statistics-0.16.4.0: 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 | Haskell2010

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
- cauchyDistributionE :: Double -> Double -> Maybe CauchyDistribution
- standardCauchy :: CauchyDistribution

# Documentation

data CauchyDistribution Source #

Cauchy-Lorentz distribution.

#### Instances

Instances details

FromJSON CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods parseJSON :: Value -> Parser CauchyDistribution Source # parseJSONList :: Value -> Parser [CauchyDistribution] Source # omittedField :: Maybe CauchyDistribution Source #
ToJSON CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods toJSON :: CauchyDistribution -> Value Source # toEncoding :: CauchyDistribution -> Encoding Source # toJSONList :: [CauchyDistribution] -> Value Source # toEncodingList :: [CauchyDistribution] -> Encoding Source # omitField :: CauchyDistribution -> Bool Source #
Binary CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods put :: CauchyDistribution -> Put Source # get :: Get CauchyDistribution Source # putList :: [CauchyDistribution] -> Put Source #
Data CauchyDistribution Source # |

Instance details

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 Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c CauchyDistribution Source #

toConstr :: CauchyDistribution -> Constr Source #

dataTypeOf :: CauchyDistribution -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c CauchyDistribution) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CauchyDistribution) Source #

gmapT :: (forall b. Data b => b -> b) -> CauchyDistribution -> CauchyDistribution Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CauchyDistribution -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CauchyDistribution -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> CauchyDistribution -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> CauchyDistribution -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CauchyDistribution -> m CauchyDistribution Source #

Generic CauchyDistribution Source # |

Instance details

Defined in Statistics.Distribution.CauchyLorentz

Associated Types

type Rep CauchyDistribution |

Instance details

Defined in Statistics.Distribution.CauchyLorentz

type Rep CauchyDistribution = D1 ('MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" 'False) (C1 ('MetaCons "CD" 'PrefixI 'True) (S1 ('MetaSel ('Just "cauchyDistribMedian") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "cauchyDistribScale") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double)))

Methods

from :: CauchyDistribution -> Rep CauchyDistribution x Source #

to :: Rep CauchyDistribution x -> CauchyDistribution Source #

Read CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods readsPrec :: Int -> ReadS CauchyDistribution Source # readList :: ReadS [CauchyDistribution] Source # readPrec :: ReadPrec CauchyDistribution Source # readListPrec :: ReadPrec [CauchyDistribution] Source #
Show CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods showsPrec :: Int -> CauchyDistribution -> ShowS Source # show :: CauchyDistribution -> String Source # showList :: [CauchyDistribution] -> ShowS Source #
Eq CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods (==) :: CauchyDistribution -> CauchyDistribution -> Bool Source # (/=) :: CauchyDistribution -> CauchyDistribution -> Bool Source #
ContDistr CauchyDistribution Source # |
Instance details 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 # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods genContVar :: StatefulGen g m => CauchyDistribution -> g -> m Double Source #
Distribution CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods cumulative :: CauchyDistribution -> Double -> Double Source # complCumulative :: CauchyDistribution -> Double -> Double Source #
Entropy CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods entropy :: CauchyDistribution -> Double Source #
MaybeEntropy CauchyDistribution Source # |
Instance details Defined in Statistics.Distribution.CauchyLorentz Methods maybeEntropy :: CauchyDistribution -> Maybe Double Source #
type Rep CauchyDistribution Source # |

Instance details

Defined in Statistics.Distribution.CauchyLorentz

type Rep CauchyDistribution = D1 ('MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" '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

cauchyDistribution Source #

Arguments

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

Cauchy distribution

cauchyDistributionE Source #

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