statistics-0.15.0.0: A library of statistical types, data, and functions

Copyright(c) 2009 Bryan O'Sullivan
LicenseBSD3
Maintainerbos@serpentine.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

Statistics.Sample.KernelDensity.Simple

Contents

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

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 
Instances
Eq Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Methods

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

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

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 #

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 Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Show Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Generic Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Associated Types

type Rep Points :: * -> * #

Methods

from :: Points -> Rep Points x #

to :: Rep Points x -> Points #

ToJSON Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

FromJSON Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Binary Points Source # 
Instance details

Defined in Statistics.Sample.KernelDensity.Simple

Methods

put :: Points -> Put #

get :: Get Points #

putList :: [Points] -> Put #

type Rep Points Source # 
Instance details

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 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.orgarticle/RSA_1977__25_3_5_0.pdf>