/////////////////////////////////////////////////////////////////////////////// | |
// 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 = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means) | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(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 |