1///////////////////////////////////////////////////////////////////////////////
2// weighted_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_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
9#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/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_mean.hpp>
28#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
29
30#ifdef _MSC_VER
31# pragma warning(push)
32# pragma warning(disable: 4127) // conditional expression is constant
33#endif
34
35namespace boost { namespace accumulators
36{
37
38namespace impl
39{
40
41 ///////////////////////////////////////////////////////////////////////////////
42 // coherent_weighted_tail_mean_impl
43 //
44 // TODO
45
46 ///////////////////////////////////////////////////////////////////////////////
47 // non_coherent_weighted_tail_mean_impl
48 //
49 /**
50 @brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)
51
52
53
54 An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean
55 of the
56
57 \f[
58 \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
59 \f]
60
61 smallest samples (left tail) or the weighted mean of the
62
63 \f[
64 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\}
65 \f]
66
67 largest samples (right tail) above a quantile \f$\hat{q}_{\alpha}\f$ of level \f$\alpha\f$, \f$n\f$ being the total number of sample
68 and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights:
69
70 \f[
71 \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i},
72 \f]
73
74 \f[
75 \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}.
76 \f]
77
78 @param quantile_probability
79 */
80 template<typename Sample, typename Weight, typename LeftRight>
81 struct non_coherent_weighted_tail_mean_impl
82 : accumulator_base
83 {
84 typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
85 typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
86 // for boost::result_of
87 typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type result_type;
88
89 non_coherent_weighted_tail_mean_impl(dont_care) {}
90
91 template<typename Args>
92 result_type result(Args const &args) const
93 {
94 float_type threshold = sum_of_weights(args)
95 * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
96
97 std::size_t n = 0;
98 Weight sum = Weight(0);
99
100 while (sum < threshold)
101 {
102 if (n < static_cast<std::size_t>(tail_weights(args).size()))
103 {
104 sum += *(tail_weights(args).begin() + n);
105 n++;
106 }
107 else
108 {
109 if (std::numeric_limits<result_type>::has_quiet_NaN)
110 {
111 return std::numeric_limits<result_type>::quiet_NaN();
112 }
113 else
114 {
115 std::ostringstream msg;
116 msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
117 boost::throw_exception(e: std::runtime_error(msg.str()));
118 return result_type(0);
119 }
120 }
121 }
122
123 return numeric::fdiv(
124 std::inner_product(
125 tail(args).begin()
126 , tail(args).begin() + n
127 , tail_weights(args).begin()
128 , weighted_sample(0)
129 )
130 , sum
131 );
132 }
133 };
134
135} // namespace impl
136
137
138///////////////////////////////////////////////////////////////////////////////
139// tag::non_coherent_weighted_tail_mean<>
140//
141namespace tag
142{
143 template<typename LeftRight>
144 struct non_coherent_weighted_tail_mean
145 : depends_on<sum_of_weights, tail_weights<LeftRight> >
146 {
147 typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl;
148 };
149}
150
151///////////////////////////////////////////////////////////////////////////////
152// extract::non_coherent_weighted_tail_mean;
153//
154namespace extract
155{
156 extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {};
157
158 BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean)
159}
160
161using extract::non_coherent_weighted_tail_mean;
162
163}} // namespace boost::accumulators
164
165#ifdef _MSC_VER
166# pragma warning(pop)
167#endif
168
169#endif
170

source code of boost/libs/accumulators/include/boost/accumulators/statistics/weighted_tail_mean.hpp