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 
non_coherent_weighted_tail_mean_implboost::accumulators::impl::non_coherent_weighted_tail_mean_impl89         non_coherent_weighted_tail_mean_impl(dont_care) {}
90 
91         template<typename Args>
resultboost::accumulators::impl::non_coherent_weighted_tail_mean_impl92         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
170