| Copyright | (c) 2011 Aleksey Khudyakov |
|---|---|
| License | BSD3 |
| Maintainer | bos@serpentine.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell2010 |
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
- data CauchyDistribution
- cauchyDistribMedian :: CauchyDistribution -> Double
- cauchyDistribScale :: CauchyDistribution -> Double
- cauchyDistribution :: Double -> Double -> CauchyDistribution
- cauchyDistributionE :: Double -> Double -> Maybe CauchyDistribution
- standardCauchy :: CauchyDistribution
Documentation
data CauchyDistribution Source #
Cauchy-Lorentz distribution.
Instances
| FromJSON CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods parseJSON :: Value -> Parser CauchyDistribution parseJSONList :: Value -> Parser [CauchyDistribution] omittedField :: Maybe CauchyDistribution | |||||
| ToJSON CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods toJSON :: CauchyDistribution -> Value toEncoding :: CauchyDistribution -> Encoding toJSONList :: [CauchyDistribution] -> Value toEncodingList :: [CauchyDistribution] -> Encoding omitField :: CauchyDistribution -> Bool | |||||
| Binary CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods put :: CauchyDistribution -> Put get :: Get CauchyDistribution putList :: [CauchyDistribution] -> Put | |||||
| Data CauchyDistribution Source # | |||||
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 :: forall r r'. (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 | |||||
| Generic CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Associated Types
Methods from :: CauchyDistribution -> Rep CauchyDistribution x to :: Rep CauchyDistribution x -> CauchyDistribution | |||||
| Read CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods readsPrec :: Int -> ReadS CauchyDistribution readList :: ReadS [CauchyDistribution] readPrec :: ReadPrec CauchyDistribution readListPrec :: ReadPrec [CauchyDistribution] | |||||
| Show CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods showsPrec :: Int -> CauchyDistribution -> ShowS show :: CauchyDistribution -> String showList :: [CauchyDistribution] -> ShowS | |||||
| Eq CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods (==) :: CauchyDistribution -> CauchyDistribution -> Bool (/=) :: CauchyDistribution -> CauchyDistribution -> Bool | |||||
| ContDistr CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods density :: CauchyDistribution -> Double -> Double Source # logDensity :: CauchyDistribution -> Double -> Double Source # quantile :: CauchyDistribution -> Double -> Double Source # complQuantile :: CauchyDistribution -> Double -> Double Source # | |||||
| ContGen CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods genContVar :: StatefulGen g m => CauchyDistribution -> g -> m Double Source # | |||||
| Distribution CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods cumulative :: CauchyDistribution -> Double -> Double Source # complCumulative :: CauchyDistribution -> Double -> Double Source # | |||||
| Entropy CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods entropy :: CauchyDistribution -> Double Source # | |||||
| MaybeEntropy CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz Methods maybeEntropy :: CauchyDistribution -> Maybe Double Source # | |||||
| type Rep CauchyDistribution Source # | |||||
Defined in Statistics.Distribution.CauchyLorentz type Rep CauchyDistribution = D1 ('MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.16.5.0-CUpwRr22xOC5RMvoidvha8" '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
Arguments
| :: Double | Central point |
| -> Double | Scale parameter (FWHM) |
| -> CauchyDistribution |
Cauchy distribution
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