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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 |