Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // weighted_tail_mean.hpp
Chris@16: //
Chris@16: //  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
Chris@16: 
Chris@16: #include <numeric>
Chris@16: #include <vector>
Chris@16: #include <limits>
Chris@16: #include <functional>
Chris@16: #include <sstream>
Chris@16: #include <stdexcept>
Chris@16: #include <boost/throw_exception.hpp>
Chris@16: #include <boost/parameter/keyword.hpp>
Chris@16: #include <boost/mpl/placeholders.hpp>
Chris@16: #include <boost/type_traits/is_same.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/tail.hpp>
Chris@16: #include <boost/accumulators/statistics/tail_mean.hpp>
Chris@16: #include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: # pragma warning(push)
Chris@16: # pragma warning(disable: 4127) // conditional expression is constant
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16: 
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // coherent_weighted_tail_mean_impl
Chris@16:     //
Chris@16:     // TODO
Chris@16: 
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // non_coherent_weighted_tail_mean_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:         An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean
Chris@16:         of the
Chris@16: 
Chris@16:         \f[
Chris@16:             \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
Chris@16:         \f]
Chris@16: 
Chris@16:         smallest samples (left tail) or the weighted mean of the
Chris@16: 
Chris@16:         \f[
Chris@16:             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\}
Chris@16:         \f]
Chris@16: 
Chris@16:         largest samples (right tail) above a quantile \f$\hat{q}_{\alpha}\f$ of level \f$\alpha\f$, \f$n\f$ being the total number of sample
Chris@16:         and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights:
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i},
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}.
Chris@16:         \f]
Chris@16: 
Chris@16:         @param quantile_probability
Chris@16:     */
Chris@16:     template<typename Sample, typename Weight, typename LeftRight>
Chris@16:     struct non_coherent_weighted_tail_mean_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
Chris@16:         typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type result_type;
Chris@16: 
Chris@16:         non_coherent_weighted_tail_mean_impl(dont_care) {}
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             float_type threshold = sum_of_weights(args)
Chris@16:                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
Chris@16: 
Chris@16:             std::size_t n = 0;
Chris@16:             Weight sum = Weight(0);
Chris@16: 
Chris@16:             while (sum < threshold)
Chris@16:             {
Chris@16:                 if (n < static_cast<std::size_t>(tail_weights(args).size()))
Chris@16:                 {
Chris@16:                     sum += *(tail_weights(args).begin() + n);
Chris@16:                     n++;
Chris@16:                 }
Chris@16:                 else
Chris@16:                 {
Chris@16:                     if (std::numeric_limits<result_type>::has_quiet_NaN)
Chris@16:                     {
Chris@16:                         return std::numeric_limits<result_type>::quiet_NaN();
Chris@16:                     }
Chris@16:                     else
Chris@16:                     {
Chris@16:                         std::ostringstream msg;
Chris@16:                         msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
Chris@16:                         boost::throw_exception(std::runtime_error(msg.str()));
Chris@16:                         return result_type(0);
Chris@16:                     }
Chris@16:                 }
Chris@16:             }
Chris@16: 
Chris@16:             return numeric::fdiv(
Chris@16:                 std::inner_product(
Chris@16:                     tail(args).begin()
Chris@16:                   , tail(args).begin() + n
Chris@16:                   , tail_weights(args).begin()
Chris@16:                   , weighted_sample(0)
Chris@16:                 )
Chris@16:               , sum
Chris@16:             );
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::non_coherent_weighted_tail_mean<>
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     template<typename LeftRight>
Chris@16:     struct non_coherent_weighted_tail_mean
Chris@16:       : depends_on<sum_of_weights, tail_weights<LeftRight> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl;
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::non_coherent_weighted_tail_mean;
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean)
Chris@16: }
Chris@16: 
Chris@16: using extract::non_coherent_weighted_tail_mean;
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: # pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: #endif