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