STRUCT TE(3)

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

SYNOPSIS

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

DESCRIPTION

The coherent tail mean [1][IMAGE][2] [$ is equal to the non-coherent tail mean [3][IMAGE][4] [$ plus a correction term that ensures coherence in case of non-continuous distributions.

Equation 1.12.  [5].sp .RS 4 [IMAGE][6] \[ \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) + \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right) \] .RE

Equation 1.13.  [7].sp .RS 4 [IMAGE][8] \[ \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) + \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right) \] .RE

  coherent_tail_mean_impl public construct/copy/destruct

    1.

    coherent_tail_mean_impl(dont_care);

  coherent_tail_mean_impl public member functions

    1.

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