statistics-0.3.1: A library of statistical types, data, and functions

Portability portable experimental bos@serpentine.com

Statistics.KernelDensity

Description

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

Synopsis

Simple entry points

Arguments

 :: Int Number of points at which to estimate -> Sample -> (Points, UArr 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

 :: Int Number of points at which to estimate -> Sample -> (Points, UArr 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 :: UArr Double

Instances

 Eq Points Show Points

Arguments

 :: Int Number of points to select, n -> Double Sample bandwidth, h -> Sample 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 :: (Double -> Bandwidth) -> Sample -> BandwidthSource

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

Bandwidth estimator for an Epanechnikov kernel.

Bandwidth estimator for a Gaussian kernel.

Kernels

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

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

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

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

Arguments

 :: (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 -> Sample Sample data -> (Points, UArr Double)

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