statistics-0.13.3.0: A library of statistical types, data, and functions

Copyright | (c) 2011 Aleksey Khudyakov
License | BSD3
Maintainer | bos@serpentine.com
Stability | experimental
Portability | portable
Safe Haskell | None
Language | Haskell98

Statistics.Distribution.CauchyLorentz

Contents

- Constructors

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
- standardCauchy :: CauchyDistribution

# Documentation

data CauchyDistribution Source #

Cauchy-Lorentz distribution.

Instances

Eq CauchyDistribution Source # |
Methods (==) :: CauchyDistribution -> CauchyDistribution -> Bool # (/=) :: CauchyDistribution -> CauchyDistribution -> Bool #
Data CauchyDistribution Source # |

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 # |
Methods readsPrec :: Int -> ReadS CauchyDistribution # readList :: ReadS [CauchyDistribution] # readPrec :: ReadPrec CauchyDistribution # readListPrec :: ReadPrec [CauchyDistribution] #
Show CauchyDistribution Source # |
Methods showsPrec :: Int -> CauchyDistribution -> ShowS # show :: CauchyDistribution -> String # showList :: [CauchyDistribution] -> ShowS #
Generic CauchyDistribution Source # |
Associated Types type Rep CauchyDistribution :: * -> * # Methods from :: CauchyDistribution -> Rep CauchyDistribution x # to :: Rep CauchyDistribution x -> CauchyDistribution #
ToJSON CauchyDistribution Source # |
Methods toJSON :: CauchyDistribution -> Value # toEncoding :: CauchyDistribution -> Encoding # toJSONList :: [CauchyDistribution] -> Value # toEncodingList :: [CauchyDistribution] -> Encoding #
FromJSON CauchyDistribution Source # |
Methods parseJSON :: Value -> Parser CauchyDistribution # parseJSONList :: Value -> Parser [CauchyDistribution] #
Binary CauchyDistribution Source # |
Methods put :: CauchyDistribution -> Put # get :: Get CauchyDistribution # putList :: [CauchyDistribution] -> Put #
ContGen CauchyDistribution Source # |
Methods genContVar :: PrimMonad m => CauchyDistribution -> Gen (PrimState m) -> m Double Source #
Entropy CauchyDistribution Source # |
Methods entropy :: CauchyDistribution -> Double Source #
MaybeEntropy CauchyDistribution Source # |
Methods maybeEntropy :: CauchyDistribution -> Maybe Double Source #
ContDistr CauchyDistribution Source # |
Methods density :: CauchyDistribution -> Double -> Double Source # quantile :: CauchyDistribution -> Double -> Double Source # logDensity :: CauchyDistribution -> Double -> Double Source #
Distribution CauchyDistribution Source # |
Methods cumulative :: CauchyDistribution -> Double -> Double Source # complCumulative :: CauchyDistribution -> Double -> Double Source #
type Rep CauchyDistribution Source # |

type Rep CauchyDistribution = D1 (MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.13.3.0-Fvkducafmyw9ljEnBhS6Nm" 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 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

standardCauchy :: CauchyDistribution Source #