Statistics.Distribution.CauchyLorentz

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

It doesn't have mean and variance.

Documentation

data CauchyDistribution

Cauchy-Lorentz distribution.

Instances

Eq CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

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

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

Data CauchyDistribution

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

Defined in Statistics.Distribution.CauchyLorentz

Methods

readsPrec :: Int -> ReadS CauchyDistribution

readList :: ReadS [CauchyDistribution]

readPrec :: ReadPrec CauchyDistribution

readListPrec :: ReadPrec [CauchyDistribution]

Show CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

showsPrec :: Int -> CauchyDistribution -> ShowS

show :: CauchyDistribution -> String

showList :: [CauchyDistribution] -> ShowS

Generic CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Associated Types

type Rep CauchyDistribution :: Type -> Type

Methods

from :: CauchyDistribution -> Rep CauchyDistribution x

to :: Rep CauchyDistribution x -> CauchyDistribution

ToJSON CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

toJSON :: CauchyDistribution -> Value

toEncoding :: CauchyDistribution -> Encoding

toJSONList :: [CauchyDistribution] -> Value

toEncodingList :: [CauchyDistribution] -> Encoding

FromJSON CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

parseJSON :: Value -> Parser CauchyDistribution

parseJSONList :: Value -> Parser [CauchyDistribution]

Binary CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

put :: CauchyDistribution -> Put

get :: Get CauchyDistribution

putList :: [CauchyDistribution] -> Put

ContGen CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

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

Entropy CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

entropy :: CauchyDistribution -> Double

MaybeEntropy CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

maybeEntropy :: CauchyDistribution -> Maybe Double

ContDistr CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

density :: CauchyDistribution -> Double -> Double

quantile :: CauchyDistribution -> Double -> Double

complQuantile :: CauchyDistribution -> Double -> Double

logDensity :: CauchyDistribution -> Double -> Double

Distribution CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

Methods

cumulative :: CauchyDistribution -> Double -> Double

complCumulative :: CauchyDistribution -> Double -> Double

type Rep CauchyDistribution

Defined in Statistics.Distribution.CauchyLorentz

type Rep CauchyDistribution = D1 (MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.15.1.1-90JrJCHkRC71X5S11QgEYW" 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

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

cauchyDistributionE

Arguments

:: Double

Central point

-> Double

Scale parameter (FWHM)

-> Maybe CauchyDistribution

Cauchy distribution

standardCauchy :: CauchyDistribution

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