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boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight > Struct Template Reference

Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails) More...

#include <statistics_fwd.hpp>

Inheritance diagram for boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >:
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Collaboration diagram for boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >:
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Public Types

typedef
numeric::functional::multiplies
< Sample, Weight >
::result_type 		weighted_sample
 
typedef
numeric::functional::fdiv
< Weight, std::size_t >
::result_type 		float_type
 
typedef
numeric::functional::fdiv
< weighted_sample, std::size_t >
::result_type 		result_type
 
typedef mpl::false_ is_droppable
 

Public Member Functions

 non_coherent_weighted_tail_mean_impl (dont_care)
 
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, typename Weight, typename LeftRight>
struct boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >

Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)

An estimation of the non-coherent, weighted tail mean $\widehat{NCTM}_{n,\alpha}(X)$ is given by the weighted mean of the

\[ \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} \]

smallest samples (left tail) or the weighted mean of the

\[ n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\} \]

largest samples (right tail) above a quantile $\hat{q}_{\alpha}$ of level $\alpha$, $n$ being the total number of sample and $\bar{w}_n$ the sum of all $n$ weights:

\[ \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i}, \]

\[ \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}. \]

Parameters
quantile_probability

Member Typedef Documentation

template<typename Sample , typename Weight , typename LeftRight >
typedef numeric::functional::fdiv<Weight, std::size_t>::result_type boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >::float_type
typedef mpl::false_ boost::accumulators::accumulator_base::is_droppable
inherited
template<typename Sample , typename Weight , typename LeftRight >
typedef numeric::functional::fdiv<weighted_sample, std::size_t>::result_type boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >::result_type
template<typename Sample , typename Weight , typename LeftRight >
typedef numeric::functional::multiplies<Sample, Weight>::result_type boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >::weighted_sample

Constructor & Destructor Documentation

template<typename Sample , typename Weight , typename LeftRight >
boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >::non_coherent_weighted_tail_mean_impl ( dont_care  )
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 , typename Weight , typename LeftRight >
template<typename Args >
result_type boost::accumulators::impl::non_coherent_weighted_tail_mean_impl< Sample, Weight, LeftRight >::result ( Args const &  args) const
inline

References boost::asio::begin, boost::inner_product(), boost::n, boost::size(), boost::accumulators::extract::sum, boost::accumulators::extract::sum_of_weights, boost::accumulators::extract::tail, boost::accumulators::extract::tail_weights, boost::throw_exception(), and boost::program_options::value().

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