statistics-0.16.1.2: 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

Description

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

It doesn't have mean and variance.

Synopsis

Documentation

data CauchyDistribution Source #

Cauchy-Lorentz distribution.

Instances

Instances details
Eq CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

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

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

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 #

Generic CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Associated Types

type Rep CauchyDistribution :: Type -> Type Source #

Methods

from :: CauchyDistribution -> Rep CauchyDistribution x Source #

to :: Rep CauchyDistribution x -> 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 #

FromJSON CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

parseJSON :: Value -> Parser CauchyDistribution Source #

parseJSONList :: Value -> Parser [ CauchyDistribution ] Source #

Binary CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

put :: CauchyDistribution -> Put Source #

get :: Get CauchyDistribution Source #

putList :: [ CauchyDistribution ] -> Put Source #

ContGen CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

genContVar :: StatefulGen g m => CauchyDistribution -> g -> m 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 #

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 #

Distribution CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

Methods

cumulative :: CauchyDistribution -> Double -> Double Source #

complCumulative :: CauchyDistribution -> Double -> Double Source #

type Rep CauchyDistribution Source #
Instance details

Defined in Statistics.Distribution.CauchyLorentz

type Rep CauchyDistribution = D1 (' MetaData "CauchyDistribution" "Statistics.Distribution.CauchyLorentz" "statistics-0.16.1.2-IkOne9g3oJ1vhHVSRLPUO" ' 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