Copyright	(c) 2015 Mihai Maruseac
License	BSD3
Maintainer	mihai.maruseac@maruseac.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

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 #

Instances

Eq LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods (==) :: LaplaceDistribution -> LaplaceDistribution -> Bool # (/=) :: LaplaceDistribution -> LaplaceDistribution -> Bool #
Data LaplaceDistribution #
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 #
Instance details Defined in Statistics.Distribution.Laplace Methods readsPrec :: Int -> ReadS LaplaceDistribution # readList :: ReadS [LaplaceDistribution] # readPrec :: ReadPrec LaplaceDistribution # readListPrec :: ReadPrec [LaplaceDistribution] #
Show LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods showsPrec :: Int -> LaplaceDistribution -> ShowS # show :: LaplaceDistribution -> String # showList :: [LaplaceDistribution] -> ShowS #
Generic LaplaceDistribution #
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 #
ToJSON LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods toJSON :: LaplaceDistribution -> Value # toEncoding :: LaplaceDistribution -> Encoding # toJSONList :: [LaplaceDistribution] -> Value # toEncodingList :: [LaplaceDistribution] -> Encoding #
FromJSON LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods parseJSON :: Value -> Parser LaplaceDistribution # parseJSONList :: Value -> Parser [LaplaceDistribution] #
Binary LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods put :: LaplaceDistribution -> Put # get :: Get LaplaceDistribution # putList :: [LaplaceDistribution] -> Put #
ContGen LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods genContVar :: PrimMonad m => LaplaceDistribution -> Gen (PrimState m) -> m Double #
Entropy LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods entropy :: LaplaceDistribution -> Double #
MaybeEntropy LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods maybeEntropy :: LaplaceDistribution -> Maybe Double #
Variance LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods variance :: LaplaceDistribution -> Double # stdDev :: LaplaceDistribution -> Double #
MaybeVariance LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods maybeVariance :: LaplaceDistribution -> Maybe Double # maybeStdDev :: LaplaceDistribution -> Maybe Double #
Mean LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods mean :: LaplaceDistribution -> Double #
MaybeMean LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods maybeMean :: LaplaceDistribution -> Maybe Double #
ContDistr LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods density :: LaplaceDistribution -> Double -> Double # quantile :: LaplaceDistribution -> Double -> Double # complQuantile :: LaplaceDistribution -> Double -> Double # logDensity :: LaplaceDistribution -> Double -> Double #
Distribution LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace Methods cumulative :: LaplaceDistribution -> Double -> Double # complCumulative :: LaplaceDistribution -> Double -> Double #
FromSample LaplaceDistribution Double #	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 #
type Rep LaplaceDistribution #
Instance details Defined in Statistics.Distribution.Laplace type Rep LaplaceDistribution = D1 (MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.15.0.0-KYJLg9h4jsl1bBm8KLc3A8" 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.