#include <yat/statistics/averager_base.h>

Inheritance diagram for theplu::yat::statistics::averager_base4< Derived >:

Public Member Functions
	averager_base4 (void)
	Constructor.

virtual	~averager_base4 (void)=0
	Destructor.

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

Detailed Description

template<class Derived>
class theplu::yat::statistics::averager_base4< Derived >

Base class for averagers calculating first (mean), second (variance), third moment, and fourth moment.

For requirement on Derived see averager_base.

Since: yat 0.9

Member Function Documentation

◆ add()

template<class Derived>

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

inlineinherited

add a data point

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

◆ add1() [1/2]

template<class Derived >

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

protectedinherited

add n data points with value x

◆ add1() [2/2]

template<class Derived >

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

protectedinherited

add one data point with value delta + mean()

◆ add2() [1/2]

template<class Derived >

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

protectedinherited

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

◆ add2() [2/2]

template<class Derived >

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

protectedinherited

add one data point with value delta + mean()

◆ add3() [1/2]

template<class Derived >

void theplu::yat::statistics::averager_base3< Derived >::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.

◆ add3() [2/2]

template<class Derived >

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

protectedinherited

add one data point with value delta + mean()

◆ add4() [1/2]

template<class Derived >

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

protected

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

◆ add4() [2/2]

template<class Derived >

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

protected

add one data point with value delta + mean()

◆ central_moment3()

template<class Derived>

double theplu::yat::statistics::averager_base3< Derived >::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.

◆ central_moment4()

template<class Derived>

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

inline

Fourth central moment.

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

◆ cv()

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::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.

◆ kurtosis()

template<class Derived>

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

inline

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.

◆ mean()

template<class Derived>

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

inlineinherited

mean

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

◆ n()

template<class Derived>

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

inlineinherited

number of data points

Returns: Number of data points

◆ rescale()

template<class Derived>

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

inlineinherited

Rescales the object.

$\forall x_i \rightarrow a*x_i$ ,

◆ rescale1()

template<class Derived >

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

protectedinherited

rescale as $mean \rightarrow x mean$

◆ rescale2()

template<class Derived >

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

protectedinherited

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

◆ rescale3()

template<class Derived >

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

protectedinherited

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

◆ rescale4()

template<class Derived >

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

protected

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

◆ reset()

template<class Derived>

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

inlineinherited

Reset object.

Restore Averager as if data were never added

◆ skewness()

template<class Derived>

double theplu::yat::statistics::averager_base3< Derived >::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.

◆ standard_error()

template<class Derived>

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

inlineinherited

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

◆ std() [1/2]

template<class Derived>

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

inlineinherited

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

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

◆ std() [2/2]

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::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).

◆ sum_x()

template<class Derived>

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

inlineinherited

Returns: The sum of data values

◆ sum_x3_centered()

template<class Derived>

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

inlineinherited

Returns: sum cubed centered

$\sum (x_i-m)^3$

◆ sum_x4_centered()

template<class Derived>

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

inline

sum quadrupled centered

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

◆ sum_xx()

template<class Derived>

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

inlineinherited

Returns: The sum of squares

◆ sum_xx_centered()

template<class Derived>

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

inlineinherited

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

◆ variance() [1/2]

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::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.

◆ variance() [2/2]

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::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

◆ variance_unbiased()

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::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.

Returns: unbiased estimation of variance

Member Data Documentation

◆ cm2_

template<class Derived>

double theplu::yat::statistics::averager_base2< Derived >::cm2_

protectedinherited

sum of values squared values centralized $\sum (x-m)^2$

◆ cm3_

template<class Derived>

double theplu::yat::statistics::averager_base3< Derived >::cm3_

protectedinherited

sum cubed centered

◆ n_

template<class Derived>

long int theplu::yat::statistics::averager_base< Derived >::n_

protectedinherited

number of data points

The documentation for this class was generated from the following file:

yat/statistics/averager_base.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<class Derived> class theplu::yat::statistics::averager_base4< Derived >

Member Function Documentation

◆ add()

◆ add1() [1/2]

◆ add1() [2/2]

◆ add2() [1/2]

◆ add2() [2/2]

◆ add3() [1/2]

◆ add3() [2/2]

◆ add4() [1/2]

◆ add4() [2/2]

◆ central_moment3()

◆ central_moment4()

◆ cv()

◆ kurtosis()

◆ mean()

◆ n()

◆ rescale()

◆ rescale1()

◆ rescale2()

◆ rescale3()

◆ rescale4()

◆ reset()

◆ skewness()

◆ standard_error()

◆ std() [1/2]

◆ std() [2/2]

◆ sum_x()

◆ sum_x3_centered()

◆ sum_x4_centered()

◆ sum_xx()

◆ sum_xx_centered()

◆ variance() [1/2]

◆ variance() [2/2]

◆ variance_unbiased()

Member Data Documentation

◆ cm2_

◆ cm3_

◆ n_

template<class Derived>
class theplu::yat::statistics::averager_base4< Derived >