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 #

Instances

Eq LaplaceDistribution #
Methods (==) :: LaplaceDistribution -> LaplaceDistribution -> Bool # (/=) :: LaplaceDistribution -> LaplaceDistribution -> Bool #
Data LaplaceDistribution #
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 #
Methods readsPrec :: Int -> ReadS LaplaceDistribution # readList :: ReadS [LaplaceDistribution] # readPrec :: ReadPrec LaplaceDistribution # readListPrec :: ReadPrec [LaplaceDistribution] #
Show LaplaceDistribution #
Methods showsPrec :: Int -> LaplaceDistribution -> ShowS # show :: LaplaceDistribution -> String # showList :: [LaplaceDistribution] -> ShowS #
Generic LaplaceDistribution #
Associated Types type Rep LaplaceDistribution :: * -> * # Methods from :: LaplaceDistribution -> Rep LaplaceDistribution x # to :: Rep LaplaceDistribution x -> LaplaceDistribution #
ToJSON LaplaceDistribution #
Methods toJSON :: LaplaceDistribution -> Value # toEncoding :: LaplaceDistribution -> Encoding # toJSONList :: [LaplaceDistribution] -> Value # toEncodingList :: [LaplaceDistribution] -> Encoding #
FromJSON LaplaceDistribution #
Methods parseJSON :: Value -> Parser LaplaceDistribution # parseJSONList :: Value -> Parser [LaplaceDistribution] #
Binary LaplaceDistribution #
Methods put :: LaplaceDistribution -> Put # get :: Get LaplaceDistribution # putList :: [LaplaceDistribution] -> Put #
ContGen LaplaceDistribution #
Methods genContVar :: PrimMonad m => LaplaceDistribution -> Gen (PrimState m) -> m Double #
Entropy LaplaceDistribution #
Methods entropy :: LaplaceDistribution -> Double #
MaybeEntropy LaplaceDistribution #
Methods maybeEntropy :: LaplaceDistribution -> Maybe Double #
Variance LaplaceDistribution #
Methods variance :: LaplaceDistribution -> Double # stdDev :: LaplaceDistribution -> Double #
MaybeVariance LaplaceDistribution #
Methods maybeVariance :: LaplaceDistribution -> Maybe Double # maybeStdDev :: LaplaceDistribution -> Maybe Double #
Mean LaplaceDistribution #
Methods mean :: LaplaceDistribution -> Double #
MaybeMean LaplaceDistribution #
Methods maybeMean :: LaplaceDistribution -> Maybe Double #
ContDistr LaplaceDistribution #
Methods density :: LaplaceDistribution -> Double -> Double # quantile :: LaplaceDistribution -> Double -> Double # logDensity :: LaplaceDistribution -> Double -> Double #
Distribution LaplaceDistribution #
Methods cumulative :: LaplaceDistribution -> Double -> Double # complCumulative :: LaplaceDistribution -> Double -> Double #
type Rep LaplaceDistribution #
type Rep LaplaceDistribution = D1 (MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.13.3.0-5G6LnnwwEAsBXhZQyOoIJ5" 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 #

Arguments

:: Double	Location
-> Double	Scale
-> LaplaceDistribution

Create an Laplace distribution.

laplaceFromSample :: Sample -> LaplaceDistribution #

Create Laplace distribution from sample. No tests are made to check whether it truly is Laplace. Location of distribution estimated as median of sample.

Accessors

ldLocation :: LaplaceDistribution -> Double #

Location.

ldScale :: LaplaceDistribution -> Double #

Scale.