statistics-0.14.0.0: A library of statistical types, data, and functions

Statistics.Sample.KernelDensity

Contents

Description

Kernel density estimation. This module provides a fast, robust, non-parametric way to estimate the probability density function of a sample.

This estimator does not use the commonly employed "Gaussian rule of thumb". As a result, it outperforms many plug-in methods on multimodal samples with widely separated modes.

Synopsis

# Estimation functions

Arguments

 :: (Vector v CD, Vector v Double, Vector v Int) => Int The number of mesh points to use in the uniform discretization of the interval (min,max). If this value is not a power of two, then it is rounded up to the next power of two. -> v Double -> (v Double, v Double)

Gaussian kernel density estimator for one-dimensional data, using the method of Botev et al.

The result is a pair of vectors, containing:

• The coordinates of each mesh point. The mesh interval is chosen to be 20% larger than the range of the sample. (To specify the mesh interval, use kde_.)
• Density estimates at each mesh point.

Arguments

 :: (Vector v CD, Vector v Double, Vector v Int) => Int The number of mesh points to use in the uniform discretization of the interval (min,max). If this value is not a power of two, then it is rounded up to the next power of two. -> Double Lower bound (min) of the mesh range. -> Double Upper bound (max) of the mesh range. -> v Double -> (v Double, v Double)

Gaussian kernel density estimator for one-dimensional data, using the method of Botev et al.

The result is a pair of vectors, containing:

• The coordinates of each mesh point.
• Density estimates at each mesh point.

# References

Botev. Z.I., Grotowski J.F., Kroese D.P. (2010). Kernel density estimation via diffusion. Annals of Statistics 38(5):2916–2957. http://arxiv.org/pdf/1011.2602