1//===----------------------------------------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// REQUIRES: long_tests
10
11// <random>
12
13// template<class RealType = double>
14// class weibull_distribution
15
16// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
17
18#include <random>
19#include <cassert>
20#include <cmath>
21#include <cstddef>
22#include <numeric>
23#include <vector>
24
25#include "test_macros.h"
26
27template <class T>
28inline
29T
30sqr(T x)
31{
32 return x * x;
33}
34
35int main(int, char**)
36{
37 {
38 typedef std::weibull_distribution<> D;
39 typedef D::param_type P;
40 typedef std::mt19937 G;
41 G g;
42 D d(0.5, 2);
43 P p(1, .5);
44 const int N = 1000000;
45 std::vector<D::result_type> u;
46 for (int i = 0; i < N; ++i)
47 {
48 D::result_type v = d(g, p);
49 assert(d.min() <= v);
50 u.push_back(x: v);
51 }
52 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
53 double var = 0;
54 double skew = 0;
55 double kurtosis = 0;
56 for (std::size_t i = 0; i < u.size(); ++i)
57 {
58 double dbl = (u[i] - mean);
59 double d2 = sqr(dbl);
60 var += d2;
61 skew += dbl * d2;
62 kurtosis += d2 * d2;
63 }
64 var /= u.size();
65 double dev = std::sqrt(x: var);
66 skew /= u.size() * dev * var;
67 kurtosis /= u.size() * var * var;
68 kurtosis -= 3;
69 double x_mean = p.b() * std::tgamma(1 + 1/p.a());
70 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);
71 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -
72 3*x_mean*x_var - sqr(x_mean)*x_mean) /
73 (std::sqrt(x: x_var)*x_var);
74 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -
75 4*x_skew*x_var*sqrt(x: x_var)*x_mean -
76 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
77 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
78 assert(std::abs((var - x_var) / x_var) < 0.01);
79 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
80 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
81 }
82 {
83 typedef std::weibull_distribution<> D;
84 typedef D::param_type P;
85 typedef std::mt19937 G;
86 G g;
87 D d(1, .5);
88 P p(2, 3);
89 const int N = 1000000;
90 std::vector<D::result_type> u;
91 for (int i = 0; i < N; ++i)
92 {
93 D::result_type v = d(g, p);
94 assert(d.min() <= v);
95 u.push_back(v);
96 }
97 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
98 double var = 0;
99 double skew = 0;
100 double kurtosis = 0;
101 for (std::size_t i = 0; i < u.size(); ++i)
102 {
103 double dbl = (u[i] - mean);
104 double d2 = sqr(dbl);
105 var += d2;
106 skew += dbl * d2;
107 kurtosis += d2 * d2;
108 }
109 var /= u.size();
110 double dev = std::sqrt(x: var);
111 skew /= u.size() * dev * var;
112 kurtosis /= u.size() * var * var;
113 kurtosis -= 3;
114 double x_mean = p.b() * std::tgamma(1 + 1/p.a());
115 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);
116 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -
117 3*x_mean*x_var - sqr(x_mean)*x_mean) /
118 (std::sqrt(x: x_var)*x_var);
119 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -
120 4*x_skew*x_var*sqrt(x: x_var)*x_mean -
121 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
122 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
123 assert(std::abs((var - x_var) / x_var) < 0.01);
124 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
125 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
126 }
127 {
128 typedef std::weibull_distribution<> D;
129 typedef D::param_type P;
130 typedef std::mt19937 G;
131 G g;
132 D d(2, 3);
133 P p(.5, 2);
134 const int N = 1000000;
135 std::vector<D::result_type> u;
136 for (int i = 0; i < N; ++i)
137 {
138 D::result_type v = d(g, p);
139 assert(d.min() <= v);
140 u.push_back(v);
141 }
142 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
143 double var = 0;
144 double skew = 0;
145 double kurtosis = 0;
146 for (std::size_t i = 0; i < u.size(); ++i)
147 {
148 double dbl = (u[i] - mean);
149 double d2 = sqr(dbl);
150 var += d2;
151 skew += dbl * d2;
152 kurtosis += d2 * d2;
153 }
154 var /= u.size();
155 double dev = std::sqrt(x: var);
156 skew /= u.size() * dev * var;
157 kurtosis /= u.size() * var * var;
158 kurtosis -= 3;
159 double x_mean = p.b() * std::tgamma(1 + 1/p.a());
160 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);
161 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -
162 3*x_mean*x_var - sqr(x_mean)*x_mean) /
163 (std::sqrt(x: x_var)*x_var);
164 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -
165 4*x_skew*x_var*sqrt(x: x_var)*x_mean -
166 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
167 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
168 assert(std::abs((var - x_var) / x_var) < 0.01);
169 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
170 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
171 }
172
173 return 0;
174}
175

source code of libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.weibull/eval_param.pass.cpp