1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
|
///////////////////////////////////////////////////////////////////////////////
// pot_tail_mean.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/pot_quantile.hpp>
#include <boost/accumulators/statistics/tail_mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// pot_tail_mean_impl
//
/**
@brief Estimation of the (coherent) tail mean based on the peaks over threshold method (for both left and right tails)
Computes an estimate for the (coherent) tail mean
\f[
\widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi},
\f]
where \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ are the parameters of the
generalized Pareto distribution that approximates the right tail of the distribution (or the
mirrored left tail, in case the left tail is used). In the latter case, the result is mirrored
back, yielding the correct result.
*/
template<typename Sample, typename Impl, typename LeftRight>
struct pot_tail_mean_impl
: accumulator_base
{
typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef float_type result_type;
pot_tail_mean_impl(dont_care)
: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
{
}
template<typename Args>
result_type result(Args const &args) const
{
typedef
typename mpl::if_<
is_same<Impl, weighted>
, tag::weighted_peaks_over_threshold<LeftRight>
, tag::peaks_over_threshold<LeftRight>
>::type
peaks_over_threshold_tag;
typedef
typename mpl::if_<
is_same<Impl, weighted>
, tag::weighted_pot_quantile<LeftRight>
, tag::pot_quantile<LeftRight>
>::type
pot_quantile_tag;
extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {};
extractor<pot_quantile_tag> const some_pot_quantile = {};
float_type beta_bar = some_peaks_over_threshold(args).template get<1>();
float_type xi_hat = some_peaks_over_threshold(args).template get<2>();
return some_pot_quantile(args) - this->sign_ * beta_bar/( xi_hat - 1. ) * std::pow(
is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability]
, -xi_hat);
}
private:
short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::pot_tail_mean
// tag::pot_tail_mean_prob
//
namespace tag
{
template<typename LeftRight>
struct pot_tail_mean
: depends_on<peaks_over_threshold<LeftRight>, pot_quantile<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct pot_tail_mean_prob
: depends_on<peaks_over_threshold_prob<LeftRight>, pot_quantile_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_tail_mean
: depends_on<weighted_peaks_over_threshold<LeftRight>, weighted_pot_quantile<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_tail_mean_prob
: depends_on<weighted_peaks_over_threshold_prob<LeftRight>, weighted_pot_quantile_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl;
};
}
// pot_tail_mean<LeftRight>(with_threshold_value) -> pot_tail_mean<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_value)>
{
typedef tag::pot_tail_mean<LeftRight> type;
};
// pot_tail_mean<LeftRight>(with_threshold_probability) -> pot_tail_mean_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_probability)>
{
typedef tag::pot_tail_mean_prob<LeftRight> type;
};
// weighted_pot_tail_mean<LeftRight>(with_threshold_value) -> weighted_pot_tail_mean<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_value)>
{
typedef tag::weighted_pot_tail_mean<LeftRight> type;
};
// weighted_pot_tail_mean<LeftRight>(with_threshold_probability) -> weighted_pot_tail_mean_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_probability)>
{
typedef tag::weighted_pot_tail_mean_prob<LeftRight> type;
};
// for the purposes of feature-based dependency resolution,
// pot_tail_mean<LeftRight> and pot_tail_mean_prob<LeftRight> provide
// the same feature as tail_mean
template<typename LeftRight>
struct feature_of<tag::pot_tail_mean<LeftRight> >
: feature_of<tag::tail_mean>
{
};
template<typename LeftRight>
struct feature_of<tag::pot_tail_mean_prob<LeftRight> >
: feature_of<tag::tail_mean>
{
};
// So that pot_tail_mean can be automatically substituted
// with weighted_pot_tail_mean when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_tail_mean<LeftRight> >
{
typedef tag::weighted_pot_tail_mean<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_tail_mean<LeftRight> >
: feature_of<tag::pot_tail_mean<LeftRight> >
{
};
// So that pot_tail_mean_prob can be automatically substituted
// with weighted_pot_tail_mean_prob when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_tail_mean_prob<LeftRight> >
{
typedef tag::weighted_pot_tail_mean_prob<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_tail_mean_prob<LeftRight> >
: feature_of<tag::pot_tail_mean_prob<LeftRight> >
{
};
}} // namespace boost::accumulators
#endif
|
