1 /////////////////////////////////////////////////////////////////////////////// 2 // weighted_tail_quantile.hpp 3 // 4 // Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost 5 // Software License, Version 1.0. (See accompanying file 6 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) 7 8 #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006 9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006 10 11 #include <vector> 12 #include <limits> 13 #include <functional> 14 #include <sstream> 15 #include <stdexcept> 16 #include <boost/throw_exception.hpp> 17 #include <boost/parameter/keyword.hpp> 18 #include <boost/mpl/placeholders.hpp> 19 #include <boost/mpl/if.hpp> 20 #include <boost/type_traits/is_same.hpp> 21 #include <boost/accumulators/numeric/functional.hpp> 22 #include <boost/accumulators/framework/depends_on.hpp> 23 #include <boost/accumulators/framework/accumulator_base.hpp> 24 #include <boost/accumulators/framework/extractor.hpp> 25 #include <boost/accumulators/framework/parameters/sample.hpp> 26 #include <boost/accumulators/statistics_fwd.hpp> 27 #include <boost/accumulators/statistics/tail.hpp> 28 #include <boost/accumulators/statistics/tail_quantile.hpp> 29 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> 30 31 #ifdef _MSC_VER 32 # pragma warning(push) 33 # pragma warning(disable: 4127) // conditional expression is constant 34 #endif 35 36 namespace boost { namespace accumulators 37 { 38 39 namespace impl 40 { 41 /////////////////////////////////////////////////////////////////////////////// 42 // weighted_tail_quantile_impl 43 // Tail quantile estimation based on order statistics of weighted samples 44 /** 45 @brief Tail quantile estimation based on order statistics of weighted samples (for both left and right tails) 46 47 An estimator \f$\hat{q}\f$ of tail quantiles with level \f$\alpha\f$ based on order statistics 48 \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) 49 and \f$X_{\rho:n}\f$ (right tail), where 50 51 \f[ 52 \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} 53 \f] 54 55 and 56 57 \f[ 58 \rho = \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\}, 59 \f] 60 61 \f$n\f$ being the number of samples and \f$\bar{w}_n\f$ the sum of all weights. 62 63 @param quantile_probability 64 */ 65 template<typename Sample, typename Weight, typename LeftRight> 66 struct weighted_tail_quantile_impl 67 : accumulator_base 68 { 69 typedef typename numeric::functional::average<Weight, std::size_t>::result_type float_type; 70 // for boost::result_of 71 typedef Sample result_type; 72 weighted_tail_quantile_implboost::accumulators::impl::weighted_tail_quantile_impl73 weighted_tail_quantile_impl(dont_care) {} 74 75 template<typename Args> resultboost::accumulators::impl::weighted_tail_quantile_impl76 result_type result(Args const &args) const 77 { 78 float_type threshold = sum_of_weights(args) 79 * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); 80 81 std::size_t n = 0; 82 Weight sum = Weight(0); 83 84 while (sum < threshold) 85 { 86 if (n < static_cast<std::size_t>(tail_weights(args).size())) 87 { 88 sum += *(tail_weights(args).begin() + n); 89 n++; 90 } 91 else 92 { 93 if (std::numeric_limits<result_type>::has_quiet_NaN) 94 { 95 return std::numeric_limits<result_type>::quiet_NaN(); 96 } 97 else 98 { 99 std::ostringstream msg; 100 msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; 101 boost::throw_exception(std::runtime_error(msg.str())); 102 return Sample(0); 103 } 104 } 105 } 106 107 // Note that the cached samples of the left are sorted in ascending order, 108 // whereas the samples of the right tail are sorted in descending order 109 return *(boost::begin(tail(args)) + n - 1); 110 } 111 }; 112 } // namespace impl 113 114 /////////////////////////////////////////////////////////////////////////////// 115 // tag::weighted_tail_quantile<> 116 // 117 namespace tag 118 { 119 template<typename LeftRight> 120 struct weighted_tail_quantile 121 : depends_on<sum_of_weights, tail_weights<LeftRight> > 122 { 123 /// INTERNAL ONLY 124 typedef accumulators::impl::weighted_tail_quantile_impl<mpl::_1, mpl::_2, LeftRight> impl; 125 }; 126 } 127 128 /////////////////////////////////////////////////////////////////////////////// 129 // extract::weighted_tail_quantile 130 // 131 namespace extract 132 { 133 extractor<tag::quantile> const weighted_tail_quantile = {}; 134 } 135 136 using extract::weighted_tail_quantile; 137 138 }} // namespace boost::accumulators 139 140 #ifdef _MSC_VER 141 # pragma warning(pop) 142 #endif 143 144 #endif 145