tail_variate_means.hpp

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///////////////////////////////////////////////////////////////////////////////
// tail_variate_means.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_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_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/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/numeric/functional.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_variate.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
{
    /**
        @brief Estimation of the absolute and relative tail variate means (for both left and right tails)

        For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
        \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
        \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
        the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
        tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.

        \f[
            \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
                \frac{1}{\lceil n(1-\alpha) \rceil}
                \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
        \f]

        \f[
            \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
                \frac{1}{\lceil n\alpha \rceil}
                \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
        \f]

        \f[
            \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
                \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
            {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
        \f]

        \f[
            \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
                \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
            {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
        \f]
    */

    ///////////////////////////////////////////////////////////////////////////////
    // tail_variate_means_impl
    //  by default: absolute tail_variate_means
    template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
    struct tail_variate_means_impl
      : accumulator_base
    {
        typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
        typedef std::vector<float_type> array_type;
        // for boost::result_of
        typedef iterator_range<typename array_type::iterator> result_type;

        tail_variate_means_impl(dont_care) {}

        template<typename Args>
        result_type result(Args const &args) const
        {
            std::size_t cnt = count(args);

            std::size_t n = static_cast<std::size_t>(
                std::ceil(
                    cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
                )
            );

            std::size_t num_variates = tail_variate(args).begin()->size();

            this->tail_means_.clear();
            this->tail_means_.resize(num_variates, Sample(0));

            // If n is in a valid range, return result, otherwise return NaN or throw exception
            if (n < static_cast<std::size_t>(tail(args).size()))
            {
                this->tail_means_ = std::accumulate(
                    tail_variate(args).begin()
                  , tail_variate(args).begin() + n
                  , this->tail_means_
                  , numeric::plus
                );

                float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );

                std::transform(
                    this->tail_means_.begin()
                  , this->tail_means_.end()
                  , this->tail_means_.begin()
                  , std::bind2nd(std::divides<float_type>(), factor)
                );
            }
            else
            {
                if (std::numeric_limits<float_type>::has_quiet_NaN)
                {
                    std::fill(
                        this->tail_means_.begin()
                      , this->tail_means_.end()
                      , std::numeric_limits<float_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 make_iterator_range(this->tail_means_);
        }

    private:

        mutable array_type tail_means_;

    };

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::absolute_tail_variate_means
// tag::relative_tail_variate_means
//
namespace tag
{
    template<typename LeftRight, typename VariateType, typename VariateTag>
    struct absolute_tail_variate_means
      : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
    {
        typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
    };
    template<typename LeftRight, typename VariateType, typename VariateTag>
    struct relative_tail_variate_means
      : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
    {
        typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
    };
    struct abstract_absolute_tail_variate_means
      : depends_on<>
    {
    };
    struct abstract_relative_tail_variate_means
      : depends_on<>
    {
    };
}

///////////////////////////////////////////////////////////////////////////////
// extract::tail_variate_means
// extract::relative_tail_variate_means
//
namespace extract
{
    extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {};
    extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {};
}

using extract::tail_variate_means;
using extract::relative_tail_variate_means;

// tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
{
    typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

// tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
{
    typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

// Provides non-templatized extractor
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
  : feature_of<tag::abstract_absolute_tail_variate_means>
{
};

// Provides non-templatized extractor
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
  : feature_of<tag::abstract_relative_tail_variate_means>
{
};

// So that absolute_tail_means can be automatically substituted
// with absolute_weighted_tail_means when the weight parameter is non-void.
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
    typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
  : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
};

// So that relative_tail_means can be automatically substituted
// with relative_weighted_tail_means when the weight parameter is non-void.
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
    typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
  : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
};

}} // namespace boost::accumulators

#ifdef _MSC_VER
# pragma warning(pop)
#endif

#endif