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///////////////////////////////////////////////////////////////////////////////
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// tail_mean.hpp
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//
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//  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
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//  Software License, Version 1.0. (See accompanying file
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//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_HPP_DE_01_01_2006
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#define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_HPP_DE_01_01_2006
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#include <numeric>
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#include <vector>
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#include <limits>
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#include <functional>
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#include <sstream>
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#include <stdexcept>
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#include <boost/throw_exception.hpp>
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#include <boost/parameter/keyword.hpp>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/type_traits/is_same.hpp>
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#include <boost/accumulators/framework/accumulator_base.hpp>
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#include <boost/accumulators/framework/extractor.hpp>
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#include <boost/accumulators/numeric/functional.hpp>
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#include <boost/accumulators/framework/parameters/sample.hpp>
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#include <boost/accumulators/statistics_fwd.hpp>
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#include <boost/accumulators/statistics/count.hpp>
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#include <boost/accumulators/statistics/tail.hpp>
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#include <boost/accumulators/statistics/tail_quantile.hpp>
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#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
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#ifdef _MSC_VER
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# pragma warning(push)
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# pragma warning(disable: 4127) // conditional expression is constant
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#endif
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namespace boost { namespace accumulators
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{
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namespace impl
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{
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    ///////////////////////////////////////////////////////////////////////////////
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    // coherent_tail_mean_impl
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    //
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    /**
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        @brief Estimation of the coherent tail mean based on order statistics (for both left and right tails)
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        The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$
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        plus a correction term that ensures coherence in case of non-continuous distributions.
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        \f[
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            \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) +
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            \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right)
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        \f]
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        \f[
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            \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) +
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            \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right)
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        \f]
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    */
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    template<typename Sample, typename LeftRight>
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    struct coherent_tail_mean_impl
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      : accumulator_base
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    {
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        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
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        // for boost::result_of
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        typedef float_type result_type;
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        coherent_tail_mean_impl(dont_care) {}
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        template<typename Args>
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        result_type result(Args const &args) const
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        {
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            std::size_t cnt = count(args);
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            std::size_t n = static_cast<std::size_t>(
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                std::ceil(
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                    cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
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                )
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            );
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            extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {};
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            return some_non_coherent_tail_mean(args)
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                 + numeric::fdiv(quantile(args), n)
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                 * (
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                     ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
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                     - numeric::fdiv(n, count(args))
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                   );
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        }
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    };
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    ///////////////////////////////////////////////////////////////////////////////
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    // non_coherent_tail_mean_impl
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    //
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    /**
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        @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails)
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        An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the
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        \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the  \f$\lceil n(1-\alpha)\rceil\f$
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        largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level:
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        \f[
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            \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n}
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        \f]
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        \f[
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            \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n}
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        \f]
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        It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$
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        largest samples.
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        @param quantile_probability
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    */
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    template<typename Sample, typename LeftRight>
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    struct non_coherent_tail_mean_impl
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      : accumulator_base
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    {
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        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
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        // for boost::result_of
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        typedef float_type result_type;
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        non_coherent_tail_mean_impl(dont_care) {}
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        template<typename Args>
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        result_type result(Args const &args) const
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        {
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            std::size_t cnt = count(args);
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            std::size_t n = static_cast<std::size_t>(
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                std::ceil(
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                    cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
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                )
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            );
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            // If n is in a valid range, return result, otherwise return NaN or throw exception
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            if (n <= static_cast<std::size_t>(tail(args).size()))
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                return numeric::fdiv(
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                    std::accumulate(
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                        tail(args).begin()
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                      , tail(args).begin() + n
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                      , Sample(0)
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                    )
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                  , n
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                );
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            else
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            {
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                if (std::numeric_limits<result_type>::has_quiet_NaN)
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                {
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                    return std::numeric_limits<result_type>::quiet_NaN();
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                }
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                else
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                {
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                    std::ostringstream msg;
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                    msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
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                    boost::throw_exception(std::runtime_error(msg.str()));
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                    return Sample(0);
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                }
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            }
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        }
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    };
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag::coherent_tail_mean<>
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// tag::non_coherent_tail_mean<>
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//
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namespace tag
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{
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    template<typename LeftRight>
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    struct coherent_tail_mean
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      : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> >
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    {
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        typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
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    };
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    template<typename LeftRight>
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    struct non_coherent_tail_mean
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      : depends_on<count, tail<LeftRight> >
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    {
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        typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
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    };
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    struct abstract_non_coherent_tail_mean
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      : depends_on<>
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    {
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    };
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::non_coherent_tail_mean;
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// extract::coherent_tail_mean;
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//
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namespace extract
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{
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    extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {};
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    extractor<tag::tail_mean> const coherent_tail_mean = {};
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    BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean)
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    BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean)
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}
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using extract::non_coherent_tail_mean;
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using extract::coherent_tail_mean;
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// for the purposes of feature-based dependency resolution,
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// coherent_tail_mean<LeftRight> provides the same feature as tail_mean
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template<typename LeftRight>
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struct feature_of<tag::coherent_tail_mean<LeftRight> >
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  : feature_of<tag::tail_mean>
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{
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};
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template<typename LeftRight>
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struct feature_of<tag::non_coherent_tail_mean<LeftRight> >
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  : feature_of<tag::abstract_non_coherent_tail_mean>
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{
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};
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// So that non_coherent_tail_mean can be automatically substituted
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// with weighted_non_coherent_tail_mean when the weight parameter is non-void.
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template<typename LeftRight>
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struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> >
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{
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    typedef tag::non_coherent_weighted_tail_mean<LeftRight> type;
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};
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template<typename LeftRight>
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struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> >
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  : feature_of<tag::non_coherent_tail_mean<LeftRight> >
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{};
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// NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean,
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// which is the base feature for coherent tail means, since (at least for
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// non-continuous distributions) non_coherent_tail_mean is a different measure!
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}} // namespace boost::accumulators
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#ifdef _MSC_VER
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# pragma warning(pop)
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#endif
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#endif