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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::fdiv<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::fdiv(quantile(args), n) | |
86 | * ( | |
87 | ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] | |
88 | - numeric::fdiv(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::fdiv<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::fdiv( | |
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 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean) | |
203 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean) | |
204 | } | |
205 | ||
206 | using extract::non_coherent_tail_mean; | |
207 | using extract::coherent_tail_mean; | |
208 | ||
209 | // for the purposes of feature-based dependency resolution, | |
210 | // coherent_tail_mean<LeftRight> provides the same feature as tail_mean | |
211 | template<typename LeftRight> | |
212 | struct feature_of<tag::coherent_tail_mean<LeftRight> > | |
213 | : feature_of<tag::tail_mean> | |
214 | { | |
215 | }; | |
216 | ||
217 | template<typename LeftRight> | |
218 | struct feature_of<tag::non_coherent_tail_mean<LeftRight> > | |
219 | : feature_of<tag::abstract_non_coherent_tail_mean> | |
220 | { | |
221 | }; | |
222 | ||
223 | // So that non_coherent_tail_mean can be automatically substituted | |
224 | // with weighted_non_coherent_tail_mean when the weight parameter is non-void. | |
225 | template<typename LeftRight> | |
226 | struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> > | |
227 | { | |
228 | typedef tag::non_coherent_weighted_tail_mean<LeftRight> type; | |
229 | }; | |
230 | ||
231 | template<typename LeftRight> | |
232 | struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> > | |
233 | : feature_of<tag::non_coherent_tail_mean<LeftRight> > | |
234 | {}; | |
235 | ||
236 | // NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean, | |
237 | // which is the base feature for coherent tail means, since (at least for | |
238 | // non-continuous distributions) non_coherent_tail_mean is a different measure! | |
239 | ||
240 | }} // namespace boost::accumulators | |
241 | ||
242 | #ifdef _MSC_VER | |
243 | # pragma warning(pop) | |
244 | #endif | |
245 | ||
246 | #endif |