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///////////////////////////////////////////////////////////////////////////////
// weighted_tail_quantile.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_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006
#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/mpl/if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.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_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
{
///////////////////////////////////////////////////////////////////////////////
// weighted_tail_quantile_impl
// Tail quantile estimation based on order statistics of weighted samples
/**
@brief Tail quantile estimation based on order statistics of weighted samples (for both left and right tails)
An estimator \f$\hat{q}\f$ of tail quantiles with level \f$\alpha\f$ based on order statistics
\f$X_{1:n} \leq X_{2:n} \leq\dots\leq X_{n:n}\f$ of weighted samples are given by \f$X_{\lambda:n}\f$ (left tail)
and \f$X_{\rho:n}\f$ (right tail), where
\f[
\lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
\f]
and
\f[
\rho = \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\},
\f]
\f$n\f$ being the number of samples and \f$\bar{w}_n\f$ the sum of all weights.
@param quantile_probability
*/
template<typename Sample, typename Weight, typename LeftRight>
struct weighted_tail_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::average<Weight, std::size_t>::result_type float_type;
// for boost::result_of
typedef Sample result_type;
weighted_tail_quantile_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 Sample(0);
}
}
}
// Note that the cached samples of the left are sorted in ascending order,
// whereas the samples of the right tail are sorted in descending order
return *(boost::begin(tail(args)) + n - 1);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_tail_quantile<>
//
namespace tag
{
template<typename LeftRight>
struct weighted_tail_quantile
: depends_on<sum_of_weights, tail_weights<LeftRight> >
{
/// INTERNAL ONLY
typedef accumulators::impl::weighted_tail_quantile_impl<mpl::_1, mpl::_2, LeftRight> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_tail_quantile
//
namespace extract
{
extractor<tag::quantile> const weighted_tail_quantile = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_quantile)
}
using extract::weighted_tail_quantile;
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif
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