accumulators/statistics/weighted_tail_mean.hpp

0001 ///////////////////////////////////////////////////////////////////////////////
0002 // weighted_tail_mean.hpp
0003 //
0004 //  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
0005 //  Software License, Version 1.0. (See accompanying file
0006 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0007
0008 #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
0009 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
0010
0011 #include <numeric>
0012 #include <vector>
0013 #include <limits>
0014 #include <functional>
0015 #include <sstream>
0016 #include <stdexcept>
0017 #include <boost/throw_exception.hpp>
0018 #include <boost/parameter/keyword.hpp>
0019 #include <boost/mpl/placeholders.hpp>
0020 #include <boost/type_traits/is_same.hpp>
0021 #include <boost/accumulators/numeric/functional.hpp>
0022 #include <boost/accumulators/framework/accumulator_base.hpp>
0023 #include <boost/accumulators/framework/extractor.hpp>
0024 #include <boost/accumulators/framework/parameters/sample.hpp>
0025 #include <boost/accumulators/statistics_fwd.hpp>
0026 #include <boost/accumulators/statistics/tail.hpp>
0027 #include <boost/accumulators/statistics/tail_mean.hpp>
0028 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
0029
0030 #ifdef _MSC_VER
0031 # pragma warning(push)
0032 # pragma warning(disable: 4127) // conditional expression is constant
0033 #endif
0034
0035 namespace boost { namespace accumulators
0036 {
0037
0038 namespace impl
0039 {
0040
0041     ///////////////////////////////////////////////////////////////////////////////
0042     // coherent_weighted_tail_mean_impl
0043     //
0044     // TODO
0045
0046     ///////////////////////////////////////////////////////////////////////////////
0047     // non_coherent_weighted_tail_mean_impl
0048     //
0049     /**
0050         @brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)
0051
0052
0053
0054         An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean
0055         of the
0056
0057         \f[
0058             \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
0059         \f]
0060
0061         smallest samples (left tail) or the weighted mean of the
0062
0063         \f[
0064             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\}
0065         \f]
0066
0067         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
0068         and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights:
0069
0070         \f[
0071             \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i},
0072         \f]
0073
0074         \f[
0075             \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}.
0076         \f]
0077
0078         @param quantile_probability
0079     */
0080     template<typename Sample, typename Weight, typename LeftRight>
0081     struct non_coherent_weighted_tail_mean_impl
0082       : accumulator_base
0083     {
0084         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
0085         typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
0086         // for boost::result_of
0087         typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type result_type;
0088
0089         non_coherent_weighted_tail_mean_impl(dont_care) {}
0090
0091         template<typename Args>
0092         result_type result(Args const &args) const
0093         {
0094             float_type threshold = sum_of_weights(args)
0095                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
0096
0097             std::size_t n = 0;
0098             Weight sum = Weight(0);
0099
0100             while (sum < threshold)
0101             {
0102                 if (n < static_cast<std::size_t>(tail_weights(args).size()))
0103                 {
0104                     sum += *(tail_weights(args).begin() + n);
0105                     n++;
0106                 }
0107                 else
0108                 {
0109                     if (std::numeric_limits<result_type>::has_quiet_NaN)
0110                     {
0111                         return std::numeric_limits<result_type>::quiet_NaN();
0112                     }
0113                     else
0114                     {
0115                         std::ostringstream msg;
0116                         msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
0117                         boost::throw_exception(std::runtime_error(msg.str()));
0118                         return result_type(0);
0119                     }
0120                 }
0121             }
0122
0123             return numeric::fdiv(
0124                 std::inner_product(
0125                     tail(args).begin()
0126                   , tail(args).begin() + n
0127                   , tail_weights(args).begin()
0128                   , weighted_sample(0)
0129                 )
0130               , sum
0131             );
0132         }
0133     };
0134
0135 } // namespace impl
0136
0137
0138 ///////////////////////////////////////////////////////////////////////////////
0139 // tag::non_coherent_weighted_tail_mean<>
0140 //
0141 namespace tag
0142 {
0143     template<typename LeftRight>
0144     struct non_coherent_weighted_tail_mean
0145       : depends_on<sum_of_weights, tail_weights<LeftRight> >
0146     {
0147         typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl;
0148     };
0149 }
0150
0151 ///////////////////////////////////////////////////////////////////////////////
0152 // extract::non_coherent_weighted_tail_mean;
0153 //
0154 namespace extract
0155 {
0156     extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {};
0157
0158     BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean)
0159 }
0160
0161 using extract::non_coherent_weighted_tail_mean;
0162
0163 }} // namespace boost::accumulators
0164
0165 #ifdef _MSC_VER
0166 # pragma warning(pop)
0167 #endif
0168
0169 #endif