statistics-0.13.3.0: 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 #

Cauchy-Lorentz distribution.

Instances

Eq CauchyDistribution # 
Data CauchyDistribution # 

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 # 
Show CauchyDistribution # 
Generic CauchyDistribution # 
ToJSON CauchyDistribution # 
FromJSON CauchyDistribution # 
Binary CauchyDistribution # 
ContGen CauchyDistribution # 
Entropy CauchyDistribution # 
MaybeEntropy CauchyDistribution # 
ContDistr CauchyDistribution # 
Distribution CauchyDistribution # 
type Rep CauchyDistribution # 
type Rep CauchyDistribution = D1 (MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.13.3.0-5G6LnnwwEAsBXhZQyOoIJ5" False) (C1 (MetaCons "CD" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "cauchyDistribMedian") SourceUnpack SourceStrict DecidedUnpack) (Rec0 Double)) (S1 (MetaSel (Just Symbol "cauchyDistribScale") SourceUnpack SourceStrict DecidedUnpack) (Rec0 Double))))

cauchyDistribMedian :: CauchyDistribution -> Double #

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 #

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

Constructors

cauchyDistribution #

Arguments

:: Double

Central point

-> Double

Scale parameter (FWHM)

-> CauchyDistribution 

Cauchy distribution