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

Documentation

data LaplaceDistribution Source #

Instances

Eq LaplaceDistribution Source #
Methods (==) :: LaplaceDistribution -> LaplaceDistribution -> Bool # (/=) :: LaplaceDistribution -> LaplaceDistribution -> Bool #
Data LaplaceDistribution Source #
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 #
Methods readsPrec :: Int -> ReadS LaplaceDistribution # readList :: ReadS [LaplaceDistribution] # readPrec :: ReadPrec LaplaceDistribution # readListPrec :: ReadPrec [LaplaceDistribution] #
Show LaplaceDistribution Source #
Methods showsPrec :: Int -> LaplaceDistribution -> ShowS # show :: LaplaceDistribution -> String # showList :: [LaplaceDistribution] -> ShowS #
Generic LaplaceDistribution Source #
Associated Types type Rep LaplaceDistribution :: * -> * # Methods from :: LaplaceDistribution -> Rep LaplaceDistribution x # to :: Rep LaplaceDistribution x -> LaplaceDistribution #
ToJSON LaplaceDistribution Source #
Methods toJSON :: LaplaceDistribution -> Value # toEncoding :: LaplaceDistribution -> Encoding # toJSONList :: [LaplaceDistribution] -> Value # toEncodingList :: [LaplaceDistribution] -> Encoding #
FromJSON LaplaceDistribution Source #
Methods parseJSON :: Value -> Parser LaplaceDistribution # parseJSONList :: Value -> Parser [LaplaceDistribution] #
Binary LaplaceDistribution Source #
Methods put :: LaplaceDistribution -> Put # get :: Get LaplaceDistribution # putList :: [LaplaceDistribution] -> Put #
ContGen LaplaceDistribution Source #
Methods genContVar :: PrimMonad m => LaplaceDistribution -> Gen (PrimState m) -> m Double Source #
Entropy LaplaceDistribution Source #
Methods entropy :: LaplaceDistribution -> Double Source #
MaybeEntropy LaplaceDistribution Source #
Methods maybeEntropy :: LaplaceDistribution -> Maybe Double Source #
Variance LaplaceDistribution Source #
Methods variance :: LaplaceDistribution -> Double Source # stdDev :: LaplaceDistribution -> Double Source #
MaybeVariance LaplaceDistribution Source #
Methods maybeVariance :: LaplaceDistribution -> Maybe Double Source # maybeStdDev :: LaplaceDistribution -> Maybe Double Source #
Mean LaplaceDistribution Source #
Methods mean :: LaplaceDistribution -> Double Source #
MaybeMean LaplaceDistribution Source #
Methods maybeMean :: LaplaceDistribution -> Maybe Double Source #
ContDistr LaplaceDistribution Source #
Methods density :: LaplaceDistribution -> Double -> Double Source # quantile :: LaplaceDistribution -> Double -> Double Source # complQuantile :: LaplaceDistribution -> Double -> Double Source # logDensity :: LaplaceDistribution -> Double -> Double Source #
Distribution LaplaceDistribution Source #
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.
Methods fromSample :: Vector v Double => v Double -> Maybe LaplaceDistribution Source #
type Rep LaplaceDistribution Source #
type Rep LaplaceDistribution = D1 (MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.14.0.2-9wDz1lVU92ZDJSrAe5uHzb" False) (C1 (MetaCons "LD" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "ldLocation") SourceUnpack SourceStrict DecidedUnpack) (Rec0 Double)) (S1 (MetaSel (Just Symbol "ldScale") SourceUnpack SourceStrict DecidedUnpack) (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.