class to calculate 1st, 2nd, 3rd, and 4th central moments More...

#include <yat/statistics/Averager4.h>

Inheritance diagram for theplu::yat::statistics::Averager4:

Public Member Functions
	Averager4 (void)
	construct empty object

template<class Derived >
const Averager4 &	operator+= (const averager_base4< Derived > &rhs)
	Third central moment. More...

double	central_moment4 (void) const
	Fourth central moment. More...

double	kurtosis (void) const
	Kurtosis. More...

double	sum_x4_centered (void) const
	sum quadrupled centered More...

double	central_moment3 (void) const
	Third central moment. More...

double	skewness (void) const
	Skewness. More...

double	sum_x3_centered (void) const

double	cv (void) const
	Coeffient of variation. More...

double	standard_error (void) const

double	std (void) const
	The standard deviation is defined as the square root of the variance. More...

double	std (double m) const
	The standard deviation is defined as the square root of the variance. More...

double	sum_xx (void) const

double	sum_xx_centered (void) const

double	variance (double m) const
	The variance with known mean. More...

double	variance (void) const
	The estimated variance. More...

double	variance_unbiased (void) const

void	add (double x, long n=1)
	add a data point More...

double	mean (void) const
	mean More...

long	n (void) const
	number of data points More...

void	rescale (double a)
	Rescales the object. More...

void	reset (void)
	Reset object. More...

double	sum_x (void) const

Protected Member Functions
void	add4 (double mean, double cm2, double cm3, double cm4, long int n)

void	add4 (double delta)

double	rescale4 (double x)

void	add3 (double mean, double cm2, double cm3, long int n)

void	add3 (double delta)

double	rescale3 (double x)

void	add2 (double mean, double cm2, long int n)

void	add2 (double delta)

double	rescale2 (double x)

void	add1 (double x, long int n)

void	add1 (double delta)

double	rescale1 (double x)

Protected Attributes
double	cm4_
	sum quadrupled centered

double	cm3_

double	cm2_

long int	n_

double	mean_
	mean

Friends
class	averager_base< Averager4 >

Detailed Description

class to calculate 1st, 2nd, 3rd, and 4th central moments

Since: yat 0.9

Member Function Documentation

void theplu::yat::statistics::averager_base< Averager4 >::add	(	double	x,
		long	n = `1`
	)

inlineinherited

add a data point

Adding n number of data point(s) with value x.

void theplu::yat::statistics::averager_base< Averager4 >::add1	(	double	x,
		long int	n
	)

protectedinherited

add n data points with value x

void theplu::yat::statistics::averager_base< Averager4 >::add1 ( double delta )

protectedinherited

add one data point with value delta + mean()

void theplu::yat::statistics::averager_base2< Averager4 >::add2	(	double	mean,
		double	cm2,
		long int	n
	)

protectedinherited

add a set of n data points with mean mean and centralized squaed sum cm

void theplu::yat::statistics::averager_base2< Averager4 >::add2 ( double delta )

protectedinherited

add one data point with value delta + mean()

void theplu::yat::statistics::averager_base3< Averager4 >::add3	(	double	mean,
		double	cm2,
		double	cm3,
		long int	n
	)

protectedinherited

add a set of n data points with mean mean, sum squared centered cm2, and sum cubed centered cm3.

void theplu::yat::statistics::averager_base3< Averager4 >::add3 ( double delta )

protectedinherited

add one data point with value delta + mean()

void theplu::yat::statistics::averager_base4< Averager4 >::add4	(	double	mean,
		double	cm2,
		double	cm3,
		double	cm4,
		long int	n
	)

protectedinherited

add a set of n data points with mean mean, sum squared centered cm2, sum cubed centered cm3, and sum quadrupled centered cm4.

void theplu::yat::statistics::averager_base4< Averager4 >::add4 ( double delta )

protectedinherited

add one data point with value delta + mean()

double theplu::yat::statistics::averager_base3< Averager4 >::central_moment3 ( void ) const

inlineinherited

Third central moment.

Third central moment is calculated as $\frac{1}{n} \sum (x_i-m)^3$ where m is the mean.

double theplu::yat::statistics::averager_base4< Averager4 >::central_moment4 ( void ) const

inlineinherited

Fourth central moment.

Fourth central moment is calculated as $\frac{1}{n} \sum (x_i-m)^4$ where m is the mean.

double theplu::yat::statistics::averager_base2< Averager4 >::cv ( void ) const

inlineinherited

Coeffient of variation.

Coeffient of variation (cv) is defined as ratio between the standard deviation and the mean: $\frac{\sigma}{\mu}$ .

Returns: standard deviation divided by mean.

double theplu::yat::statistics::averager_base4< Averager4 >::kurtosis ( void ) const

inlineinherited

Kurtosis.

Kurtosis is calculated as $\frac{1}{n} \sum (x-m)^4 / \sigma^4 - 3.0$ where m is mean, and $\sigma$ is standard deviation.

Note: this function uses a biased variance estimate [1/n] compared to kurtosis(utility::VectorBase&), which uses an unbiased variance estimate [1/(n-1)] and may thus give different results for small n.

double theplu::yat::statistics::averager_base< Averager4 >::mean ( void ) const

inlineinherited

mean

Returns: Mean of presented data, $\frac{1}{n}\sum x_i$

long theplu::yat::statistics::averager_base< Averager4 >::n ( void ) const

inlineinherited

number of data points

Returns: Number of data points

template<class Derived >

const Averager4 & theplu::yat::statistics::Averager4::operator+= ( const averager_base4< Derived > & rhs )

Third central moment.

Access Averager that holds first and second moments

Returns: $\frac{1}{N} \sum (x_i-m)^3$ Fourth central moment; $\frac{1}{N} \sum (x_i-m)^4$ The kurtosis is calculated as where and are the fourth central moment and variance, respectively.; kurtosis

See Also: central_moment4 and Averager::variance

Note: This function uses a biased estimator of the variance (see Averager::variance) whereas function kurtosis(const utility::VectorBase&) uses an unbiased estimator (Averger::variance_unbiased) and therefore the result may differ for small N. The skewness is calculated as $M_3 / {\sigma}^3$ where and $\sigma$ are the third central moment and standard deviation, respectively.

Returns: skewness

See Also: central_moment3 and Averager::std

Note: This function uses a biased estimator of the variance (see Averager::variance) whereas function skewness(const utility::VectorBase&) uses an unbiased estimator (Averger::variance_unbiased) and therefore the result may differ for small N.

void theplu::yat::statistics::averager_base< Averager4 >::rescale ( double a )

inlineinherited

Rescales the object.

$\forall x_i \rightarrow a*x_i$ ,

double theplu::yat::statistics::averager_base< Averager4 >::rescale1 ( double x )

protectedinherited

rescale as $mean \rightarrow x mean$

double theplu::yat::statistics::averager_base2< Averager4 >::rescale2 ( double x )

protectedinherited

rescales $cm2 \rightarrow x^2 cm2$ and calles rescale1(double)

double theplu::yat::statistics::averager_base3< Averager4 >::rescale3 ( double x )

protectedinherited

rescales $ cm3 = x^3 cm3 $ and calles rescale2(double)

double theplu::yat::statistics::averager_base4< Averager4 >::rescale4 ( double x )

protectedinherited

rescales $ cm4 = x^4 cm4 $ and calles rescale2(double)

void theplu::yat::statistics::averager_base< Averager4 >::reset ( void )

inlineinherited

Reset object.

Restore Averager as if data were never added

double theplu::yat::statistics::averager_base3< Averager4 >::skewness ( void ) const

inlineinherited

Skewness.

Skewness is calculated as $\frac{1}{n} \sum (x_i-m) / \sigma^3$ where $\sigma$ is standard deviation.

Note: this function uses a biased variance estimate [1/n] compared to skewness(utility::VectorBase&), which uses an unbiased variance estimate [1/(n-1)] and may thus give different results for small n.

double theplu::yat::statistics::averager_base2< Averager4 >::standard_error ( void ) const

inlineinherited

Returns: Standard error, i.e. standard deviation of the mean $\sqrt{variance()/n}$

double theplu::yat::statistics::averager_base2< Averager4 >::std ( void ) const

inlineinherited

The standard deviation is defined as the square root of the variance.

Returns: The standard deviation, root of the variance().

double theplu::yat::statistics::averager_base2< Averager4 >::std ( double m ) const

inlineinherited

The standard deviation is defined as the square root of the variance.

Returns: Standard deviation around m, root of the variance(m).

double theplu::yat::statistics::averager_base< Averager4 >::sum_x ( void ) const

inlineinherited

Returns: The sum of data values

double theplu::yat::statistics::averager_base3< Averager4 >::sum_x3_centered ( void ) const

inlineinherited

Returns: sum cubed centered

$\sum (x_i-m)^3$

double theplu::yat::statistics::averager_base4< Averager4 >::sum_x4_centered ( void ) const

inlineinherited

sum quadrupled centered

Calculated as $\frac{1}{n} \sum (x_i-m)^4$

double theplu::yat::statistics::averager_base2< Averager4 >::sum_xx ( void ) const

inlineinherited

Returns: The sum of squares

double theplu::yat::statistics::averager_base2< Averager4 >::sum_xx_centered ( void ) const

inlineinherited

Returns: $\sum_i (x_i-m)^2$

double theplu::yat::statistics::averager_base2< Averager4 >::variance ( double m ) const

inlineinherited

The variance with known mean.

The variance is calculated as $\frac{1}{n}\sum (x_i-m)^2$ .

Returns: Variance when the mean is known to be m.

double theplu::yat::statistics::averager_base2< Averager4 >::variance ( void ) const

inlineinherited

The estimated variance.

The variance is calculated as $\frac{1}{N}\sum_i (x_i-m)^2$ , where $ m $ is the mean.

Returns: Estimation of variance

double theplu::yat::statistics::averager_base2< Averager4 >::variance_unbiased ( void ) const

inlineinherited

The variance is calculated using the $ (n-1) $ correction, which means it is the best unbiased estimator of the variance $\frac{1}{N-1}\sum_i (x_i-m)^2$ , where $ m $ is the mean.