statistics-0.16.2.0: A library of statistical types, data, and functions
Copyright(c) 2020 Ximin Luo
LicenseBSD3
Maintainerinfinity0@pwned.gg
Stabilityexperimental
Portabilityportable
Safe HaskellSafe-Inferred
LanguageHaskell2010

Statistics.Distribution.Weibull

Contents

Description

The Weibull distribution. This is a continuous probability distribution that describes the occurrence of a single event whose probability changes over time, controlled by the shape parameter.

Synopsis

Documentation

data WeibullDistribution Source #

The Weibull distribution.

Instances

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FromJSON WeibullDistribution Source # 
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ToJSON WeibullDistribution Source # 
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Data WeibullDistribution Source # 
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Methods

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

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

toConstr :: WeibullDistribution -> Constr #

dataTypeOf :: WeibullDistribution -> DataType #

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

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

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

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

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

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

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

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

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

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

Generic WeibullDistribution Source # 
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Defined in Statistics.Distribution.Weibull

Associated Types

type Rep WeibullDistribution :: Type -> Type #

Read WeibullDistribution Source # 
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Show WeibullDistribution Source # 
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Binary WeibullDistribution Source # 
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Eq WeibullDistribution Source # 
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ContDistr WeibullDistribution Source # 
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ContGen WeibullDistribution Source # 
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Distribution WeibullDistribution Source # 
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Entropy WeibullDistribution Source # 
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MaybeEntropy WeibullDistribution Source # 
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MaybeMean WeibullDistribution Source # 
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MaybeVariance WeibullDistribution Source # 
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Mean WeibullDistribution Source # 
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Variance WeibullDistribution Source # 
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FromSample WeibullDistribution Double Source #

Uses an approximation based on the mean and standard deviation in weibullDistrEstMeanStddevErr, with standard deviation estimated using maximum likelihood method (unbiased estimation).

Returns Nothing if sample contains less than one element or variance is zero (all elements are equal), or if the estimated mean and standard-deviation lies outside the range for which the approximation is accurate.

Instance details

Defined in Statistics.Distribution.Weibull

type Rep WeibullDistribution Source # 
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Defined in Statistics.Distribution.Weibull

type Rep WeibullDistribution = D1 ('MetaData "WeibullDistribution" "Statistics.Distribution.Weibull" "statistics-0.16.2.0-Iazw6pxXVUYHaurUiPE2b2" 'False) (C1 ('MetaCons "WD" 'PrefixI 'True) (S1 ('MetaSel ('Just "wdShape") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double) :*: S1 ('MetaSel ('Just "wdLambda") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Double)))

Constructors

weibullDistr Source #

Arguments

:: Double

Shape

-> Double

Lambda (scale)

-> WeibullDistribution 

Create Weibull distribution from parameters.

If the shape (first) parameter is 1.0, the distribution is equivalent to a ExponentialDistribution with parameter 1 / lambda the scale (second) parameter.

weibullDistrErr Source #

Arguments

:: Double

Shape

-> Double

Lambda (scale)

-> Either String WeibullDistribution 

Create Weibull distribution from parameters.

If the shape (first) parameter is 1.0, the distribution is equivalent to a ExponentialDistribution with parameter 1 / lambda the scale (second) parameter.

weibullStandard :: Double -> WeibullDistribution Source #

Standard Weibull distribution with scale factor (lambda) 1.

weibullDistrApproxMeanStddevErr Source #

Arguments

:: Double

Mean

-> Double

Stddev

-> Either String WeibullDistribution 

Create Weibull distribution from mean and standard deviation.

The algorithm is from "Methods for Estimating Wind Speed Frequency Distributions", C. G. Justus, W. R. Hargreaves, A. Mikhail, D. Graber, 1977. Given the identity:

\[ (\frac{\sigma}{\mu})^2 = \frac{\Gamma(1+2/k)}{\Gamma(1+1/k)^2} - 1 \]

\(k\) can be approximated by

\[ k \approx (\frac{\sigma}{\mu})^{-1.086} \]

\(\lambda\) is then calculated straightforwardly via the identity

\[ \lambda = \frac{\mu}{\Gamma(1+1/k)} \]

Numerically speaking, the approximation for \(k\) is accurate only within a certain range. We arbitrarily pick the range \(0.033 \le \frac{\sigma}{\mu} \le 1.45\) where it is good to ~6%, and will refuse to create a distribution outside of this range. The paper does not cover these details but it is straightforward to check them numerically.