statistics-0.14.0.2: A library of statistical types, data, and functions

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.

# Documentation

Cauchy-Lorentz distribution.

Instances

 Source # Methods Source # Methodsgfoldl :: (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 #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 # Source # Methods Source # MethodsshowList :: [CauchyDistribution] -> ShowS # Source # Associated Typestype Rep CauchyDistribution :: * -> * # Methods Source # Methods Source # Methods Source # MethodsputList :: [CauchyDistribution] -> Put # Source # MethodsgenContVar :: PrimMonad m => CauchyDistribution -> Gen (PrimState m) -> m Double Source # Source # Methods Source # Methods Source # Methods Source # Methods Source # type Rep CauchyDistribution = D1 (MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.14.0.2-9wDz1lVU92ZDJSrAe5uHzb" 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))))

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

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

# Constructors

Arguments

 :: Double Central point -> Double Scale parameter (FWHM) -> CauchyDistribution

Cauchy distribution

Arguments

 :: Double Central point -> Double Scale parameter (FWHM) -> Maybe CauchyDistribution

Cauchy distribution

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