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(e: 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 = {}; |
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 |
170 | |