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

#include </scratch/bob/jari/tmp/pristine/yat-0.10.x/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.
double	central_moment4 (void) const
	Fourth central moment.
double	kurtosis (void) const
	Kurtosis.
double	sum_x4_centered (void) const
	sum quadrupled centered
double	central_moment3 (void) const
	Third central moment.
double	skewness (void) const
	Skewness.
double	sum_x3_centered (void) const
double	cv (void) const
	Coeffient of variation.
double	standard_error (void) const
double	std (void) const
	The standard deviation is defined as the square root of the variance.
double	std (double m) const
	The standard deviation is defined as the square root of the variance.
double	sum_xx (void) const
double	sum_xx_centered (void) const
double	variance (double m) const
	The variance with known mean.
double	variance (void) const
	The estimated variance.
double	variance_unbiased (void) const
void	add (double x, long n=1)
	add a data point
double	mean (void) const
	mean
long	n (void) const
	number of data points
void	rescale (double a)
	Rescales the object.
void	reset (void)
	Reset object.
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
   \return  \form#241

Fourth central moment

   \return  \form#242

The kurtosis is calculated as \form#243 where \form#244@_fakenl and \form#245 are the fourth central moment and
variance, respectively.

\return kurtosis

\see 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 \a N.

   The skewness is calculated as \form#246 where \form#247@_fakenl and \form#161 are the third central moment and
   standard deviation, respectively.

   \return skewness

   \see 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 \a 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

  \return 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

  \return 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

$\frac{1}{n}\sum (x_i-m)^2$ .

  \return Variance when the mean is known to be \a 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 \form#230 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

double theplu::yat::statistics::averager_base2< Averager4 >::cm2_

protectedinherited

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

double theplu::yat::statistics::averager_base3< Averager4 >::cm3_

protectedinherited

sum cubed centered

long int theplu::yat::statistics::averager_base< Averager4 >::n_

protectedinherited

number of data points

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

/scratch/bob/jari/tmp/pristine/yat-0.10.x/yat/statistics/Averager4.h

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Function Documentation

Member Data Documentation