Class to calulate averages with weights. More...

#include <yat/statistics/AveragerWeighted.h>

Public Member Functions
	AveragerWeighted (void)
	The default constructor.

	AveragerWeighted (const AveragerWeighted &)
	The copy constructor.

void	add (const double d, const double w=1)

double	mean (void) const
	Calculate the weighted mean. More...

double	n (void) const
	Weighted version of number of data points. More...

void	rescale (double a)
	Rescale object. More...

void	reset (void)
	Reset everything to zero.

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

double	standard_error (void) const
	Calculates standard deviation of the mean(). More...

double	sum_w (void) const

double	sum_ww (void) const

double	sum_wx (void) const

double	sum_wxx (void) const

double	sum_xx_centered (void) const

double	variance (const double m) const

double	variance (void) const

const AveragerWeighted &	operator+= (const AveragerWeighted &)

Related Functions
(Note that these are not member functions.)
template<typename InputIterator >
void	add (AveragerWeighted &a, InputIterator first, InputIterator last)
	adding a range of values to AveragerWeighted a More...

template<typename InputIterator1 , typename InputIterator2 >
void	add (AveragerWeighted &a, InputIterator1 first1, InputIterator1 last1, InputIterator2 first2)
	add values from two ranges to AveragerWeighted a More...

Detailed Description

Class to calulate averages with weights.

There are several different reasons why a statistical analysis needs to adjust for weighting. In the litterature reasons are mainly divided into two kinds of weights - probablity weights and analytical weights. 1) Analytical weights are appropriate for scientific experiments where some measurements are known to be more precise than others. The larger weight a measurement has the more precise is is assumed to be, or more formally the weight is proportional to the reciprocal variance $\sigma_i^2 = \frac{\sigma^2}{w_i}$ . 2) Probability weights are used for the situation when calculating averages over a distribution $ f $ , but sampling from a distribution $ f' $ . Compensating for this discrepancy averages of observables are taken to be $\sum \frac{f}{f'}X$ For further discussion: see Weighted Statistics

If nothing else stated, each function fulfills the following:

Setting a weight to zero corresponds to removing the data point from the dataset.
Setting all weights to unity, the yields the same result as from corresponding function in Averager.
Rescaling weights does not change the performance of the object.

See Also: Averager AveragerPair AveragerPairWeighted

Member Function Documentation

void theplu::yat::statistics::AveragerWeighted::add	(	const double	d,
		const double	w = `1`
	)

Adding a data point d, with weight w (default is 1)

double theplu::yat::statistics::AveragerWeighted::mean ( void ) const

Calculate the weighted mean.

Returns: $\frac{\sum w_ix_i}{\sum w_i}$

double theplu::yat::statistics::AveragerWeighted::n ( void ) const

Weighted version of number of data points.

If all weights are equal, the unweighted version is identical to the non-weighted version. Adding a data point with zero weight does not change n(). The calculated value is always smaller than the actual number of data points added to object.

Returns: $\frac{\left(\sum w_i\right)^2}{\sum w_i^2}$

const AveragerWeighted& theplu::yat::statistics::AveragerWeighted::operator+= ( const AveragerWeighted & )

operator to add an AveragerWeighted

Since: New in yat 0.6

void theplu::yat::statistics::AveragerWeighted::rescale ( double a )

Rescale object.

Each data point is rescaled as $ x = a * x $

double theplu::yat::statistics::AveragerWeighted::standard_error ( void ) const

Calculates standard deviation of the mean().

Variance from the weights are here neglected. This is true when the weight is known before the measurement. In case this is not a good approximation, use bootstrapping to estimate the error.

Returns: $\frac{\sum w^2}{\left(\sum w\right)^3}\sum w(x-m)^2$ where is the mean()

double theplu::yat::statistics::AveragerWeighted::std ( void ) const

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

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

double theplu::yat::statistics::AveragerWeighted::sum_w ( void ) const

Calculating the sum of weights

Returns: $\sum w_i$

double theplu::yat::statistics::AveragerWeighted::sum_ww ( void ) const

Returns: $\sum w_i^2$

double theplu::yat::statistics::AveragerWeighted::sum_wx ( void ) const

$\sum w_ix_i$

Returns: weighted sum of x

double theplu::yat::statistics::AveragerWeighted::sum_wxx ( void ) const

Returns: $\sum w_i x_i^2$

double theplu::yat::statistics::AveragerWeighted::sum_xx_centered ( void ) const

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

double theplu::yat::statistics::AveragerWeighted::variance ( const double m ) const

The variance is calculated as $\frac{\sum w_i (x_i - m)^2 }{\sum w_i}$ , where m is the known mean.

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

double theplu::yat::statistics::AveragerWeighted::variance ( void ) const

The variance is calculated as $\frac{\sum w_i (x_i - m)^2 }{\sum w_i}$ , where m is the mean(). Here the weight are interpreted as probability weights. For analytical weights the variance has no meaning as each data point has its own variance.

Returns: The variance.

Friends And Related Function Documentation

template<typename InputIterator >

void add	(	AveragerWeighted &	a,
		InputIterator	first,
		InputIterator	last
	)

If InputIterator is non-weighted unitary weights are used.

Type Requirement:

InputIterator models Data Iterator
InputIterator is Single Pass Iterator

template<typename InputIterator1 , typename InputIterator2 >

void add	(	AveragerWeighted &	a,
		InputIterator1	first1,
		InputIterator1	last1,
		InputIterator2	first2
	)

Add data from range [first1, last1) with their corresponding weight in range [first2, first2 + distance(first, last) ).

Type Requirement:

InputIterator1 models Single Pass Iterator
InputIterator1 models Readable Iterator
InputIterator1 is unweighted
InputIterator2 models Single Pass Iterator
InputIterator2 models Readable Iterator
InputIterator2 is unweighted

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

yat/statistics/AveragerWeighted.h

Public Member Functions

Related Functions

Detailed Description

Member Function Documentation

Friends And Related Function Documentation