1 ///////////////////////////////////////////////////////////////////////////////
2 // weighted_tail_quantile.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_QUANTILE_HPP_DE_01_01_2006
9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006
10 
11 #include <vector>
12 #include <limits>
13 #include <functional>
14 #include <sstream>
15 #include <stdexcept>
16 #include <boost/throw_exception.hpp>
17 #include <boost/parameter/keyword.hpp>
18 #include <boost/mpl/placeholders.hpp>
19 #include <boost/mpl/if.hpp>
20 #include <boost/type_traits/is_same.hpp>
21 #include <boost/accumulators/numeric/functional.hpp>
22 #include <boost/accumulators/framework/depends_on.hpp>
23 #include <boost/accumulators/framework/accumulator_base.hpp>
24 #include <boost/accumulators/framework/extractor.hpp>
25 #include <boost/accumulators/framework/parameters/sample.hpp>
26 #include <boost/accumulators/statistics_fwd.hpp>
27 #include <boost/accumulators/statistics/tail.hpp>
28 #include <boost/accumulators/statistics/tail_quantile.hpp>
29 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
30 
31 #ifdef _MSC_VER
32 # pragma warning(push)
33 # pragma warning(disable: 4127) // conditional expression is constant
34 #endif
35 
36 namespace boost { namespace accumulators
37 {
38 
39 namespace impl
40 {
41     ///////////////////////////////////////////////////////////////////////////////
42     // weighted_tail_quantile_impl
43     //  Tail quantile estimation based on order statistics of weighted samples
44     /**
45         @brief Tail quantile estimation based on order statistics of weighted samples (for both left and right tails)
46 
47         An estimator \f$\hat{q}\f$ of tail quantiles with level \f$\alpha\f$ based on order statistics
48         \f$X_{1:n} \leq X_{2:n} \leq\dots\leq X_{n:n}\f$ of weighted samples are given by \f$X_{\lambda:n}\f$ (left tail)
49         and \f$X_{\rho:n}\f$ (right tail), where
50 
51             \f[
52                 \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
53             \f]
54 
55         and
56 
57             \f[
58                 \rho = \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\},
59             \f]
60 
61         \f$n\f$ being the number of samples and \f$\bar{w}_n\f$ the sum of all weights.
62 
63         @param quantile_probability
64     */
65     template<typename Sample, typename Weight, typename LeftRight>
66     struct weighted_tail_quantile_impl
67       : accumulator_base
68     {
69         typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
70         // for boost::result_of
71         typedef Sample result_type;
72 
weighted_tail_quantile_implboost::accumulators::impl::weighted_tail_quantile_impl73         weighted_tail_quantile_impl(dont_care) {}
74 
75         template<typename Args>
resultboost::accumulators::impl::weighted_tail_quantile_impl76         result_type result(Args const &args) const
77         {
78             float_type threshold = sum_of_weights(args)
79                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
80 
81             std::size_t n = 0;
82             Weight sum = Weight(0);
83 
84             while (sum < threshold)
85             {
86                 if (n < static_cast<std::size_t>(tail_weights(args).size()))
87                 {
88                     sum += *(tail_weights(args).begin() + n);
89                     n++;
90                 }
91                 else
92                 {
93                     if (std::numeric_limits<result_type>::has_quiet_NaN)
94                     {
95                         return std::numeric_limits<result_type>::quiet_NaN();
96                     }
97                     else
98                     {
99                         std::ostringstream msg;
100                         msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
101                         boost::throw_exception(std::runtime_error(msg.str()));
102                         return Sample(0);
103                     }
104                 }
105             }
106 
107             // Note that the cached samples of the left are sorted in ascending order,
108             // whereas the samples of the right tail are sorted in descending order
109             return *(boost::begin(tail(args)) + n - 1);
110         }
111     };
112 } // namespace impl
113 
114 ///////////////////////////////////////////////////////////////////////////////
115 // tag::weighted_tail_quantile<>
116 //
117 namespace tag
118 {
119     template<typename LeftRight>
120     struct weighted_tail_quantile
121       : depends_on<sum_of_weights, tail_weights<LeftRight> >
122     {
123         /// INTERNAL ONLY
124         typedef accumulators::impl::weighted_tail_quantile_impl<mpl::_1, mpl::_2, LeftRight> impl;
125     };
126 }
127 
128 ///////////////////////////////////////////////////////////////////////////////
129 // extract::weighted_tail_quantile
130 //
131 namespace extract
132 {
133     extractor<tag::quantile> const weighted_tail_quantile = {};
134 
135     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_quantile)
136 }
137 
138 using extract::weighted_tail_quantile;
139 
140 }} // namespace boost::accumulators
141 
142 #ifdef _MSC_VER
143 # pragma warning(pop)
144 #endif
145 
146 #endif
147