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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // pot_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_POT_TAIL_MEAN_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006 | |
10 | ||
11 | #include <vector> | |
12 | #include <limits> | |
13 | #include <numeric> | |
14 | #include <functional> | |
15 | #include <boost/range.hpp> | |
16 | #include <boost/parameter/keyword.hpp> | |
17 | #include <boost/tuple/tuple.hpp> | |
18 | #include <boost/mpl/if.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/peaks_over_threshold.hpp> | |
27 | #include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp> | |
28 | #include <boost/accumulators/statistics/pot_quantile.hpp> | |
29 | #include <boost/accumulators/statistics/tail_mean.hpp> | |
30 | ||
31 | namespace boost { namespace accumulators | |
32 | { | |
33 | ||
34 | namespace impl | |
35 | { | |
36 | /////////////////////////////////////////////////////////////////////////////// | |
37 | // pot_tail_mean_impl | |
38 | // | |
39 | /** | |
40 | @brief Estimation of the (coherent) tail mean based on the peaks over threshold method (for both left and right tails) | |
41 | ||
42 | Computes an estimate for the (coherent) tail mean | |
43 | \f[ | |
44 | \widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi}, | |
45 | \f] | |
46 | where \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ are the parameters of the | |
47 | generalized Pareto distribution that approximates the right tail of the distribution (or the | |
48 | mirrored left tail, in case the left tail is used). In the latter case, the result is mirrored | |
49 | back, yielding the correct result. | |
50 | */ | |
51 | template<typename Sample, typename Impl, typename LeftRight> | |
52 | struct pot_tail_mean_impl | |
53 | : accumulator_base | |
54 | { | |
55 | typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; | |
56 | // for boost::result_of | |
57 | typedef float_type result_type; | |
58 | ||
59 | pot_tail_mean_impl(dont_care) | |
60 | : sign_((is_same<LeftRight, left>::value) ? -1 : 1) | |
61 | { | |
62 | } | |
63 | ||
64 | template<typename Args> | |
65 | result_type result(Args const &args) const | |
66 | { | |
67 | typedef | |
68 | typename mpl::if_< | |
69 | is_same<Impl, weighted> | |
70 | , tag::weighted_peaks_over_threshold<LeftRight> | |
71 | , tag::peaks_over_threshold<LeftRight> | |
72 | >::type | |
73 | peaks_over_threshold_tag; | |
74 | ||
75 | typedef | |
76 | typename mpl::if_< | |
77 | is_same<Impl, weighted> | |
78 | , tag::weighted_pot_quantile<LeftRight> | |
79 | , tag::pot_quantile<LeftRight> | |
80 | >::type | |
81 | pot_quantile_tag; | |
82 | ||
83 | extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {}; | |
84 | extractor<pot_quantile_tag> const some_pot_quantile = {}; | |
85 | ||
86 | float_type beta_bar = some_peaks_over_threshold(args).template get<1>(); | |
87 | float_type xi_hat = some_peaks_over_threshold(args).template get<2>(); | |
88 | ||
89 | return some_pot_quantile(args) - this->sign_ * beta_bar/( xi_hat - 1. ) * std::pow( | |
90 | is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability] | |
91 | , -xi_hat); | |
92 | } | |
93 | private: | |
94 | short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result | |
95 | }; | |
96 | } // namespace impl | |
97 | ||
98 | /////////////////////////////////////////////////////////////////////////////// | |
99 | // tag::pot_tail_mean | |
100 | // tag::pot_tail_mean_prob | |
101 | // | |
102 | namespace tag | |
103 | { | |
104 | template<typename LeftRight> | |
105 | struct pot_tail_mean | |
106 | : depends_on<peaks_over_threshold<LeftRight>, pot_quantile<LeftRight> > | |
107 | { | |
108 | /// INTERNAL ONLY | |
109 | /// | |
110 | typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; | |
111 | }; | |
112 | template<typename LeftRight> | |
113 | struct pot_tail_mean_prob | |
114 | : depends_on<peaks_over_threshold_prob<LeftRight>, pot_quantile_prob<LeftRight> > | |
115 | { | |
116 | /// INTERNAL ONLY | |
117 | /// | |
118 | typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; | |
119 | }; | |
120 | template<typename LeftRight> | |
121 | struct weighted_pot_tail_mean | |
122 | : depends_on<weighted_peaks_over_threshold<LeftRight>, weighted_pot_quantile<LeftRight> > | |
123 | { | |
124 | /// INTERNAL ONLY | |
125 | /// | |
126 | typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; | |
127 | }; | |
128 | template<typename LeftRight> | |
129 | struct weighted_pot_tail_mean_prob | |
130 | : depends_on<weighted_peaks_over_threshold_prob<LeftRight>, weighted_pot_quantile_prob<LeftRight> > | |
131 | { | |
132 | /// INTERNAL ONLY | |
133 | /// | |
134 | typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; | |
135 | }; | |
136 | } | |
137 | ||
138 | // pot_tail_mean<LeftRight>(with_threshold_value) -> pot_tail_mean<LeftRight> | |
139 | template<typename LeftRight> | |
140 | struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_value)> | |
141 | { | |
142 | typedef tag::pot_tail_mean<LeftRight> type; | |
143 | }; | |
144 | ||
145 | // pot_tail_mean<LeftRight>(with_threshold_probability) -> pot_tail_mean_prob<LeftRight> | |
146 | template<typename LeftRight> | |
147 | struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_probability)> | |
148 | { | |
149 | typedef tag::pot_tail_mean_prob<LeftRight> type; | |
150 | }; | |
151 | ||
152 | // weighted_pot_tail_mean<LeftRight>(with_threshold_value) -> weighted_pot_tail_mean<LeftRight> | |
153 | template<typename LeftRight> | |
154 | struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_value)> | |
155 | { | |
156 | typedef tag::weighted_pot_tail_mean<LeftRight> type; | |
157 | }; | |
158 | ||
159 | // weighted_pot_tail_mean<LeftRight>(with_threshold_probability) -> weighted_pot_tail_mean_prob<LeftRight> | |
160 | template<typename LeftRight> | |
161 | struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_probability)> | |
162 | { | |
163 | typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; | |
164 | }; | |
165 | ||
166 | // for the purposes of feature-based dependency resolution, | |
167 | // pot_tail_mean<LeftRight> and pot_tail_mean_prob<LeftRight> provide | |
168 | // the same feature as tail_mean | |
169 | template<typename LeftRight> | |
170 | struct feature_of<tag::pot_tail_mean<LeftRight> > | |
171 | : feature_of<tag::tail_mean> | |
172 | { | |
173 | }; | |
174 | ||
175 | template<typename LeftRight> | |
176 | struct feature_of<tag::pot_tail_mean_prob<LeftRight> > | |
177 | : feature_of<tag::tail_mean> | |
178 | { | |
179 | }; | |
180 | ||
181 | // So that pot_tail_mean can be automatically substituted | |
182 | // with weighted_pot_tail_mean when the weight parameter is non-void. | |
183 | template<typename LeftRight> | |
184 | struct as_weighted_feature<tag::pot_tail_mean<LeftRight> > | |
185 | { | |
186 | typedef tag::weighted_pot_tail_mean<LeftRight> type; | |
187 | }; | |
188 | ||
189 | template<typename LeftRight> | |
190 | struct feature_of<tag::weighted_pot_tail_mean<LeftRight> > | |
191 | : feature_of<tag::pot_tail_mean<LeftRight> > | |
192 | { | |
193 | }; | |
194 | ||
195 | // So that pot_tail_mean_prob can be automatically substituted | |
196 | // with weighted_pot_tail_mean_prob when the weight parameter is non-void. | |
197 | template<typename LeftRight> | |
198 | struct as_weighted_feature<tag::pot_tail_mean_prob<LeftRight> > | |
199 | { | |
200 | typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; | |
201 | }; | |
202 | ||
203 | template<typename LeftRight> | |
204 | struct feature_of<tag::weighted_pot_tail_mean_prob<LeftRight> > | |
205 | : feature_of<tag::pot_tail_mean_prob<LeftRight> > | |
206 | { | |
207 | }; | |
208 | ||
209 | }} // namespace boost::accumulators | |
210 | ||
211 | #endif |