| 1 | /////////////////////////////////////////////////////////////////////////////// |
| 2 | // weighted_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_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006 |
| 9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/numeric/functional.hpp> |
| 22 | #include <boost/accumulators/framework/accumulator_base.hpp> |
| 23 | #include <boost/accumulators/framework/extractor.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_variate_means.hpp> |
| 29 | #include <boost/accumulators/statistics/weighted_tail_mean.hpp> |
| 30 | #include <boost/accumulators/statistics/parameters/quantile_probability.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 |
| 38 | { |
| 39 | // for _BinaryOperatrion2 in std::inner_product below |
| 40 | // multiplies two values and promotes the result to double |
| 41 | namespace numeric { namespace functional |
| 42 | { |
| 43 | /////////////////////////////////////////////////////////////////////////////// |
| 44 | // numeric::functional::multiply_and_promote_to_double |
| 45 | template<typename T, typename U> |
| 46 | struct multiply_and_promote_to_double |
| 47 | : multiplies<T, double const> |
| 48 | { |
| 49 | }; |
| 50 | }} |
| 51 | } |
| 52 | |
| 53 | namespace boost { namespace accumulators |
| 54 | { |
| 55 | |
| 56 | namespace impl |
| 57 | { |
| 58 | /** |
| 59 | @brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails) |
| 60 | |
| 61 | For all \f$j\f$-th variates associated to the |
| 62 | |
| 63 | \f[ |
| 64 | \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} |
| 65 | \f] |
| 66 | |
| 67 | smallest samples (left tail) or the weighted mean of the |
| 68 | |
| 69 | \f[ |
| 70 | 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\} |
| 71 | \f] |
| 72 | |
| 73 | largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ |
| 74 | are computed and returned as an iterator range. Alternatively, the relative weighted tail means |
| 75 | \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means |
| 76 | normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$. |
| 77 | |
| 78 | \f[ |
| 79 | \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = |
| 80 | \frac{1}{\sum_{i=\rho}^n w_i} |
| 81 | \sum_{i=\rho}^n w_i \xi_{j,i} |
| 82 | \f] |
| 83 | |
| 84 | \f[ |
| 85 | \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = |
| 86 | \frac{1}{\sum_{i=1}^{\lambda}} |
| 87 | \sum_{i=1}^{\lambda} w_i \xi_{j,i} |
| 88 | \f] |
| 89 | |
| 90 | \f[ |
| 91 | \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = |
| 92 | \frac{\sum_{i=\rho}^n w_i \xi_{j,i}} |
| 93 | {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} |
| 94 | \f] |
| 95 | |
| 96 | \f[ |
| 97 | \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = |
| 98 | \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}} |
| 99 | {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} |
| 100 | \f] |
| 101 | */ |
| 102 | |
| 103 | /////////////////////////////////////////////////////////////////////////////// |
| 104 | // weighted_tail_variate_means_impl |
| 105 | // by default: absolute weighted_tail_variate_means |
| 106 | template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType> |
| 107 | struct weighted_tail_variate_means_impl |
| 108 | : accumulator_base |
| 109 | { |
| 110 | typedef typename numeric::functional::fdiv<Weight, Weight>::result_type float_type; |
| 111 | typedef typename numeric::functional::fdiv<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type; |
| 112 | // for boost::result_of |
| 113 | typedef iterator_range<typename array_type::iterator> result_type; |
| 114 | |
| 115 | weighted_tail_variate_means_impl(dont_care) {} |
| 116 | |
| 117 | template<typename Args> |
| 118 | result_type result(Args const &args) const |
| 119 | { |
| 120 | float_type threshold = sum_of_weights(args) |
| 121 | * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); |
| 122 | |
| 123 | std::size_t n = 0; |
| 124 | Weight sum = Weight(0); |
| 125 | |
| 126 | while (sum < threshold) |
| 127 | { |
| 128 | if (n < static_cast<std::size_t>(tail_weights(args).size())) |
| 129 | { |
| 130 | sum += *(tail_weights(args).begin() + n); |
| 131 | n++; |
| 132 | } |
| 133 | else |
| 134 | { |
| 135 | if (std::numeric_limits<float_type>::has_quiet_NaN) |
| 136 | { |
| 137 | std::fill( |
| 138 | this->tail_means_.begin() |
| 139 | , this->tail_means_.end() |
| 140 | , std::numeric_limits<float_type>::quiet_NaN() |
| 141 | ); |
| 142 | } |
| 143 | else |
| 144 | { |
| 145 | std::ostringstream msg; |
| 146 | msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")" ; |
| 147 | boost::throw_exception(e: std::runtime_error(msg.str())); |
| 148 | } |
| 149 | } |
| 150 | } |
| 151 | |
| 152 | std::size_t num_variates = tail_variate(args).begin()->size(); |
| 153 | |
| 154 | this->tail_means_.clear(); |
| 155 | this->tail_means_.resize(num_variates, Sample(0)); |
| 156 | |
| 157 | this->tail_means_ = std::inner_product( |
| 158 | tail_variate(args).begin() |
| 159 | , tail_variate(args).begin() + n |
| 160 | , tail_weights(args).begin() |
| 161 | , this->tail_means_ |
| 162 | , numeric::functional::plus<array_type const, array_type const>() |
| 163 | , numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>() |
| 164 | ); |
| 165 | |
| 166 | float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. ); |
| 167 | |
| 168 | std::transform( |
| 169 | this->tail_means_.begin() |
| 170 | , this->tail_means_.end() |
| 171 | , this->tail_means_.begin() |
| 172 | #ifdef BOOST_NO_CXX98_BINDERS |
| 173 | , std::bind(numeric::functional::divides<typename array_type::value_type const, float_type const>(), std::placeholders::_1, factor) |
| 174 | #else |
| 175 | , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor) |
| 176 | #endif |
| 177 | ); |
| 178 | |
| 179 | return make_iterator_range(this->tail_means_); |
| 180 | } |
| 181 | |
| 182 | // make this accumulator serializeable |
| 183 | template<class Archive> |
| 184 | void serialize(Archive & ar, const unsigned int file_version) |
| 185 | { |
| 186 | ar & tail_means_; |
| 187 | } |
| 188 | |
| 189 | private: |
| 190 | |
| 191 | mutable array_type tail_means_; |
| 192 | |
| 193 | }; |
| 194 | |
| 195 | } // namespace impl |
| 196 | |
| 197 | /////////////////////////////////////////////////////////////////////////////// |
| 198 | // tag::absolute_weighted_tail_variate_means |
| 199 | // tag::relative_weighted_tail_variate_means |
| 200 | // |
| 201 | namespace tag |
| 202 | { |
| 203 | template<typename LeftRight, typename VariateType, typename VariateTag> |
| 204 | struct absolute_weighted_tail_variate_means |
| 205 | : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > |
| 206 | { |
| 207 | typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl; |
| 208 | }; |
| 209 | template<typename LeftRight, typename VariateType, typename VariateTag> |
| 210 | struct relative_weighted_tail_variate_means |
| 211 | : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > |
| 212 | { |
| 213 | typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl; |
| 214 | }; |
| 215 | } |
| 216 | |
| 217 | /////////////////////////////////////////////////////////////////////////////// |
| 218 | // extract::weighted_tail_variate_means |
| 219 | // extract::relative_weighted_tail_variate_means |
| 220 | // |
| 221 | namespace extract |
| 222 | { |
| 223 | extractor<tag::abstract_absolute_tail_variate_means> const = {}; |
| 224 | extractor<tag::abstract_relative_tail_variate_means> const = {}; |
| 225 | |
| 226 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means) |
| 227 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_weighted_tail_variate_means) |
| 228 | } |
| 229 | |
| 230 | using extract::weighted_tail_variate_means; |
| 231 | using extract::relative_weighted_tail_variate_means; |
| 232 | |
| 233 | // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> |
| 234 | template<typename LeftRight, typename VariateType, typename VariateTag> |
| 235 | struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)> |
| 236 | { |
| 237 | typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; |
| 238 | }; |
| 239 | |
| 240 | // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> |
| 241 | template<typename LeftRight, typename VariateType, typename VariateTag> |
| 242 | struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)> |
| 243 | { |
| 244 | typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; |
| 245 | }; |
| 246 | |
| 247 | }} // namespace boost::accumulators |
| 248 | |
| 249 | #ifdef _MSC_VER |
| 250 | # pragma warning(pop) |
| 251 | #endif |
| 252 | |
| 253 | #endif |
| 254 | |