Base class for averagers calculating mean and variance. More...

#include <yat/statistics/averager_base.h>

Inheritance diagram for theplu::yat::statistics::averager_base2< Derived >:

Public Member Functions
	averager_base2 (void)
	Constructor.

virtual	~averager_base2 (void)=0
	Destructor.

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	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	cm2_

long int	n_

double	mean_
	mean

Detailed Description

template<class Derived>
class theplu::yat::statistics::averager_base2< Derived >

Base class for averagers calculating mean and variance.

This is an extension of averager_base and provides more functionality related to the second moment (variance).

For requirement on Derived see averager_base.

See Also: Averager which is an example derived class

Since: yat 0.9

Member Function Documentation

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.

template<class Derived >

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

protectedinherited

add n data points with value x

template<class Derived >

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

protectedinherited

add one data point with value delta + mean()

template<class Derived >

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

protected

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

template<class Derived >

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

protected

add one data point with value delta + mean()

template<class Derived>

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

inline

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.

template<class Derived>

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

inlineinherited

mean

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

template<class Derived>

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

inlineinherited

number of data points

Returns: Number of data points

template<class Derived>

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

inlineinherited

Rescales the object.

$\forall x_i \rightarrow a*x_i$ ,

template<class Derived >

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

protectedinherited

rescale as $mean \rightarrow x mean$

template<class Derived >

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

protected

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

template<class Derived>

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

inlineinherited

Reset object.

Restore Averager as if data were never added

template<class Derived>

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

inline

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

template<class Derived>

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

inline

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

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

template<class Derived>

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

inline

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

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

template<class Derived>

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

inlineinherited

Returns: The sum of data values

template<class Derived>

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

inline

Returns: The sum of squares

template<class Derived>

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

inline

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

template<class Derived>

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

inline

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.

template<class Derived>

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

inline

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

template<class Derived>

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

inline

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.