boost/accumulators/statistics/tail_variate_means.hpp

   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
  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         @brief Estimation of the absolute and relative tail variate means (for both left and right tails)
  43
  44         For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
  45         \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
  46         \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
  47         the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
  48         tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
  49
  50         \f[
  51             \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
  52                 \frac{1}{\lceil n(1-\alpha) \rceil}
  53                 \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
  54         \f]
  55
  56         \f[
  57             \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
  58                 \frac{1}{\lceil n\alpha \rceil}
  59                 \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
  60         \f]
  61
  62         \f[
  63             \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
  64                 \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
  65             {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
  66         \f]
  67
  68         \f[
  69             \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
  70                 \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
  71             {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
  72         \f]
  73     */
  74
  75     ///////////////////////////////////////////////////////////////////////////////
  76     // tail_variate_means_impl
  77     //  by default: absolute tail_variate_means
  78     template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
  79     struct tail_variate_means_impl
  80       : accumulator_base
  81     {
  82         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
  83         typedef std::vector<float_type> array_type;
  84         // for boost::result_of
  85         typedef iterator_range<typename array_type::iterator> result_type;
  86
  87         tail_variate_means_impl(dont_care) {}
  88
  89         template<typename Args>
  90         result_type result(Args const &args) const
  91         {
  92             std::size_t cnt = count(args);
  93
  94             std::size_t n = static_cast<std::size_t>(
  95                 std::ceil(
  96                     cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
  97                 )
  98             );
  99
 100             std::size_t num_variates = tail_variate(args).begin()->size();
 101
 102             this->tail_means_.clear();
 103             this->tail_means_.resize(num_variates, Sample(0));
 104
 105             // If n is in a valid range, return result, otherwise return NaN or throw exception
 106             if (n < static_cast<std::size_t>(tail(args).size()))
 107             {
 108                 this->tail_means_ = std::accumulate(
 109                     tail_variate(args).begin()
 110                   , tail_variate(args).begin() + n
 111                   , this->tail_means_
 112                   , numeric::plus
 113                 );
 114
 115                 float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );
 116
 117                 std::transform(
 118                     this->tail_means_.begin()
 119                   , this->tail_means_.end()
 120                   , this->tail_means_.begin()
 121                   , std::bind2nd(std::divides<float_type>(), factor)
 122                 );
 123             }
 124             else
 125             {
 126                 if (std::numeric_limits<float_type>::has_quiet_NaN)
 127                 {
 128                     std::fill(
 129                         this->tail_means_.begin()
 130                       , this->tail_means_.end()
 131                       , std::numeric_limits<float_type>::quiet_NaN()
 132                     );
 133                 }
 134                 else
 135                 {
 136                     std::ostringstream msg;
 137                     msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
 138                     boost::throw_exception(std::runtime_error(msg.str()));
 139                 }
 140             }
 141             return make_iterator_range(this->tail_means_);
 142         }
 143
 144     private:
 145
 146         mutable array_type tail_means_;
 147
 148     };
 149
 150 } // namespace impl
 151
 152 ///////////////////////////////////////////////////////////////////////////////
 153 // tag::absolute_tail_variate_means
 154 // tag::relative_tail_variate_means
 155 //
 156 namespace tag
 157 {
 158     template<typename LeftRight, typename VariateType, typename VariateTag>
 159     struct absolute_tail_variate_means
 160       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
 161     {
 162         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
 163     };
 164     template<typename LeftRight, typename VariateType, typename VariateTag>
 165     struct relative_tail_variate_means
 166       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
 167     {
 168         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
 169     };
 170     struct abstract_absolute_tail_variate_means
 171       : depends_on<>
 172     {
 173     };
 174     struct abstract_relative_tail_variate_means
 175       : depends_on<>
 176     {
 177     };
 178 }
 179
 180 ///////////////////////////////////////////////////////////////////////////////
 181 // extract::tail_variate_means
 182 // extract::relative_tail_variate_means
 183 //
 184 namespace extract
 185 {
 186     extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {};
 187     extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {};
 188
 189     BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means)
 190     BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means)
 191 }
 192
 193 using extract::tail_variate_means;
 194 using extract::relative_tail_variate_means;
 195
 196 // tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
 197 template<typename LeftRight, typename VariateType, typename VariateTag>
 198 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
 199 {
 200     typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 201 };
 202
 203 // tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
 204 template<typename LeftRight, typename VariateType, typename VariateTag>
 205 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
 206 {
 207     typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 208 };
 209
 210 // Provides non-templatized extractor
 211 template<typename LeftRight, typename VariateType, typename VariateTag>
 212 struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 213   : feature_of<tag::abstract_absolute_tail_variate_means>
 214 {
 215 };
 216
 217 // Provides non-templatized extractor
 218 template<typename LeftRight, typename VariateType, typename VariateTag>
 219 struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 220   : feature_of<tag::abstract_relative_tail_variate_means>
 221 {
 222 };
 223
 224 // So that absolute_tail_means can be automatically substituted
 225 // with absolute_weighted_tail_means when the weight parameter is non-void.
 226 template<typename LeftRight, typename VariateType, typename VariateTag>
 227 struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 228 {
 229     typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 230 };
 231
 232 template<typename LeftRight, typename VariateType, typename VariateTag>
 233 struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
 234   : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 235 {
 236 };
 237
 238 // So that relative_tail_means can be automatically substituted
 239 // with relative_weighted_tail_means when the weight parameter is non-void.
 240 template<typename LeftRight, typename VariateType, typename VariateTag>
 241 struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 242 {
 243     typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 244 };
 245
 246 template<typename LeftRight, typename VariateType, typename VariateTag>
 247 struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
 248   : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 249 {
 250 };
 251
 252 }} // namespace boost::accumulators
 253
 254 #ifdef _MSC_VER
 255 # pragma warning(pop)
 256 #endif
 257
 258 #endif