Statistics.Sample.KernelDensity.Simple

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).

Simple entry points

epanechnikovPDF

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

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

Points from the range of a Sample.

Constructors

Points

Fields

• fromPoints :: Vector Double

Instances

Eq Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

(==) :: Points -> Points -> Bool

(/=) :: Points -> Points -> Bool

Data Points

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

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

toConstr :: Points -> Constr

dataTypeOf :: Points -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> Points -> Points

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

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

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

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

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

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

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

Read Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

readsPrec :: Int -> ReadS Points

readList :: ReadS [Points]

readPrec :: ReadPrec Points

readListPrec :: ReadPrec [Points]

Show Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

showsPrec :: Int -> Points -> ShowS

show :: Points -> String

showList :: [Points] -> ShowS

Generic Points

Defined in Statistics.Sample.KernelDensity.Simple

Associated Types

type Rep Points :: * -> *

Methods

from :: Points -> Rep Points x

to :: Rep Points x -> Points

ToJSON Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

toJSON :: Points -> Value

toEncoding :: Points -> Encoding

toJSONList :: [Points] -> Value

toEncodingList :: [Points] -> Encoding

FromJSON Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

parseJSON :: Value -> Parser Points

parseJSONList :: Value -> Parser [Points]

Binary Points

Defined in Statistics.Sample.KernelDensity.Simple

Methods

put :: Points -> Put

get :: Get Points

putList :: [Points] -> Put

type Rep Points

Defined in Statistics.Sample.KernelDensity.Simple

type Rep Points = D1 (MetaData "Points" "Statistics.Sample.KernelDensity.Simple" "statistics-0.15.0.0-AkglZgHZAgx3cdskkvnxTn" True) (C1 (MetaCons "Points" PrefixI True) (S1 (MetaSel (Just "fromPoints") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector Double))))

choosePoints

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

The width of the convolution kernel used.

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

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

Bandwidth estimator for an Epanechnikov kernel.

gaussianBW :: Double -> Bandwidth

Bandwidth estimator for a Gaussian kernel.

Kernels

type Kernel = Double -> Double -> Double -> Double -> Double

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

Epanechnikov kernel for probability density function estimation.

gaussianKernel :: Kernel

Gaussian kernel for probability density function estimation.

Low-level estimation

estimatePDF

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

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.orgarticle/RSA_1977__25_3_5_0.pdf>