boost/accumulators/statistics/weighted_tail_quantile.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // weighted_tail_quantile.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_QUANTILE_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006
  10
  11 #include <vector>
  12 #include <limits>
  13 #include <functional>
  14 #include <sstream>
  15 #include <stdexcept>
  16 #include <boost/throw_exception.hpp>
  17 #include <boost/parameter/keyword.hpp>
  18 #include <boost/mpl/placeholders.hpp>
  19 #include <boost/mpl/if.hpp>
  20 #include <boost/type_traits/is_same.hpp>
  21 #include <boost/accumulators/numeric/functional.hpp>
  22 #include <boost/accumulators/framework/depends_on.hpp>
  23 #include <boost/accumulators/framework/accumulator_base.hpp>
  24 #include <boost/accumulators/framework/extractor.hpp>
  25 #include <boost/accumulators/framework/parameters/sample.hpp>
  26 #include <boost/accumulators/statistics_fwd.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     // weighted_tail_quantile_impl
  43     //  Tail quantile estimation based on order statistics of weighted samples
  44     /**
  45         @brief Tail quantile estimation based on order statistics of weighted samples (for both left and right tails)
  46
  47         An estimator \f$\hat{q}\f$ of tail quantiles with level \f$\alpha\f$ based on order statistics
  48         \f$X_{1:n} \leq X_{2:n} \leq\dots\leq X_{n:n}\f$ of weighted samples are given by \f$X_{\lambda:n}\f$ (left tail)
  49         and \f$X_{\rho:n}\f$ (right tail), where
  50
  51             \f[
  52                 \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
  53             \f]
  54
  55         and
  56
  57             \f[
  58                 \rho = \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\},
  59             \f]
  60
  61         \f$n\f$ being the number of samples and \f$\bar{w}_n\f$ the sum of all weights.
  62
  63         @param quantile_probability
  64     */
  65     template<typename Sample, typename Weight, typename LeftRight>
  66     struct weighted_tail_quantile_impl
  67       : accumulator_base
  68     {
  69         typedef typename numeric::functional::average<Weight, std::size_t>::result_type float_type;
  70         // for boost::result_of
  71         typedef Sample result_type;
  72
  73         weighted_tail_quantile_impl(dont_care) {}
  74
  75         template<typename Args>
  76         result_type result(Args const &args) const
  77         {
  78             float_type threshold = sum_of_weights(args)
  79                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
  80
  81             std::size_t n = 0;
  82             Weight sum = Weight(0);
  83
  84             while (sum < threshold)
  85             {
  86                 if (n < static_cast<std::size_t>(tail_weights(args).size()))
  87                 {
  88                     sum += *(tail_weights(args).begin() + n);
  89                     n++;
  90                 }
  91                 else
  92                 {
  93                     if (std::numeric_limits<result_type>::has_quiet_NaN)
  94                     {
  95                         return std::numeric_limits<result_type>::quiet_NaN();
  96                     }
  97                     else
  98                     {
  99                         std::ostringstream msg;
 100                         msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
 101                         boost::throw_exception(std::runtime_error(msg.str()));
 102                         return Sample(0);
 103                     }
 104                 }
 105             }
 106
 107             // Note that the cached samples of the left are sorted in ascending order,
 108             // whereas the samples of the right tail are sorted in descending order
 109             return *(boost::begin(tail(args)) + n - 1);
 110         }
 111     };
 112 } // namespace impl
 113
 114 ///////////////////////////////////////////////////////////////////////////////
 115 // tag::weighted_tail_quantile<>
 116 //
 117 namespace tag
 118 {
 119     template<typename LeftRight>
 120     struct weighted_tail_quantile
 121       : depends_on<sum_of_weights, tail_weights<LeftRight> >
 122     {
 123         /// INTERNAL ONLY
 124         typedef accumulators::impl::weighted_tail_quantile_impl<mpl::_1, mpl::_2, LeftRight> impl;
 125     };
 126 }
 127
 128 ///////////////////////////////////////////////////////////////////////////////
 129 // extract::weighted_tail_quantile
 130 //
 131 namespace extract
 132 {
 133     extractor<tag::quantile> const weighted_tail_quantile = {};
 134 }
 135
 136 using extract::weighted_tail_quantile;
 137
 138 }} // namespace boost::accumulators
 139
 140 #ifdef _MSC_VER
 141 # pragma warning(pop)
 142 #endif
 143
 144 #endif