Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tail_variate_means.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_VARIATE_MEANS_HPP_DE_01_01_2006
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_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/tail.hpp>
Chris@16: #include <boost/accumulators/statistics/tail_variate.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:         @brief Estimation of the absolute and relative tail variate means (for both left and right tails)
Chris@16: 
Chris@16:         For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
Chris@16:         \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
Chris@16:         \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
Chris@16:         the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
Chris@16:         tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
Chris@16:                 \frac{1}{\lceil n(1-\alpha) \rceil}
Chris@16:                 \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
Chris@16:                 \frac{1}{\lceil n\alpha \rceil}
Chris@16:                 \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
Chris@16:                 \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
Chris@16:             {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
Chris@16:         \f]
Chris@16: 
Chris@16:         \f[
Chris@16:             \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
Chris@16:                 \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
Chris@16:             {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
Chris@16:         \f]
Chris@16:     */
Chris@16: 
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // tail_variate_means_impl
Chris@16:     //  by default: absolute tail_variate_means
Chris@16:     template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
Chris@16:     struct tail_variate_means_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
Chris@16:         typedef std::vector<float_type> array_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef iterator_range<typename array_type::iterator> result_type;
Chris@16: 
Chris@16:         tail_variate_means_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:             std::size_t num_variates = tail_variate(args).begin()->size();
Chris@16: 
Chris@16:             this->tail_means_.clear();
Chris@16:             this->tail_means_.resize(num_variates, Sample(0));
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:             {
Chris@16:                 this->tail_means_ = std::accumulate(
Chris@16:                     tail_variate(args).begin()
Chris@16:                   , tail_variate(args).begin() + n
Chris@16:                   , this->tail_means_
Chris@16:                   , numeric::plus
Chris@16:                 );
Chris@16: 
Chris@16:                 float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );
Chris@16: 
Chris@16:                 std::transform(
Chris@16:                     this->tail_means_.begin()
Chris@16:                   , this->tail_means_.end()
Chris@16:                   , this->tail_means_.begin()
Chris@16:                   , std::bind2nd(std::divides<float_type>(), factor)
Chris@16:                 );
Chris@16:             }
Chris@16:             else
Chris@16:             {
Chris@16:                 if (std::numeric_limits<float_type>::has_quiet_NaN)
Chris@16:                 {
Chris@16:                     std::fill(
Chris@16:                         this->tail_means_.begin()
Chris@16:                       , this->tail_means_.end()
Chris@16:                       , std::numeric_limits<float_type>::quiet_NaN()
Chris@16:                     );
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:                 }
Chris@16:             }
Chris@16:             return make_iterator_range(this->tail_means_);
Chris@16:         }
Chris@16: 
Chris@16:     private:
Chris@16: 
Chris@16:         mutable array_type tail_means_;
Chris@16: 
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::absolute_tail_variate_means
Chris@16: // tag::relative_tail_variate_means
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16:     struct absolute_tail_variate_means
Chris@16:       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
Chris@16:     };
Chris@16:     template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16:     struct relative_tail_variate_means
Chris@16:       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
Chris@16:     };
Chris@16:     struct abstract_absolute_tail_variate_means
Chris@16:       : depends_on<>
Chris@16:     {
Chris@16:     };
Chris@16:     struct abstract_relative_tail_variate_means
Chris@16:       : depends_on<>
Chris@16:     {
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::tail_variate_means
Chris@16: // extract::relative_tail_variate_means
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {};
Chris@16:     extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means)
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means)
Chris@16: }
Chris@16: 
Chris@16: using extract::tail_variate_means;
Chris@16: using extract::relative_tail_variate_means;
Chris@16: 
Chris@16: // tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
Chris@16: {
Chris@16:     typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
Chris@16: };
Chris@16: 
Chris@16: // tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
Chris@16: {
Chris@16:     typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
Chris@16: };
Chris@16: 
Chris@16: // Provides non-templatized extractor
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16:   : feature_of<tag::abstract_absolute_tail_variate_means>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // Provides non-templatized extractor
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16:   : feature_of<tag::abstract_relative_tail_variate_means>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that absolute_tail_means can be automatically substituted
Chris@16: // with absolute_weighted_tail_means when the weight parameter is non-void.
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16: {
Chris@16:     typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
Chris@16: };
Chris@16: 
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16:   : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that relative_tail_means can be automatically substituted
Chris@16: // with relative_weighted_tail_means when the weight parameter is non-void.
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16: {
Chris@16:     typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
Chris@16: };
Chris@16: 
Chris@16: template<typename LeftRight, typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16:   : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
Chris@16: {
Chris@16: };
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