STRUCT TE(3)

NAME
boost::accumulators::impl::tail_variate_means_impl - Estimation of the absolute and relative tail variate means (for both left and right tails)

SYNOPSIS

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

DESCRIPTION

For all [1][IMAGE][2] [$j$]-th variates associated to the [3][IMAGE][4] [$eil$] largest samples (or the [5][IMAGE][4] [$eil$] smallest samples in case of the left tail), the absolute tail means [6][IMAGE][7] [$ are computed and returned as an iterator range. Alternatively, the relative tail means [8][IMAGE][9] [$ are returned, which are the absolute tail means normalized with the (non-coherent) sample tail mean [10][IMAGE][11] [$

Equation 1.17.  [12].sp .RS 4 [IMAGE][13] \[ \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{1}{\lceil n(1-\alpha) \rceil} \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i} \] .RE

Equation 1.18.  [14].sp .RS 4 [IMAGE][15] \[ \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{1}{\lceil n\alpha \rceil} \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i} \] .RE

Equation 1.19.  [16].sp .RS 4 [IMAGE][17] \[ \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}} {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} \] .RE

Equation 1.20.  [18].sp .RS 4 [IMAGE][19] \[ \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}} {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} \] .RE

  tail_variate_means_impl public construct/copy/destruct

    1.

    tail_variate_means_impl(dont_care);

  tail_variate_means_impl public member functions

    1.

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