STRU(3)

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

SYNOPSIS

// In header: <boost/accumulators/statistics/weighted_tail_variate_means.hpp>
template<typename Sample, typename Weight, typename Impl, typename LeftRight,
         typename VariateType>
struct weighted_tail_variate_means_impl {
  // types
  typedef numeric::functional::average< Weight, Weight >::result_type                                                                       float_type;
  typedef numeric::functional::average< typename numeric::functional::multiplies< VariateType, Weight >::result_type, Weight >::result_type array_type;
  typedef iterator_range< typename array_type::iterator >                                                                                   result_type;
  // construct/copy/destruct
  weighted_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

Equation 1.36.  [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 1.37.  [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), the absolute weighted tail means [7][IMAGE][8] [$ are computed and returned as an iterator range. Alternatively, the relative weighted tail means [9][IMAGE][10] [$ are returned, which are the absolute weighted tail means normalized with the weighted (non-coherent) sample tail mean [11][IMAGE][12] [$

Equation 1.38.  [13].sp .RS 4 [IMAGE][14] \[ \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{1}{\sum_{i=\rho}^n w_i} \sum_{i=\rho}^n w_i \xi_{j,i} \] .RE

Equation 1.39.  [15].sp .RS 4 [IMAGE][16] \[ \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{1}{\sum_{i=1}^{\lambda}} \sum_{i=1}^{\lambda} w_i \xi_{j,i} \] .RE

Equation 1.40.  [17].sp .RS 4 [IMAGE][18] \[ \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{\sum_{i=\rho}^n w_i \xi_{j,i}} {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} \] .RE

Equation 1.41.  [19].sp .RS 4 [IMAGE][20] \[ \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}} {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} \] .RE

  weighted_tail_variate_means_impl public construct/copy/destruct

    1.

    weighted_tail_variate_means_impl(dont_care);

  weighted_tail_variate_means_impl public member functions

    1.

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