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

Statistics.Sample.KernelDensity.Simple

Contents

Simple entry points
Building blocks
References

Description

Deprecated: Use Statistics.Sample.KernelDensity instead.

Kernel density estimation code, providing non-parametric ways to estimate the probability density function of a sample.

The techniques used by functions in this module are relatively fast, but they generally give inferior results to the KDE function in the main KernelDensity module (due to the oversmoothing documented for bandwidth below).

Synopsis

epanechnikovPDF :: Vector v Double => Int -> v Double -> ( Points , Vector Double )
gaussianPDF :: Vector v Double => Int -> v Double -> ( Points , Vector Double )
newtype Points = Points {
- fromPoints :: Vector Double
}
choosePoints :: Vector v Double => Int -> Double -> v Double -> Points
type Bandwidth = Double
bandwidth :: Vector v Double => ( Double -> Bandwidth ) -> v Double -> Bandwidth
epanechnikovBW :: Double -> Bandwidth
gaussianBW :: Double -> Bandwidth
type Kernel = Double -> Double -> Double -> Double -> Double
epanechnikovKernel :: Kernel
gaussianKernel :: Kernel
estimatePDF :: Vector v Double => Kernel -> Bandwidth -> v Double -> Points -> Vector Double
simplePDF :: Vector v Double => ( Double -> Double ) -> Kernel -> Double -> Int -> v Double -> ( Points , Vector Double )

Simple entry points

epanechnikovPDF Source #

Arguments

:: Vector v Double
=> Int	Number of points at which to estimate
-> v Double	Data sample
-> ( Points , Vector Double )

Simple Epanechnikov kernel density estimator. Returns the uniformly spaced points from the sample range at which the density function was estimated, and the estimates at those points.

gaussianPDF Source #

Arguments

:: Vector v Double
=> Int	Number of points at which to estimate
-> v Double	Data sample
-> ( Points , Vector Double )

Simple Gaussian kernel density estimator. Returns the uniformly spaced points from the sample range at which the density function was estimated, and the estimates at those points.

Building blocks

Choosing points from a sample

newtype Points Source #

Points from the range of a Sample .

Constructors

Points
Fields fromPoints :: Vector Double

Instances

Instances details

Eq Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods (==) :: Points -> Points -> Bool Source # (/=) :: Points -> Points -> Bool Source #
Data Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Points -> c Points Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c Points Source # toConstr :: Points -> Constr Source # dataTypeOf :: Points -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c Points ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c Points ) Source # gmapT :: ( forall b. Data b => b -> b) -> Points -> Points Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Points -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Points -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Points -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Points -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Points -> m Points Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Points -> m Points Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Points -> m Points Source #
Read Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods readsPrec :: Int -> ReadS Points Source # readList :: ReadS [ Points ] Source # readPrec :: ReadPrec Points Source # readListPrec :: ReadPrec [ Points ] Source #
Show Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods showsPrec :: Int -> Points -> ShowS Source # show :: Points -> String Source # showList :: [ Points ] -> ShowS Source #
Generic Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Associated Types type Rep Points :: Type -> Type Source # Methods from :: Points -> Rep Points x Source # to :: Rep Points x -> Points Source #
ToJSON Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods toJSON :: Points -> Value Source # toEncoding :: Points -> Encoding Source # toJSONList :: [ Points ] -> Value Source # toEncodingList :: [ Points ] -> Encoding Source #
FromJSON Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods parseJSON :: Value -> Parser Points Source # parseJSONList :: Value -> Parser [ Points ] Source #
Binary Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple Methods put :: Points -> Put Source # get :: Get Points Source # putList :: [ Points ] -> Put Source #
type Rep Points Source #
Instance details Defined in Statistics.Sample.KernelDensity.Simple type Rep Points = D1 (' MetaData "Points" "Statistics.Sample.KernelDensity.Simple" "statistics-0.16.1.2-IkOne9g3oJ1vhHVSRLPUO" ' True ) ( C1 (' MetaCons "Points" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "fromPoints") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 ( Vector Double ))))

choosePoints Source #

Arguments

:: Vector v Double
=> Int	Number of points to select, n
-> Double	Sample bandwidth, h
-> v Double	Input data
-> Points

Choose a uniform range of points at which to estimate a sample's probability density function.

If you are using a Gaussian kernel, multiply the sample's bandwidth by 3 before passing it to this function.

If this function is passed an empty vector, it returns values of positive and negative infinity.

Bandwidth estimation

type Bandwidth = Double Source #

The width of the convolution kernel used.

bandwidth :: Vector v Double => ( Double -> Bandwidth ) -> v Double -> Bandwidth Source #

Compute the optimal bandwidth from the observed data for the given kernel.

This function uses an estimate based on the standard deviation of a sample (due to Deheuvels), which performs reasonably well for unimodal distributions but leads to oversmoothing for more complex ones.

epanechnikovBW :: Double -> Bandwidth Source #

Bandwidth estimator for an Epanechnikov kernel.

gaussianBW :: Double -> Bandwidth Source #

Bandwidth estimator for a Gaussian kernel.

Kernels

type Kernel = Double -> Double -> Double -> Double -> Double Source #

The convolution kernel. Its parameters are as follows:

Scaling factor, 1/ nh
Bandwidth, h
A point at which to sample the input, p
One sample value, v

epanechnikovKernel :: Kernel Source #

Epanechnikov kernel for probability density function estimation.

gaussianKernel :: Kernel Source #

Gaussian kernel for probability density function estimation.

Low-level estimation

estimatePDF Source #

Arguments

:: Vector v Double
=> Kernel	Kernel function
-> Bandwidth	Bandwidth, h
-> v Double	Sample data
-> Points	Points at which to estimate
-> Vector Double

Kernel density estimator, providing a non-parametric way of estimating the PDF of a random variable.

simplePDF Source #

Arguments

:: Vector v Double
=> ( Double -> Double )	Bandwidth function
-> Kernel	Kernel function
-> Double	Bandwidth scaling factor (3 for a Gaussian kernel, 1 for all others)
-> Int	Number of points at which to estimate
-> v Double	sample data
-> ( Points , Vector Double )

A helper for creating a simple kernel density estimation function with automatically chosen bandwidth and estimation points.

References

Deheuvels, P. (1977) Estimation non paramétrique de la densité par histogrammes généralisés. Mhttp:/ archive.numdam.org article/RSA_1977__25_3_5_0.pdf>