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