statistics-0.16.4.0: A library of statistical types, data, and functions

Copyright | (c) 2009 Bryan O'Sullivan
License | BSD3
Maintainer | bos@serpentine.com
Stability | experimental
Portability | portable
Safe Haskell | None
Language | Haskell2010

Statistics.Distribution.Normal

Contents

- Constructors

Description

The normal distribution. This is a continuous probability distribution that describes data that cluster around a mean.

Synopsis

- data NormalDistribution
- normalDistr :: Double -> Double -> NormalDistribution
- normalDistrE :: Double -> Double -> Maybe NormalDistribution
- normalDistrErr :: Double -> Double -> Either String NormalDistribution
- standard :: NormalDistribution

# Documentation

data NormalDistribution Source #

The normal distribution.

#### Instances

Instances details

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

Instance details

Defined in Statistics.Distribution.Normal

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NormalDistribution -> c NormalDistribution Source #

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

toConstr :: NormalDistribution -> Constr Source #

dataTypeOf :: NormalDistribution -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Generic NormalDistribution Source # |

Instance details

Defined in Statistics.Distribution.Normal

Associated Types

type Rep NormalDistribution |

Instance details

Defined in Statistics.Distribution.Normal

type Rep NormalDistribution = D1 ('MetaData "NormalDistribution" "Statistics.Distribution.Normal" "statistics-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" 'False) (C1 ('MetaCons "ND" 'PrefixI 'True) ((S1 ('MetaSel ('Just "mean") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "stdDev") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double)) :*: (S1 ('MetaSel ('Just "ndPdfDenom") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "ndCdfDenom") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double))))

Methods

from :: NormalDistribution -> Rep NormalDistribution x Source #

to :: Rep NormalDistribution x -> NormalDistribution Source #

Read NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods readsPrec :: Int -> ReadS NormalDistribution Source # readList :: ReadS [NormalDistribution] Source # readPrec :: ReadPrec NormalDistribution Source # readListPrec :: ReadPrec [NormalDistribution] Source #
Show NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods showsPrec :: Int -> NormalDistribution -> ShowS Source # show :: NormalDistribution -> String Source # showList :: [NormalDistribution] -> ShowS Source #
Eq NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods (==) :: NormalDistribution -> NormalDistribution -> Bool Source # (/=) :: NormalDistribution -> NormalDistribution -> Bool Source #
ContDistr NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods density :: NormalDistribution -> Double -> Double Source # logDensity :: NormalDistribution -> Double -> Double Source # quantile :: NormalDistribution -> Double -> Double Source # complQuantile :: NormalDistribution -> Double -> Double Source #
ContGen NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods genContVar :: StatefulGen g m => NormalDistribution -> g -> m Double Source #
Distribution NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods cumulative :: NormalDistribution -> Double -> Double Source # complCumulative :: NormalDistribution -> Double -> Double Source #
Entropy NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods entropy :: NormalDistribution -> Double Source #
MaybeEntropy NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods maybeEntropy :: NormalDistribution -> Maybe Double Source #
MaybeMean NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods maybeMean :: NormalDistribution -> Maybe Double Source #
MaybeVariance NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods maybeVariance :: NormalDistribution -> Maybe Double Source # maybeStdDev :: NormalDistribution -> Maybe Double Source #
Mean NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods mean :: NormalDistribution -> Double Source #
Variance NormalDistribution Source # |
Instance details Defined in Statistics.Distribution.Normal Methods variance :: NormalDistribution -> Double Source # stdDev :: NormalDistribution -> Double Source #
FromSample NormalDistribution Double Source # | Variance is estimated using maximum likelihood method (biased estimation). Returns `Nothing` if sample contains less than one element or variance is zero (all elements are equal)
Instance details Defined in Statistics.Distribution.Normal Methods fromSample :: Vector v Double => v Double -> Maybe NormalDistribution Source #
type Rep NormalDistribution Source # |

Instance details

Defined in Statistics.Distribution.Normal

type Rep NormalDistribution = D1 ('MetaData "NormalDistribution" "Statistics.Distribution.Normal" "statistics-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" 'False) (C1 ('MetaCons "ND" 'PrefixI 'True) ((S1 ('MetaSel ('Just "mean") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "stdDev") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double)) :*: (S1 ('MetaSel ('Just "ndPdfDenom") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "ndCdfDenom") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double))))

# Constructors

normalDistr Source #

Arguments

:: Double | Mean of distribution
-> Double | Standard deviation of distribution
-> NormalDistribution |

Create normal distribution from parameters.

IMPORTANT: prior to 0.10 release second parameter was variance not standard deviation.

normalDistrE Source #

Arguments

:: Double | Mean of distribution
-> Double | Standard deviation of distribution
-> Maybe NormalDistribution |

Create normal distribution from parameters.

IMPORTANT: prior to 0.10 release second parameter was variance not standard deviation.

normalDistrErr Source #

Arguments

:: Double | Mean of distribution
-> Double | Standard deviation of distribution
-> Either String NormalDistribution |

Create normal distribution from parameters.

standard :: NormalDistribution Source #

Standard normal distribution with mean equal to 0 and variance equal to 1