statistics.Distribution.Laplace Methods readsPrec :: Int -> ReadS LaplaceDistribution # readList :: ReadS [LaplaceDistribution] # readPrec :: ReadPrec LaplaceDistribution # readListPrec :: ReadPrec [LaplaceDistribution] #
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 Methods put :: LaplaceDistribution -> Put # get :: Get LaplaceDistribution # putList :: [LaplaceDistribution] -> Put #
Eq LaplaceDistribution Source #
Instance details Defined in Statistics.Distribution.Laplace Methods (==) :: LaplaceDistribution -> LaplaceDistribution -> Bool # (/=) :: LaplaceDistribution -> LaplaceDistribution -> Bool #
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 Methods variance :: LaplaceDistribution -> Double Source # stdDev :: LaplaceDistribution -> Double Source #
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-CZx41IRMcmf3DlPKOW81PQ" '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.