ST(3)

NAME
boost::accumulators::impl::non_coherent_weighted_tail_mean_impl - Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)

SYNOPSIS

// In header: <boost/accumulators/statistics/weighted_tail_mean.hpp>
template<typename Sample, typename Weight, typename LeftRight>
struct non_coherent_weighted_tail_mean_impl {
  // types
  typedef numeric::functional::multiplies< Sample, Weight >::result_type            weighted_sample;
  typedef numeric::functional::average< Weight, std::size_t >::result_type          float_type;
  typedef numeric::functional::average< weighted_sample, std::size_t >::result_type result_type;
  // construct/copy/destruct
  non_coherent_weighted_tail_mean_impl(dont_care);
  // public member functions
  template<typename Args> result_type result(Args const &) const;
};

DESCRIPTION

An estimation of the non-coherent, weighted tail mean [1][IMAGE][2] [$ is given by the weighted mean of the

Equation 1.30.  [3].sp .RS 4 [IMAGE][4] \[ \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} \] .RE

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

Equation 1.31.  [5].sp .RS 4 [IMAGE][6] \[ n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\} \] .RE

largest samples (right tail) above a quantile [7][IMAGE][8] [$ lpha}$] of level [9][IMAGE][10] [$lpha$], [11][IMAGE][12] [$n$] being the total number of sample and [13][IMAGE][14] [$ the sum of all [15][IMAGE][12] [$n$] weights:

Equation 1.32.  [16].sp .RS 4 [IMAGE][17] \[ \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i}, \] .RE

Equation 1.33.  [18].sp .RS 4 [IMAGE][19] \[ \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}. \] .RE

  non_coherent_weighted_tail_mean_impl public construct/copy/destruct

    1.

    non_coherent_weighted_tail_mean_impl(dont_care);

  non_coherent_weighted_tail_mean_impl public member functions

    1.

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