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