statistics-0.13.3.0: A library of statistical types, data, and functions

Statistics.Sample.KernelDensity.Simple

Description

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

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.

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 FieldsfromPoints :: Vector Double

Instances

 Source # Methods(==) :: Points -> Points -> Bool #(/=) :: Points -> Points -> Bool # Source # Methodsgfoldl :: (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 #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 # Source # Methods Source # MethodsshowsPrec :: Int -> Points -> ShowS #showList :: [Points] -> ShowS # Source # Associated Typestype Rep Points :: * -> * # Methodsfrom :: Points -> Rep Points x #to :: Rep Points x -> Points # Source # Methods Source # Methods Source # Methodsput :: Points -> Put #putList :: [Points] -> Put # type Rep Points Source # type Rep Points = D1 (MetaData "Points" "Statistics.Sample.KernelDensity.Simple" "statistics-0.13.3.0-4cjYwUsSjEQGDMfnb5oeqe" True) (C1 (MetaCons "Points" PrefixI True) (S1 (MetaSel (Just Symbol "fromPoints") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector Double))))

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

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.

Bandwidth estimator for an Epanechnikov kernel.

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

Epanechnikov kernel for probability density function estimation.

Gaussian kernel for probability density function estimation.

## Low-level estimation

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.

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>