boost/accumulators/statistics/tail_mean.hpp

   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::average<Sample, std::size_t>::result_type float_type;
  66         // for boost::result_of
  67         typedef float_type result_type;
  68
  69         coherent_tail_mean_impl(dont_care) {}
  70
  71         template<typename Args>
  72         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::average(quantile(args), n)
  86                  * (
  87                      ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
  88                      - numeric::average(n, count(args))
  89                    );
  90         }
  91     };
  92
  93     ///////////////////////////////////////////////////////////////////////////////
  94     // non_coherent_tail_mean_impl
  95     //
  96     /**
  97         @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails)
  98
  99         An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the
 100         \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the  \f$\lceil n(1-\alpha)\rceil\f$
 101         largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level:
 102
 103         \f[
 104             \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n}
 105         \f]
 106
 107         \f[
 108             \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n}
 109         \f]
 110
 111         It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$
 112         largest samples.
 113
 114         @param quantile_probability
 115     */
 116     template<typename Sample, typename LeftRight>
 117     struct non_coherent_tail_mean_impl
 118       : accumulator_base
 119     {
 120         typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
 121         // for boost::result_of
 122         typedef float_type result_type;
 123
 124         non_coherent_tail_mean_impl(dont_care) {}
 125
 126         template<typename Args>
 127         result_type result(Args const &args) const
 128         {
 129             std::size_t cnt = count(args);
 130
 131             std::size_t n = static_cast<std::size_t>(
 132                 std::ceil(
 133                     cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
 134                 )
 135             );
 136
 137             // If n is in a valid range, return result, otherwise return NaN or throw exception
 138             if (n <= static_cast<std::size_t>(tail(args).size()))
 139                 return numeric::average(
 140                     std::accumulate(
 141                         tail(args).begin()
 142                       , tail(args).begin() + n
 143                       , Sample(0)
 144                     )
 145                   , n
 146                 );
 147             else
 148             {
 149                 if (std::numeric_limits<result_type>::has_quiet_NaN)
 150                 {
 151                     return std::numeric_limits<result_type>::quiet_NaN();
 152                 }
 153                 else
 154                 {
 155                     std::ostringstream msg;
 156                     msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
 157                     boost::throw_exception(std::runtime_error(msg.str()));
 158                     return Sample(0);
 159                 }
 160             }
 161         }
 162     };
 163
 164 } // namespace impl
 165
 166
 167 ///////////////////////////////////////////////////////////////////////////////
 168 // tag::coherent_tail_mean<>
 169 // tag::non_coherent_tail_mean<>
 170 //
 171 namespace tag
 172 {
 173     template<typename LeftRight>
 174     struct coherent_tail_mean
 175       : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> >
 176     {
 177         typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
 178     };
 179
 180     template<typename LeftRight>
 181     struct non_coherent_tail_mean
 182       : depends_on<count, tail<LeftRight> >
 183     {
 184         typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
 185     };
 186
 187     struct abstract_non_coherent_tail_mean
 188       : depends_on<>
 189     {
 190     };
 191 }
 192
 193 ///////////////////////////////////////////////////////////////////////////////
 194 // extract::non_coherent_tail_mean;
 195 // extract::coherent_tail_mean;
 196 //
 197 namespace extract
 198 {
 199     extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {};
 200     extractor<tag::tail_mean> const coherent_tail_mean = {};
 201 }
 202
 203 using extract::non_coherent_tail_mean;
 204 using extract::coherent_tail_mean;
 205
 206 // for the purposes of feature-based dependency resolution,
 207 // coherent_tail_mean<LeftRight> provides the same feature as tail_mean
 208 template<typename LeftRight>
 209 struct feature_of<tag::coherent_tail_mean<LeftRight> >
 210   : feature_of<tag::tail_mean>
 211 {
 212 };
 213
 214 template<typename LeftRight>
 215 struct feature_of<tag::non_coherent_tail_mean<LeftRight> >
 216   : feature_of<tag::abstract_non_coherent_tail_mean>
 217 {
 218 };
 219
 220 // So that non_coherent_tail_mean can be automatically substituted
 221 // with weighted_non_coherent_tail_mean when the weight parameter is non-void.
 222 template<typename LeftRight>
 223 struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> >
 224 {
 225     typedef tag::non_coherent_weighted_tail_mean<LeftRight> type;
 226 };
 227
 228 template<typename LeftRight>
 229 struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> >
 230   : feature_of<tag::non_coherent_tail_mean<LeftRight> >
 231 {};
 232
 233 // NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean,
 234 // which is the base feature for coherent tail means, since (at least for
 235 // non-continuous distributions) non_coherent_tail_mean is a different measure!
 236
 237 }} // namespace boost::accumulators
 238
 239 #ifdef _MSC_VER
 240 # pragma warning(pop)
 241 #endif
 242
 243 #endif