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