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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_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_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/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_variate.hpp> | |
28 | #include <boost/accumulators/statistics/tail_variate_means.hpp> | |
29 | #include <boost/accumulators/statistics/weighted_tail_mean.hpp> | |
30 | #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> | |
31 | ||
32 | #ifdef _MSC_VER | |
33 | # pragma warning(push) | |
34 | # pragma warning(disable: 4127) // conditional expression is constant | |
35 | #endif | |
36 | ||
37 | namespace boost | |
38 | { | |
39 | // for _BinaryOperatrion2 in std::inner_product below | |
40 | // multiplies two values and promotes the result to double | |
41 | namespace numeric { namespace functional | |
42 | { | |
43 | /////////////////////////////////////////////////////////////////////////////// | |
44 | // numeric::functional::multiply_and_promote_to_double | |
45 | template<typename T, typename U> | |
46 | struct multiply_and_promote_to_double | |
47 | : multiplies<T, double const> | |
48 | { | |
49 | }; | |
50 | }} | |
51 | } | |
52 | ||
53 | namespace boost { namespace accumulators | |
54 | { | |
55 | ||
56 | namespace impl | |
57 | { | |
58 | /** | |
59 | @brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails) | |
60 | ||
61 | For all \f$j\f$-th variates associated to the | |
62 | ||
63 | \f[ | |
64 | \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} | |
65 | \f] | |
66 | ||
67 | smallest samples (left tail) or the weighted mean of the | |
68 | ||
69 | \f[ | |
70 | 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\} | |
71 | \f] | |
72 | ||
73 | largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ | |
74 | are computed and returned as an iterator range. Alternatively, the relative weighted tail means | |
75 | \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means | |
76 | normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$. | |
77 | ||
78 | \f[ | |
79 | \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = | |
80 | \frac{1}{\sum_{i=\rho}^n w_i} | |
81 | \sum_{i=\rho}^n w_i \xi_{j,i} | |
82 | \f] | |
83 | ||
84 | \f[ | |
85 | \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = | |
86 | \frac{1}{\sum_{i=1}^{\lambda}} | |
87 | \sum_{i=1}^{\lambda} w_i \xi_{j,i} | |
88 | \f] | |
89 | ||
90 | \f[ | |
91 | \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = | |
92 | \frac{\sum_{i=\rho}^n w_i \xi_{j,i}} | |
93 | {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} | |
94 | \f] | |
95 | ||
96 | \f[ | |
97 | \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = | |
98 | \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}} | |
99 | {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} | |
100 | \f] | |
101 | */ | |
102 | ||
103 | /////////////////////////////////////////////////////////////////////////////// | |
104 | // weighted_tail_variate_means_impl | |
105 | // by default: absolute weighted_tail_variate_means | |
106 | template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType> | |
107 | struct weighted_tail_variate_means_impl | |
108 | : accumulator_base | |
109 | { | |
110 | typedef typename numeric::functional::fdiv<Weight, Weight>::result_type float_type; | |
111 | typedef typename numeric::functional::fdiv<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type; | |
112 | // for boost::result_of | |
113 | typedef iterator_range<typename array_type::iterator> result_type; | |
114 | ||
115 | weighted_tail_variate_means_impl(dont_care) {} | |
116 | ||
117 | template<typename Args> | |
118 | result_type result(Args const &args) const | |
119 | { | |
120 | float_type threshold = sum_of_weights(args) | |
121 | * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); | |
122 | ||
123 | std::size_t n = 0; | |
124 | Weight sum = Weight(0); | |
125 | ||
126 | while (sum < threshold) | |
127 | { | |
128 | if (n < static_cast<std::size_t>(tail_weights(args).size())) | |
129 | { | |
130 | sum += *(tail_weights(args).begin() + n); | |
131 | n++; | |
132 | } | |
133 | else | |
134 | { | |
135 | if (std::numeric_limits<float_type>::has_quiet_NaN) | |
136 | { | |
137 | std::fill( | |
138 | this->tail_means_.begin() | |
139 | , this->tail_means_.end() | |
140 | , std::numeric_limits<float_type>::quiet_NaN() | |
141 | ); | |
142 | } | |
143 | else | |
144 | { | |
145 | std::ostringstream msg; | |
146 | msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; | |
147 | boost::throw_exception(std::runtime_error(msg.str())); | |
148 | } | |
149 | } | |
150 | } | |
151 | ||
152 | std::size_t num_variates = tail_variate(args).begin()->size(); | |
153 | ||
154 | this->tail_means_.clear(); | |
155 | this->tail_means_.resize(num_variates, Sample(0)); | |
156 | ||
157 | this->tail_means_ = std::inner_product( | |
158 | tail_variate(args).begin() | |
159 | , tail_variate(args).begin() + n | |
160 | , tail_weights(args).begin() | |
161 | , this->tail_means_ | |
162 | , numeric::functional::plus<array_type const, array_type const>() | |
163 | , numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>() | |
164 | ); | |
165 | ||
166 | float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. ); | |
167 | ||
168 | std::transform( | |
169 | this->tail_means_.begin() | |
170 | , this->tail_means_.end() | |
171 | , this->tail_means_.begin() | |
172 | , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor) | |
173 | ); | |
174 | ||
175 | return make_iterator_range(this->tail_means_); | |
176 | } | |
177 | ||
178 | private: | |
179 | ||
180 | mutable array_type tail_means_; | |
181 | ||
182 | }; | |
183 | ||
184 | } // namespace impl | |
185 | ||
186 | /////////////////////////////////////////////////////////////////////////////// | |
187 | // tag::absolute_weighted_tail_variate_means | |
188 | // tag::relative_weighted_tail_variate_means | |
189 | // | |
190 | namespace tag | |
191 | { | |
192 | template<typename LeftRight, typename VariateType, typename VariateTag> | |
193 | struct absolute_weighted_tail_variate_means | |
194 | : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > | |
195 | { | |
196 | typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl; | |
197 | }; | |
198 | template<typename LeftRight, typename VariateType, typename VariateTag> | |
199 | struct relative_weighted_tail_variate_means | |
200 | : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > | |
201 | { | |
202 | typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl; | |
203 | }; | |
204 | } | |
205 | ||
206 | /////////////////////////////////////////////////////////////////////////////// | |
207 | // extract::weighted_tail_variate_means | |
208 | // extract::relative_weighted_tail_variate_means | |
209 | // | |
210 | namespace extract | |
211 | { | |
212 | extractor<tag::abstract_absolute_tail_variate_means> const weighted_tail_variate_means = {}; | |
213 | extractor<tag::abstract_relative_tail_variate_means> const relative_weighted_tail_variate_means = {}; | |
214 | ||
215 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means) | |
216 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_weighted_tail_variate_means) | |
217 | } | |
218 | ||
219 | using extract::weighted_tail_variate_means; | |
220 | using extract::relative_weighted_tail_variate_means; | |
221 | ||
222 | // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> | |
223 | template<typename LeftRight, typename VariateType, typename VariateTag> | |
224 | struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)> | |
225 | { | |
226 | typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; | |
227 | }; | |
228 | ||
229 | // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> | |
230 | template<typename LeftRight, typename VariateType, typename VariateTag> | |
231 | struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)> | |
232 | { | |
233 | typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; | |
234 | }; | |
235 | ||
236 | }} // namespace boost::accumulators | |
237 | ||
238 | #ifdef _MSC_VER | |
239 | # pragma warning(pop) | |
240 | #endif | |
241 | ||
242 | #endif |