statistics-0.15.0.0: A library of statistical types, data, and functions

Copyright(c) 2011 Aleksey Khudyakov
LicenseBSD3
Maintainerbos@serpentine.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

Statistics.Distribution.CauchyLorentz

Contents

Description

The Cauchy-Lorentz distribution. It's also known as Lorentz distribution or Breit–Wigner distribution.

It doesn't have mean and variance.

Synopsis

Documentation

data CauchyDistribution Source #

Cauchy-Lorentz distribution.

Instances
Eq CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

(==) :: CauchyDistribution -> CauchyDistribution -> Bool #

(/=) :: CauchyDistribution -> CauchyDistribution -> Bool #

Data CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CauchyDistribution -> c CauchyDistribution #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CauchyDistribution #

toConstr :: CauchyDistribution -> Constr #

dataTypeOf :: CauchyDistribution -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CauchyDistribution) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CauchyDistribution) #

gmapT :: (forall b. Data b => b -> b) -> CauchyDistribution -> CauchyDistribution #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CauchyDistribution -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CauchyDistribution -> r #

gmapQ :: (forall d. Data d => d -> u) -> CauchyDistribution -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> CauchyDistribution -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution #

Read CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

readsPrec :: Int -> ReadS CauchyDistribution #

readList :: ReadS [CauchyDistribution] #

readPrec :: ReadPrec CauchyDistribution #

readListPrec :: ReadPrec [CauchyDistribution] #

Show CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

showsPrec :: Int -> CauchyDistribution -> ShowS #

show :: CauchyDistribution -> String #

showList :: [CauchyDistribution] -> ShowS #

Generic CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Associated Types

type Rep CauchyDistribution :: * -> * #

Methods

from :: CauchyDistribution -> Rep CauchyDistribution x #

to :: Rep CauchyDistribution x -> CauchyDistribution #

ToJSON CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

toJSON :: CauchyDistribution -> Value #

toEncoding :: CauchyDistribution -> Encoding #

toJSONList :: [CauchyDistribution] -> Value #

toEncodingList :: [CauchyDistribution] -> Encoding #

FromJSON CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

parseJSON :: Value -> Parser CauchyDistribution #

parseJSONList :: Value -> Parser [CauchyDistribution] #

Binary CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

put :: CauchyDistribution -> Put #

get :: Get CauchyDistribution #

putList :: [CauchyDistribution] -> Put #

ContGen CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

genContVar :: PrimMonad m => CauchyDistribution -> Gen (PrimState m) -> m Double Source #

Entropy CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

entropy :: CauchyDistribution -> Double Source #

MaybeEntropy CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

maybeEntropy :: CauchyDistribution -> Maybe Double Source #

ContDistr CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

density :: CauchyDistribution -> Double -> Double Source #

quantile :: CauchyDistribution -> Double -> Double Source #

complQuantile :: CauchyDistribution -> Double -> Double Source #

logDensity :: CauchyDistribution -> Double -> Double Source #

Distribution CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

cumulative :: CauchyDistribution -> Double -> Double Source #

complCumulative :: CauchyDistribution -> Double -> Double Source #

type Rep CauchyDistribution Source # 
Instance details

Defined in Statistics.Distribution.CauchyLorentz

type Rep CauchyDistribution = D1 (MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.15.0.0-AkglZgHZAgx3cdskkvnxTn" False) (C1 (MetaCons "CD" PrefixI True) (S1 (MetaSel (Just "cauchyDistribMedian") SourceUnpack SourceStrict DecidedStrict) (Rec0 Double) :*: S1 (MetaSel (Just "cauchyDistribScale") SourceUnpack SourceStrict DecidedStrict) (Rec0 Double)))

cauchyDistribMedian :: CauchyDistribution -> Double Source #

Central value of Cauchy-Lorentz distribution which is its mode and median. Distribution doesn't have mean so function is named after median.

cauchyDistribScale :: CauchyDistribution -> Double Source #

Scale parameter of Cauchy-Lorentz distribution. It's different from variance and specify half width at half maximum (HWHM).

Constructors

cauchyDistribution Source #

Arguments

:: Double

Central point

-> Double

Scale parameter (FWHM)

-> CauchyDistribution 

Cauchy distribution

cauchyDistributionE Source #

Arguments

:: Double

Central point

-> Double

Scale parameter (FWHM)

-> Maybe CauchyDistribution 

Cauchy distribution

standardCauchy :: CauchyDistribution Source #

Standard Cauchy distribution. It's centered at 0 and have 1 FWHM