1 /////////////////////////////////////////////////////////////////////////////// 2 // tail_variate_means.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_VARIATE_MEANS_HPP_DE_01_01_2006 9 #define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_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/tail.hpp> 27 #include <boost/accumulators/statistics/tail_variate.hpp> 28 #include <boost/accumulators/statistics/tail_mean.hpp> 29 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> 30 #include <boost/serialization/vector.hpp> 31 32 #ifdef _MSC_VER 33 # pragma warning(push) 34 # pragma warning(disable: 4127) // conditional expression is constant 35 #endif 36 37 namespace boost { namespace accumulators 38 { 39 40 namespace impl 41 { 42 /** 43 @brief Estimation of the absolute and relative tail variate means (for both left and right tails) 44 45 For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the 46 \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means 47 \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively, 48 the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute 49 tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$. 50 51 \f[ 52 \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = 53 \frac{1}{\lceil n(1-\alpha) \rceil} 54 \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i} 55 \f] 56 57 \f[ 58 \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = 59 \frac{1}{\lceil n\alpha \rceil} 60 \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i} 61 \f] 62 63 \f[ 64 \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = 65 \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}} 66 {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} 67 \f] 68 69 \f[ 70 \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = 71 \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}} 72 {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} 73 \f] 74 */ 75 76 /////////////////////////////////////////////////////////////////////////////// 77 // tail_variate_means_impl 78 // by default: absolute tail_variate_means 79 template<typename Sample, typename Impl, typename LeftRight, typename VariateTag> 80 struct tail_variate_means_impl 81 : accumulator_base 82 { 83 typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; 84 typedef std::vector<float_type> array_type; 85 // for boost::result_of 86 typedef iterator_range<typename array_type::iterator> result_type; 87 tail_variate_means_implboost::accumulators::impl::tail_variate_means_impl88 tail_variate_means_impl(dont_care) {} 89 90 template<typename Args> resultboost::accumulators::impl::tail_variate_means_impl91 result_type result(Args const &args) const 92 { 93 std::size_t cnt = count(args); 94 95 std::size_t n = static_cast<std::size_t>( 96 std::ceil( 97 cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) 98 ) 99 ); 100 101 std::size_t num_variates = tail_variate(args).begin()->size(); 102 103 this->tail_means_.clear(); 104 this->tail_means_.resize(num_variates, Sample(0)); 105 106 // If n is in a valid range, return result, otherwise return NaN or throw exception 107 if (n < static_cast<std::size_t>(tail(args).size())) 108 { 109 this->tail_means_ = std::accumulate( 110 tail_variate(args).begin() 111 , tail_variate(args).begin() + n 112 , this->tail_means_ 113 , numeric::plus 114 ); 115 116 float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. ); 117 118 std::transform( 119 this->tail_means_.begin() 120 , this->tail_means_.end() 121 , this->tail_means_.begin() 122 #ifdef BOOST_NO_CXX98_BINDERS 123 , std::bind(std::divides<float_type>(), std::placeholders::_1, factor) 124 #else 125 , std::bind2nd(std::divides<float_type>(), factor) 126 #endif 127 ); 128 } 129 else 130 { 131 if (std::numeric_limits<float_type>::has_quiet_NaN) 132 { 133 std::fill( 134 this->tail_means_.begin() 135 , this->tail_means_.end() 136 , std::numeric_limits<float_type>::quiet_NaN() 137 ); 138 } 139 else 140 { 141 std::ostringstream msg; 142 msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; 143 boost::throw_exception(std::runtime_error(msg.str())); 144 } 145 } 146 return make_iterator_range(this->tail_means_); 147 } 148 149 // make this accumulator serializeable 150 template<class Archive> serializeboost::accumulators::impl::tail_variate_means_impl151 void serialize(Archive & ar, const unsigned int file_version) 152 { 153 ar & tail_means_; 154 } 155 156 private: 157 158 mutable array_type tail_means_; 159 160 }; 161 162 } // namespace impl 163 164 /////////////////////////////////////////////////////////////////////////////// 165 // tag::absolute_tail_variate_means 166 // tag::relative_tail_variate_means 167 // 168 namespace tag 169 { 170 template<typename LeftRight, typename VariateType, typename VariateTag> 171 struct absolute_tail_variate_means 172 : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> > 173 { 174 typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl; 175 }; 176 template<typename LeftRight, typename VariateType, typename VariateTag> 177 struct relative_tail_variate_means 178 : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> > 179 { 180 typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl; 181 }; 182 struct abstract_absolute_tail_variate_means 183 : depends_on<> 184 { 185 }; 186 struct abstract_relative_tail_variate_means 187 : depends_on<> 188 { 189 }; 190 } 191 192 /////////////////////////////////////////////////////////////////////////////// 193 // extract::tail_variate_means 194 // extract::relative_tail_variate_means 195 // 196 namespace extract 197 { 198 extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {}; 199 extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {}; 200 201 BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means) 202 BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means) 203 } 204 205 using extract::tail_variate_means; 206 using extract::relative_tail_variate_means; 207 208 // tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag> 209 template<typename LeftRight, typename VariateType, typename VariateTag> 210 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)> 211 { 212 typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type; 213 }; 214 215 // tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag> 216 template<typename LeftRight, typename VariateType, typename VariateTag> 217 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)> 218 { 219 typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type; 220 }; 221 222 // Provides non-templatized extractor 223 template<typename LeftRight, typename VariateType, typename VariateTag> 224 struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > 225 : feature_of<tag::abstract_absolute_tail_variate_means> 226 { 227 }; 228 229 // Provides non-templatized extractor 230 template<typename LeftRight, typename VariateType, typename VariateTag> 231 struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > 232 : feature_of<tag::abstract_relative_tail_variate_means> 233 { 234 }; 235 236 // So that absolute_tail_means can be automatically substituted 237 // with absolute_weighted_tail_means when the weight parameter is non-void. 238 template<typename LeftRight, typename VariateType, typename VariateTag> 239 struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > 240 { 241 typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; 242 }; 243 244 template<typename LeftRight, typename VariateType, typename VariateTag> 245 struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> > 246 : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > 247 { 248 }; 249 250 // So that relative_tail_means can be automatically substituted 251 // with relative_weighted_tail_means when the weight parameter is non-void. 252 template<typename LeftRight, typename VariateType, typename VariateTag> 253 struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > 254 { 255 typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; 256 }; 257 258 template<typename LeftRight, typename VariateType, typename VariateTag> 259 struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> > 260 : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > 261 { 262 }; 263 264 }} // namespace boost::accumulators 265 266 #ifdef _MSC_VER 267 # pragma warning(pop) 268 #endif 269 270 #endif 271