1 /////////////////////////////////////////////////////////////////////////////// 2 // tail_mean.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_TAIL_MEAN_HPP_DE_01_01_2006 9 #define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_HPP_DE_01_01_2006 10 11 #include <numeric> 12 #include <vector> 13 #include <limits> 14 #include <functional> 15 #include <sstream> 16 #include <stdexcept> 17 #include <boost/throw_exception.hpp> 18 #include <boost/parameter/keyword.hpp> 19 #include <boost/mpl/placeholders.hpp> 20 #include <boost/type_traits/is_same.hpp> 21 #include <boost/accumulators/framework/accumulator_base.hpp> 22 #include <boost/accumulators/framework/extractor.hpp> 23 #include <boost/accumulators/numeric/functional.hpp> 24 #include <boost/accumulators/framework/parameters/sample.hpp> 25 #include <boost/accumulators/statistics_fwd.hpp> 26 #include <boost/accumulators/statistics/count.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 /////////////////////////////////////////////////////////////////////////////// 43 // coherent_tail_mean_impl 44 // 45 /** 46 @brief Estimation of the coherent tail mean based on order statistics (for both left and right tails) 47 48 The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ 49 plus a correction term that ensures coherence in case of non-continuous distributions. 50 51 \f[ 52 \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) + 53 \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right) 54 \f] 55 56 \f[ 57 \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) + 58 \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right) 59 \f] 60 */ 61 template<typename Sample, typename LeftRight> 62 struct coherent_tail_mean_impl 63 : accumulator_base 64 { 65 typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; 66 // for boost::result_of 67 typedef float_type result_type; 68 coherent_tail_mean_implboost::accumulators::impl::coherent_tail_mean_impl69 coherent_tail_mean_impl(dont_care) {} 70 71 template<typename Args> resultboost::accumulators::impl::coherent_tail_mean_impl72 result_type result(Args const &args) const 73 { 74 std::size_t cnt = count(args); 75 76 std::size_t n = static_cast<std::size_t>( 77 std::ceil( 78 cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) 79 ) 80 ); 81 82 extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {}; 83 84 return some_non_coherent_tail_mean(args) 85 + numeric::fdiv(quantile(args), n) 86 * ( 87 ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] 88 - numeric::fdiv(n, count(args)) 89 ); 90 } 91 92 // serialization is done by accumulators it depends on 93 template<class Archive> serializeboost::accumulators::impl::coherent_tail_mean_impl94 void serialize(Archive & ar, const unsigned int file_version) {} 95 }; 96 97 /////////////////////////////////////////////////////////////////////////////// 98 // non_coherent_tail_mean_impl 99 // 100 /** 101 @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails) 102 103 An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the 104 \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the \f$\lceil n(1-\alpha)\rceil\f$ 105 largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level: 106 107 \f[ 108 \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n} 109 \f] 110 111 \f[ 112 \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n} 113 \f] 114 115 It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$ 116 largest samples. 117 118 @param quantile_probability 119 */ 120 template<typename Sample, typename LeftRight> 121 struct non_coherent_tail_mean_impl 122 : accumulator_base 123 { 124 typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; 125 // for boost::result_of 126 typedef float_type result_type; 127 non_coherent_tail_mean_implboost::accumulators::impl::non_coherent_tail_mean_impl128 non_coherent_tail_mean_impl(dont_care) {} 129 130 template<typename Args> resultboost::accumulators::impl::non_coherent_tail_mean_impl131 result_type result(Args const &args) const 132 { 133 std::size_t cnt = count(args); 134 135 std::size_t n = static_cast<std::size_t>( 136 std::ceil( 137 cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) 138 ) 139 ); 140 141 // If n is in a valid range, return result, otherwise return NaN or throw exception 142 if (n <= static_cast<std::size_t>(tail(args).size())) 143 return numeric::fdiv( 144 std::accumulate( 145 tail(args).begin() 146 , tail(args).begin() + n 147 , Sample(0) 148 ) 149 , n 150 ); 151 else 152 { 153 if (std::numeric_limits<result_type>::has_quiet_NaN) 154 { 155 return std::numeric_limits<result_type>::quiet_NaN(); 156 } 157 else 158 { 159 std::ostringstream msg; 160 msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; 161 boost::throw_exception(std::runtime_error(msg.str())); 162 return Sample(0); 163 } 164 } 165 } 166 167 // serialization is done by accumulators it depends on 168 template<class Archive> serializeboost::accumulators::impl::non_coherent_tail_mean_impl169 void serialize(Archive & ar, const unsigned int file_version) {} 170 }; 171 172 } // namespace impl 173 174 175 /////////////////////////////////////////////////////////////////////////////// 176 // tag::coherent_tail_mean<> 177 // tag::non_coherent_tail_mean<> 178 // 179 namespace tag 180 { 181 template<typename LeftRight> 182 struct coherent_tail_mean 183 : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> > 184 { 185 typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl; 186 }; 187 188 template<typename LeftRight> 189 struct non_coherent_tail_mean 190 : depends_on<count, tail<LeftRight> > 191 { 192 typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl; 193 }; 194 195 struct abstract_non_coherent_tail_mean 196 : depends_on<> 197 { 198 }; 199 } 200 201 /////////////////////////////////////////////////////////////////////////////// 202 // extract::non_coherent_tail_mean; 203 // extract::coherent_tail_mean; 204 // 205 namespace extract 206 { 207 extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {}; 208 extractor<tag::tail_mean> const coherent_tail_mean = {}; 209 210 BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean) 211 BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean) 212 } 213 214 using extract::non_coherent_tail_mean; 215 using extract::coherent_tail_mean; 216 217 // for the purposes of feature-based dependency resolution, 218 // coherent_tail_mean<LeftRight> provides the same feature as tail_mean 219 template<typename LeftRight> 220 struct feature_of<tag::coherent_tail_mean<LeftRight> > 221 : feature_of<tag::tail_mean> 222 { 223 }; 224 225 template<typename LeftRight> 226 struct feature_of<tag::non_coherent_tail_mean<LeftRight> > 227 : feature_of<tag::abstract_non_coherent_tail_mean> 228 { 229 }; 230 231 // So that non_coherent_tail_mean can be automatically substituted 232 // with weighted_non_coherent_tail_mean when the weight parameter is non-void. 233 template<typename LeftRight> 234 struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> > 235 { 236 typedef tag::non_coherent_weighted_tail_mean<LeftRight> type; 237 }; 238 239 template<typename LeftRight> 240 struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> > 241 : feature_of<tag::non_coherent_tail_mean<LeftRight> > 242 {}; 243 244 // NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean, 245 // which is the base feature for coherent tail means, since (at least for 246 // non-continuous distributions) non_coherent_tail_mean is a different measure! 247 248 }} // namespace boost::accumulators 249 250 #ifdef _MSC_VER 251 # pragma warning(pop) 252 #endif 253 254 #endif 255