boost/accumulators/statistics/weighted_tail_variate_means.hpp

   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     // mutliplies 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::average<Weight, Weight>::result_type float_type;
 111         typedef typename numeric::functional::average<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(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               , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor)
 173             );
 174
 175             return make_iterator_range(this->tail_means_);
 176         }
 177
 178     private:
 179
 180         mutable array_type tail_means_;
 181
 182     };
 183
 184 } // namespace impl
 185
 186 ///////////////////////////////////////////////////////////////////////////////
 187 // tag::absolute_weighted_tail_variate_means
 188 // tag::relative_weighted_tail_variate_means
 189 //
 190 namespace tag
 191 {
 192     template<typename LeftRight, typename VariateType, typename VariateTag>
 193     struct absolute_weighted_tail_variate_means
 194       : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
 195     {
 196         typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl;
 197     };
 198     template<typename LeftRight, typename VariateType, typename VariateTag>
 199     struct relative_weighted_tail_variate_means
 200       : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
 201     {
 202         typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl;
 203     };
 204 }
 205
 206 ///////////////////////////////////////////////////////////////////////////////
 207 // extract::weighted_tail_variate_means
 208 // extract::relative_weighted_tail_variate_means
 209 //
 210 namespace extract
 211 {
 212     extractor<tag::abstract_absolute_tail_variate_means> const weighted_tail_variate_means = {};
 213     extractor<tag::abstract_relative_tail_variate_means> const relative_weighted_tail_variate_means = {};
 214 }
 215
 216 using extract::weighted_tail_variate_means;
 217 using extract::relative_weighted_tail_variate_means;
 218
 219 // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
 220 template<typename LeftRight, typename VariateType, typename VariateTag>
 221 struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
 222 {
 223     typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 224 };
 225
 226 // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
 227 template<typename LeftRight, typename VariateType, typename VariateTag>
 228 struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
 229 {
 230     typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 231 };
 232
 233 }} // namespace boost::accumulators
 234
 235 #ifdef _MSC_VER
 236 # pragma warning(pop)
 237 #endif
 238
 239 #endif