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#include <boost/serialization/vector.hpp>
31
32#ifdef _MSC_VER
33# pragma warning(push)
34# pragma warning(disable: 4127) // conditional expression is constant
35#endif
36
37namespace boost { namespace accumulators
38{
39
40namespace impl
41{
42 /**
43 @brief Estimation of the absolute and relative tail variate means (for both left and right tails)
44
45 For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
46 \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
47 \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
48 the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
49 tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
50
51 \f[
52 \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
53 \frac{1}{\lceil n(1-\alpha) \rceil}
54 \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
55 \f]
56
57 \f[
58 \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
59 \frac{1}{\lceil n\alpha \rceil}
60 \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
61 \f]
62
63 \f[
64 \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
65 \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
66 {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
67 \f]
68
69 \f[
70 \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
71 \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
72 {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
73 \f]
74 */
75
76 ///////////////////////////////////////////////////////////////////////////////
77 // tail_variate_means_impl
78 // by default: absolute tail_variate_means
79 template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
80 struct tail_variate_means_impl
81 : accumulator_base
82 {
83 typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
84 typedef std::vector<float_type> array_type;
85 // for boost::result_of
86 typedef iterator_range<typename array_type::iterator> result_type;
87
88 tail_variate_means_impl(dont_care) {}
89
90 template<typename Args>
91 result_type result(Args const &args) const
92 {
93 std::size_t cnt = count(args);
94
95 std::size_t n = static_cast<std::size_t>(
96 std::ceil(
97 cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
98 )
99 );
100
101 std::size_t num_variates = tail_variate(args).begin()->size();
102
103 this->tail_means_.clear();
104 this->tail_means_.resize(num_variates, Sample(0));
105
106 // If n is in a valid range, return result, otherwise return NaN or throw exception
107 if (n < static_cast<std::size_t>(tail(args).size()))
108 {
109 this->tail_means_ = std::accumulate(
110 tail_variate(args).begin()
111 , tail_variate(args).begin() + n
112 , this->tail_means_
113 , numeric::plus
114 );
115
116 float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );
117
118 std::transform(
119 this->tail_means_.begin()
120 , this->tail_means_.end()
121 , this->tail_means_.begin()
122#ifdef BOOST_NO_CXX98_BINDERS
123 , std::bind(std::divides<float_type>(), std::placeholders::_1, factor)
124#else
125 , std::bind2nd(std::divides<float_type>(), factor)
126#endif
127 );
128 }
129 else
130 {
131 if (std::numeric_limits<float_type>::has_quiet_NaN)
132 {
133 std::fill(
134 this->tail_means_.begin()
135 , this->tail_means_.end()
136 , std::numeric_limits<float_type>::quiet_NaN()
137 );
138 }
139 else
140 {
141 std::ostringstream msg;
142 msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
143 boost::throw_exception(e: std::runtime_error(msg.str()));
144 }
145 }
146 return make_iterator_range(this->tail_means_);
147 }
148
149 // make this accumulator serializeable
150 template<class Archive>
151 void serialize(Archive & ar, const unsigned int file_version)
152 {
153 ar & tail_means_;
154 }
155
156 private:
157
158 mutable array_type tail_means_;
159
160 };
161
162} // namespace impl
163
164///////////////////////////////////////////////////////////////////////////////
165// tag::absolute_tail_variate_means
166// tag::relative_tail_variate_means
167//
168namespace tag
169{
170 template<typename LeftRight, typename VariateType, typename VariateTag>
171 struct absolute_tail_variate_means
172 : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
173 {
174 typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
175 };
176 template<typename LeftRight, typename VariateType, typename VariateTag>
177 struct relative_tail_variate_means
178 : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
179 {
180 typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
181 };
182 struct abstract_absolute_tail_variate_means
183 : depends_on<>
184 {
185 };
186 struct abstract_relative_tail_variate_means
187 : depends_on<>
188 {
189 };
190}
191
192///////////////////////////////////////////////////////////////////////////////
193// extract::tail_variate_means
194// extract::relative_tail_variate_means
195//
196namespace extract
197{
198 extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {};
199 extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {};
200
201 BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means)
202 BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means)
203}
204
205using extract::tail_variate_means;
206using extract::relative_tail_variate_means;
207
208// tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
209template<typename LeftRight, typename VariateType, typename VariateTag>
210struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
211{
212 typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
213};
214
215// tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
216template<typename LeftRight, typename VariateType, typename VariateTag>
217struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
218{
219 typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
220};
221
222// Provides non-templatized extractor
223template<typename LeftRight, typename VariateType, typename VariateTag>
224struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
225 : feature_of<tag::abstract_absolute_tail_variate_means>
226{
227};
228
229// Provides non-templatized extractor
230template<typename LeftRight, typename VariateType, typename VariateTag>
231struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
232 : feature_of<tag::abstract_relative_tail_variate_means>
233{
234};
235
236// So that absolute_tail_means can be automatically substituted
237// with absolute_weighted_tail_means when the weight parameter is non-void.
238template<typename LeftRight, typename VariateType, typename VariateTag>
239struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
240{
241 typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
242};
243
244template<typename LeftRight, typename VariateType, typename VariateTag>
245struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
246 : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
247{
248};
249
250// So that relative_tail_means can be automatically substituted
251// with relative_weighted_tail_means when the weight parameter is non-void.
252template<typename LeftRight, typename VariateType, typename VariateTag>
253struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
254{
255 typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
256};
257
258template<typename LeftRight, typename VariateType, typename VariateTag>
259struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
260 : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
261{
262};
263
264}} // namespace boost::accumulators
265
266#ifdef _MSC_VER
267# pragma warning(pop)
268#endif
269
270#endif
271

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