Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // 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_TAIL_MEAN_HPP_DE_01_01_2006
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_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/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/count.hpp>
Chris@16: #include <boost/accumulators/statistics/tail.hpp>
Chris@16: #include <boost/accumulators/statistics/tail_quantile.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_tail_mean_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Estimation of the coherent tail mean based on order statistics (for both left and right tails)
Chris@16: 
Chris@16:         The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$
Chris@16:         plus a correction term that ensures coherence in case of non-continuous distributions.
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) +
Chris@16:             \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right)
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) +
Chris@16:             \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right)
Chris@16:         \f]
Chris@16:     */
Chris@16:     template<typename Sample, typename LeftRight>
Chris@16:     struct coherent_tail_mean_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef float_type result_type;
Chris@16: 
Chris@16:         coherent_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:             std::size_t cnt = count(args);
Chris@16: 
Chris@16:             std::size_t n = static_cast<std::size_t>(
Chris@16:                 std::ceil(
Chris@16:                     cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
Chris@16:                 )
Chris@16:             );
Chris@16: 
Chris@16:             extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {};
Chris@16: 
Chris@16:             return some_non_coherent_tail_mean(args)
Chris@16:                  + numeric::fdiv(quantile(args), n)
Chris@16:                  * (
Chris@16:                      ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
Chris@16:                      - numeric::fdiv(n, count(args))
Chris@16:                    );
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // non_coherent_tail_mean_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails)
Chris@16: 
Chris@16:         An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the
Chris@16:         \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the  \f$\lceil n(1-\alpha)\rceil\f$
Chris@16:         largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level:
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n}
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n}
Chris@16:         \f]
Chris@16: 
Chris@16:         It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$
Chris@16:         largest samples.
Chris@16: 
Chris@16:         @param quantile_probability
Chris@16:     */
Chris@16:     template<typename Sample, typename LeftRight>
Chris@16:     struct non_coherent_tail_mean_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef float_type result_type;
Chris@16: 
Chris@16:         non_coherent_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:             std::size_t cnt = count(args);
Chris@16: 
Chris@16:             std::size_t n = static_cast<std::size_t>(
Chris@16:                 std::ceil(
Chris@16:                     cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
Chris@16:                 )
Chris@16:             );
Chris@16: 
Chris@16:             // If n is in a valid range, return result, otherwise return NaN or throw exception
Chris@16:             if (n <= static_cast<std::size_t>(tail(args).size()))
Chris@16:                 return numeric::fdiv(
Chris@16:                     std::accumulate(
Chris@16:                         tail(args).begin()
Chris@16:                       , tail(args).begin() + n
Chris@16:                       , Sample(0)
Chris@16:                     )
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 Sample(0);
Chris@16:                 }
Chris@16:             }
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::coherent_tail_mean<>
Chris@16: // tag::non_coherent_tail_mean<>
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     template<typename LeftRight>
Chris@16:     struct coherent_tail_mean
Chris@16:       : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
Chris@16:     };
Chris@16: 
Chris@16:     template<typename LeftRight>
Chris@16:     struct non_coherent_tail_mean
Chris@16:       : depends_on<count, tail<LeftRight> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
Chris@16:     };
Chris@16: 
Chris@16:     struct abstract_non_coherent_tail_mean
Chris@16:       : depends_on<>
Chris@16:     {
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::non_coherent_tail_mean;
Chris@16: // extract::coherent_tail_mean;
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {};
Chris@16:     extractor<tag::tail_mean> const coherent_tail_mean = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean)
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean)
Chris@16: }
Chris@16: 
Chris@16: using extract::non_coherent_tail_mean;
Chris@16: using extract::coherent_tail_mean;
Chris@16: 
Chris@16: // for the purposes of feature-based dependency resolution,
Chris@16: // coherent_tail_mean<LeftRight> provides the same feature as tail_mean
Chris@16: template<typename LeftRight>
Chris@16: struct feature_of<tag::coherent_tail_mean<LeftRight> >
Chris@16:   : feature_of<tag::tail_mean>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: template<typename LeftRight>
Chris@16: struct feature_of<tag::non_coherent_tail_mean<LeftRight> >
Chris@16:   : feature_of<tag::abstract_non_coherent_tail_mean>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that non_coherent_tail_mean can be automatically substituted
Chris@16: // with weighted_non_coherent_tail_mean when the weight parameter is non-void.
Chris@16: template<typename LeftRight>
Chris@16: struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> >
Chris@16: {
Chris@16:     typedef tag::non_coherent_weighted_tail_mean<LeftRight> type;
Chris@16: };
Chris@16: 
Chris@16: template<typename LeftRight>
Chris@16: struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> >
Chris@16:   : feature_of<tag::non_coherent_tail_mean<LeftRight> >
Chris@16: {};
Chris@16: 
Chris@16: // NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean,
Chris@16: // which is the base feature for coherent tail means, since (at least for
Chris@16: // non-continuous distributions) non_coherent_tail_mean is a different measure!
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