boost/accumulators/statistics/tail_mean.hpp
///////////////////////////////////////////////////////////////////////////////
// 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::fdiv<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::fdiv(quantile(args), n)
* (
( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
- numeric::fdiv(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::fdiv<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::fdiv(
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