/////////////////////////////////////////////////////////////////////////////// | |
// tail_mean.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_MEAN_HPP_DE_01_01_2006 | |
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_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/count.hpp> | |
#include <boost/accumulators/statistics/tail.hpp> | |
#include <boost/accumulators/statistics/tail_quantile.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 | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// coherent_tail_mean_impl | |
// | |
/** | |
@brief Estimation of the coherent tail mean based on order statistics (for both left and right tails) | |
The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ | |
plus a correction term that ensures coherence in case of non-continuous distributions. | |
\f[ | |
\widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) + | |
\frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right) | |
\f] | |
\f[ | |
\widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) + | |
\frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right) | |
\f] | |
*/ | |
template<typename Sample, typename LeftRight> | |
struct coherent_tail_mean_impl | |
: accumulator_base | |
{ | |
typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type; | |
// for boost::result_of | |
typedef float_type result_type; | |
coherent_tail_mean_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] ) | |
) | |
); | |
extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {}; | |
return some_non_coherent_tail_mean(args) | |
+ numeric::average(quantile(args), n) | |
* ( | |
( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] | |
- numeric::average(n, count(args)) | |
); | |
} | |
}; | |
/////////////////////////////////////////////////////////////////////////////// | |
// non_coherent_tail_mean_impl | |
// | |
/** | |
@brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails) | |
An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the | |
\f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the \f$\lceil n(1-\alpha)\rceil\f$ | |
largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level: | |
\f[ | |
\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n} | |
\f] | |
\f[ | |
\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n} | |
\f] | |
It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$ | |
largest samples. | |
@param quantile_probability | |
*/ | |
template<typename Sample, typename LeftRight> | |
struct non_coherent_tail_mean_impl | |
: accumulator_base | |
{ | |
typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type; | |
// for boost::result_of | |
typedef float_type result_type; | |
non_coherent_tail_mean_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] ) | |
) | |
); | |
// 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())) | |
return numeric::average( | |
std::accumulate( | |
tail(args).begin() | |
, tail(args).begin() + n | |
, Sample(0) | |
) | |
, n | |
); | |
else | |
{ | |
if (std::numeric_limits<result_type>::has_quiet_NaN) | |
{ | |
return std::numeric_limits<result_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 Sample(0); | |
} | |
} | |
} | |
}; | |
} // namespace impl | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::coherent_tail_mean<> | |
// tag::non_coherent_tail_mean<> | |
// | |
namespace tag | |
{ | |
template<typename LeftRight> | |
struct coherent_tail_mean | |
: depends_on<count, quantile, non_coherent_tail_mean<LeftRight> > | |
{ | |
typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl; | |
}; | |
template<typename LeftRight> | |
struct non_coherent_tail_mean | |
: depends_on<count, tail<LeftRight> > | |
{ | |
typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl; | |
}; | |
struct abstract_non_coherent_tail_mean | |
: depends_on<> | |
{ | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::non_coherent_tail_mean; | |
// extract::coherent_tail_mean; | |
// | |
namespace extract | |
{ | |
extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {}; | |
extractor<tag::tail_mean> const coherent_tail_mean = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean) | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean) | |
} | |
using extract::non_coherent_tail_mean; | |
using extract::coherent_tail_mean; | |
// for the purposes of feature-based dependency resolution, | |
// coherent_tail_mean<LeftRight> provides the same feature as tail_mean | |
template<typename LeftRight> | |
struct feature_of<tag::coherent_tail_mean<LeftRight> > | |
: feature_of<tag::tail_mean> | |
{ | |
}; | |
template<typename LeftRight> | |
struct feature_of<tag::non_coherent_tail_mean<LeftRight> > | |
: feature_of<tag::abstract_non_coherent_tail_mean> | |
{ | |
}; | |
// So that non_coherent_tail_mean can be automatically substituted | |
// with weighted_non_coherent_tail_mean when the weight parameter is non-void. | |
template<typename LeftRight> | |
struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> > | |
{ | |
typedef tag::non_coherent_weighted_tail_mean<LeftRight> type; | |
}; | |
template<typename LeftRight> | |
struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> > | |
: feature_of<tag::non_coherent_tail_mean<LeftRight> > | |
{}; | |
// NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean, | |
// which is the base feature for coherent tail means, since (at least for | |
// non-continuous distributions) non_coherent_tail_mean is a different measure! | |
}} // namespace boost::accumulators | |
#ifdef _MSC_VER | |
# pragma warning(pop) | |
#endif | |
#endif |