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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_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_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/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_mean.hpp> | |
28 | #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> | |
29 | ||
30 | #ifdef _MSC_VER | |
31 | # pragma warning(push) | |
32 | # pragma warning(disable: 4127) // conditional expression is constant | |
33 | #endif | |
34 | ||
35 | namespace boost { namespace accumulators | |
36 | { | |
37 | ||
38 | namespace impl | |
39 | { | |
40 | ||
41 | /////////////////////////////////////////////////////////////////////////////// | |
42 | // coherent_weighted_tail_mean_impl | |
43 | // | |
44 | // TODO | |
45 | ||
46 | /////////////////////////////////////////////////////////////////////////////// | |
47 | // non_coherent_weighted_tail_mean_impl | |
48 | // | |
49 | /** | |
50 | @brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails) | |
51 | ||
52 | ||
53 | ||
54 | An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean | |
55 | of the | |
56 | ||
57 | \f[ | |
58 | \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} | |
59 | \f] | |
60 | ||
61 | smallest samples (left tail) or the weighted mean of the | |
62 | ||
63 | \f[ | |
64 | 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\} | |
65 | \f] | |
66 | ||
67 | largest samples (right tail) above a quantile \f$\hat{q}_{\alpha}\f$ of level \f$\alpha\f$, \f$n\f$ being the total number of sample | |
68 | and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights: | |
69 | ||
70 | \f[ | |
71 | \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i}, | |
72 | \f] | |
73 | ||
74 | \f[ | |
75 | \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}. | |
76 | \f] | |
77 | ||
78 | @param quantile_probability | |
79 | */ | |
80 | template<typename Sample, typename Weight, typename LeftRight> | |
81 | struct non_coherent_weighted_tail_mean_impl | |
82 | : accumulator_base | |
83 | { | |
84 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
85 | typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type; | |
86 | // for boost::result_of | |
87 | typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type result_type; | |
88 | ||
89 | non_coherent_weighted_tail_mean_impl(dont_care) {} | |
90 | ||
91 | template<typename Args> | |
92 | result_type result(Args const &args) const | |
93 | { | |
94 | float_type threshold = sum_of_weights(args) | |
95 | * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); | |
96 | ||
97 | std::size_t n = 0; | |
98 | Weight sum = Weight(0); | |
99 | ||
100 | while (sum < threshold) | |
101 | { | |
102 | if (n < static_cast<std::size_t>(tail_weights(args).size())) | |
103 | { | |
104 | sum += *(tail_weights(args).begin() + n); | |
105 | n++; | |
106 | } | |
107 | else | |
108 | { | |
109 | if (std::numeric_limits<result_type>::has_quiet_NaN) | |
110 | { | |
111 | return std::numeric_limits<result_type>::quiet_NaN(); | |
112 | } | |
113 | else | |
114 | { | |
115 | std::ostringstream msg; | |
116 | msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; | |
117 | boost::throw_exception(std::runtime_error(msg.str())); | |
118 | return result_type(0); | |
119 | } | |
120 | } | |
121 | } | |
122 | ||
123 | return numeric::fdiv( | |
124 | std::inner_product( | |
125 | tail(args).begin() | |
126 | , tail(args).begin() + n | |
127 | , tail_weights(args).begin() | |
128 | , weighted_sample(0) | |
129 | ) | |
130 | , sum | |
131 | ); | |
132 | } | |
133 | }; | |
134 | ||
135 | } // namespace impl | |
136 | ||
137 | ||
138 | /////////////////////////////////////////////////////////////////////////////// | |
139 | // tag::non_coherent_weighted_tail_mean<> | |
140 | // | |
141 | namespace tag | |
142 | { | |
143 | template<typename LeftRight> | |
144 | struct non_coherent_weighted_tail_mean | |
145 | : depends_on<sum_of_weights, tail_weights<LeftRight> > | |
146 | { | |
147 | typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl; | |
148 | }; | |
149 | } | |
150 | ||
151 | /////////////////////////////////////////////////////////////////////////////// | |
152 | // extract::non_coherent_weighted_tail_mean; | |
153 | // | |
154 | namespace extract | |
155 | { | |
156 | extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {}; | |
157 | ||
158 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean) | |
159 | } | |
160 | ||
161 | using extract::non_coherent_weighted_tail_mean; | |
162 | ||
163 | }} // namespace boost::accumulators | |
164 | ||
165 | #ifdef _MSC_VER | |
166 | # pragma warning(pop) | |
167 | #endif | |
168 | ||
169 | #endif |