#include <kernel.h>

Inheritance diagram for EpanechnikovKernel:

Collaboration diagram for EpanechnikovKernel:

Public Member Functions
	EpanechnikovKernel (void)

	EpanechnikovKernel (double stdev)

virtual	~EpanechnikovKernel (void)

double	operator() (double x) const

virtual double	value (double x) const

virtual void	setScale (double scale)

virtual double	mean (void) const

virtual double	stdev (void) const

virtual void	setStdev (double stdev)

virtual double	max (void) const

virtual double	left (void) const

virtual double	right (void) const

Public Member Functions inherited from Kernel
	Kernel (void)

	Kernel (double stdev)

virtual	~Kernel (void)

double	operator() (double x) const

double	scale (void) const

Detailed Description

A quadratic kernel.

Author: Jan Benda

Version

1.0

$f(x) = \left\{ \begin{array}{lcl} \left( \frac{3}{4 s} \right)^{\frac{2}{3}} - \left( \frac{x}{s} \right)^2 & ; & - s \sqrt[3]{\frac{3}{4s}} \le x \le s \sqrt[3]{\frac{3}{4s}} \\ 0 & ; & else \end{array} \right.$

$\sigma = s^{2/3} \sqrt{\frac{1}{5}} \sqrt[3]{\frac{3}{4}}$

$s = \sqrt{\frac{4}{3}} 5^{3/4} \sigma^{3/2}$

$f(x) = \left\{ \begin{array}{lcl} \frac{3}{4\sqrt{5}\sigma}\left( 1 - \frac{x^2}{5\sigma^2} \right) & ; & -\sqrt{5}\sigma \le x \le \sqrt{5}\sigma \\ 0 & ; & else \end{array} \right.$