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