/////////////////////////////////////////////////////////////////////////////// | |
// weighted_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_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006 | |
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/numeric/functional.hpp> | |
#include <boost/accumulators/framework/accumulator_base.hpp> | |
#include <boost/accumulators/framework/extractor.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_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 | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// coherent_weighted_tail_mean_impl | |
// | |
// TODO | |
/////////////////////////////////////////////////////////////////////////////// | |
// non_coherent_weighted_tail_mean_impl | |
// | |
/** | |
@brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails) | |
An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean | |
of the | |
\f[ | |
\lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} | |
\f] | |
smallest samples (left tail) or the weighted mean of the | |
\f[ | |
n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\} | |
\f] | |
largest samples (right tail) above a quantile \f$\hat{q}_{\alpha}\f$ of level \f$\alpha\f$, \f$n\f$ being the total number of sample | |
and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights: | |
\f[ | |
\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i}, | |
\f] | |
\f[ | |
\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}. | |
\f] | |
@param quantile_probability | |
*/ | |
template<typename Sample, typename Weight, typename LeftRight> | |
struct non_coherent_weighted_tail_mean_impl | |
: accumulator_base | |
{ | |
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
typedef typename numeric::functional::average<Weight, std::size_t>::result_type float_type; | |
// for boost::result_of | |
typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type result_type; | |
non_coherent_weighted_tail_mean_impl(dont_care) {} | |
template<typename Args> | |
result_type result(Args const &args) const | |
{ | |
float_type threshold = sum_of_weights(args) | |
* ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); | |
std::size_t n = 0; | |
Weight sum = Weight(0); | |
while (sum < threshold) | |
{ | |
if (n < static_cast<std::size_t>(tail_weights(args).size())) | |
{ | |
sum += *(tail_weights(args).begin() + n); | |
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 result_type(0); | |
} | |
} | |
} | |
return numeric::average( | |
std::inner_product( | |
tail(args).begin() | |
, tail(args).begin() + n | |
, tail_weights(args).begin() | |
, weighted_sample(0) | |
) | |
, sum | |
); | |
} | |
}; | |
} // namespace impl | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::non_coherent_weighted_tail_mean<> | |
// | |
namespace tag | |
{ | |
template<typename LeftRight> | |
struct non_coherent_weighted_tail_mean | |
: depends_on<sum_of_weights, tail_weights<LeftRight> > | |
{ | |
typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl; | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::non_coherent_weighted_tail_mean; | |
// | |
namespace extract | |
{ | |
extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean) | |
} | |
using extract::non_coherent_weighted_tail_mean; | |
}} // namespace boost::accumulators | |
#ifdef _MSC_VER | |
# pragma warning(pop) | |
#endif | |
#endif |