Iterative calculation of the rolling variance. More...

#include <rolling_variance.hpp>

Inheritance diagram for boost::accumulators::impl::immediate_rolling_variance_impl< Sample >:

Collaboration diagram for boost::accumulators::impl::immediate_rolling_variance_impl< Sample >:

Public Types
typedef numeric::functional::fdiv < Sample, std::size_t > ::result_type	result_type

typedef mpl::false_	is_droppable

Public Member Functions
template<typename Args >
	immediate_rolling_variance_impl (Args const &args)

template<typename Args >
void	operator() (Args const &args)

template<typename Args >
result_type	result (Args const &args) const

detail::void_	operator() (dont_care)

detail::void_	add_ref (dont_care)

detail::void_	drop (dont_care)

detail::void_	on_drop (dont_care)

Detailed Description

template<typename Sample>
struct boost::accumulators::impl::immediate_rolling_variance_impl< Sample >

Iterative calculation of the rolling variance.

Iterative calculation of sample variance $\sigma_n^2$ is done as follows, see also http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance. For a rolling window of size $N$ , for the first $N$ samples, the variance is computed according to the formula

$\sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},$

where the sum of squares $M_{2,n}$ can be recursively computed as:

$M_{2,n} = \sum_{i = 1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}),$

and the estimate of the sample mean as:

$\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - \mu_{n-1}).$

For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest sample $x_{n-N}$ is dropped from the window. The sample variance over the window now becomes:

$\sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},$

where the sum of squares $M_{2,n}$ now equals:

$M_{2,n} = \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}) - (x_{n-N} - \mu_n)(x_{n-N} - \mu_{n-1}),$

and the estimated mean is:

$\mu_n = \frac{1}{N} \sum_{i = n-N+1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - x_{n-N}).$

Note that the sample variance is not defined for $n <= 1$ .

Member Typedef Documentation

typedef mpl::false_ boost::accumulators::accumulator_base::is_droppable

inherited

template<typename Sample >

typedef numeric::functional::fdiv<Sample, std::size_t>::result_type boost::accumulators::impl::immediate_rolling_variance_impl< Sample >::result_type

Constructor & Destructor Documentation

template<typename Sample >

template<typename Args >

boost::accumulators::impl::immediate_rolling_variance_impl< Sample >::immediate_rolling_variance_impl ( Args const & args )

inline

Member Function Documentation

detail::void_ boost::accumulators::accumulator_base::add_ref ( dont_care )

inlineinherited

detail::void_ boost::accumulators::accumulator_base::drop ( dont_care )

inlineinherited

detail::void_ boost::accumulators::accumulator_base::on_drop ( dont_care )

inlineinherited

detail::void_ boost::accumulators::accumulator_base::operator() ( dont_care )

inlineinherited

template<typename Sample >

template<typename Args >

void boost::accumulators::impl::immediate_rolling_variance_impl< Sample >::operator() ( Args const & args )

inline

References boost::accumulators::extract::immediate_rolling_mean, boost::accumulators::impl::is_rolling_window_plus1_full(), boost::accumulators::extract::mean, and boost::accumulators::extract::rolling_window_plus1.

template<typename Sample >

template<typename Args >

result_type boost::accumulators::impl::immediate_rolling_variance_impl< Sample >::result ( Args const & args ) const

inline

References boost::accumulators::extract::rolling_count.

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

boost_1_57_0/boost/accumulators/statistics/rolling_variance.hpp

Public Types

Public Member Functions

Detailed Description

template<typename Sample> struct boost::accumulators::impl::immediate_rolling_variance_impl< Sample >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename Sample>
struct boost::accumulators::impl::immediate_rolling_variance_impl< Sample >