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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::average<Weight, std::size_t>::result_type float_type; | |
70 | // for boost::result_of | |
71 | typedef Sample result_type; | |
72 | ||
73 | weighted_tail_quantile_impl(dont_care) {} | |
74 | ||
75 | template<typename Args> | |
76 | 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 | ||
136 | using extract::weighted_tail_quantile; | |
137 | ||
138 | }} // namespace boost::accumulators | |
139 | ||
140 | #ifdef _MSC_VER | |
141 | # pragma warning(pop) | |
142 | #endif | |
143 | ||
144 | #endif |