Statistics.Distribution.Laplace

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)

Documentation

data LaplaceDistribution

Instances

Eq LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

(==) :: LaplaceDistribution -> LaplaceDistribution -> Bool

(/=) :: LaplaceDistribution -> LaplaceDistribution -> Bool

Data LaplaceDistribution

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

Defined in Statistics.Distribution.Laplace

Methods

readsPrec :: Int -> ReadS LaplaceDistribution

readList :: ReadS [LaplaceDistribution]

readPrec :: ReadPrec LaplaceDistribution

readListPrec :: ReadPrec [LaplaceDistribution]

Show LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

showsPrec :: Int -> LaplaceDistribution -> ShowS

show :: LaplaceDistribution -> String

showList :: [LaplaceDistribution] -> ShowS

Generic LaplaceDistribution

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

Defined in Statistics.Distribution.Laplace

Methods

toJSON :: LaplaceDistribution -> Value

toEncoding :: LaplaceDistribution -> Encoding

toJSONList :: [LaplaceDistribution] -> Value

toEncodingList :: [LaplaceDistribution] -> Encoding

FromJSON LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

parseJSON :: Value -> Parser LaplaceDistribution

parseJSONList :: Value -> Parser [LaplaceDistribution]

Binary LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

put :: LaplaceDistribution -> Put

get :: Get LaplaceDistribution

putList :: [LaplaceDistribution] -> Put

ContGen LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

genContVar :: PrimMonad m => LaplaceDistribution -> Gen (PrimState m) -> m Double

Entropy LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

entropy :: LaplaceDistribution -> Double

MaybeEntropy LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

maybeEntropy :: LaplaceDistribution -> Maybe Double

Variance LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

variance :: LaplaceDistribution -> Double

stdDev :: LaplaceDistribution -> Double

MaybeVariance LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

maybeVariance :: LaplaceDistribution -> Maybe Double

maybeStdDev :: LaplaceDistribution -> Maybe Double

Mean LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

mean :: LaplaceDistribution -> Double

MaybeMean LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

maybeMean :: LaplaceDistribution -> Maybe Double

ContDistr LaplaceDistribution

Defined in Statistics.Distribution.Laplace

Methods

density :: LaplaceDistribution -> Double -> Double

quantile :: LaplaceDistribution -> Double -> Double

complQuantile :: LaplaceDistribution -> Double -> Double

logDensity :: LaplaceDistribution -> Double -> Double

Distribution LaplaceDistribution

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.

Defined in Statistics.Distribution.Laplace

Methods

fromSample :: Vector v Double => v Double -> Maybe LaplaceDistribution

type Rep LaplaceDistribution

Defined in Statistics.Distribution.Laplace

type Rep LaplaceDistribution = D1 (MetaData "LaplaceDistribution" "Statistics.Distribution.Laplace" "statistics-0.15.2.0-FCVAYbUNN6k6ys2hOZ1wTy" 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.