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);
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         const int N = 1000000;
41         std::vector<D::result_type> u;
42         for (int i = 0; i < N; ++i)
43         {
44             D::result_type v = d(g);
45             assert(d.min() <= v);
46             u.push_back(v);
47         }
48         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
49         double var = 0;
50         double skew = 0;
51         double kurtosis = 0;
52         for (int i = 0; i < u.size(); ++i)
53         {
54             double d = (u[i] - mean);
55             double d2 = sqr(d);
56             var += d2;
57             skew += d * d2;
58             kurtosis += d2 * d2;
59         }
60         var /= u.size();
61         double dev = std::sqrt(var);
62         skew /= u.size() * dev * var;
63         kurtosis /= u.size() * var * var;
64         kurtosis -= 3;
65         double x_mean = d.b() * std::tgamma(1 + 1/d.a());
66         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
67         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) -
68                         3*x_mean*x_var - sqr(x_mean)*x_mean) /
69                         (std::sqrt(x_var)*x_var);
70         double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) -
71                        4*x_skew*x_var*sqrt(x_var)*x_mean -
72                        6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
73         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
74         assert(std::abs((var - x_var) / x_var) < 0.01);
75         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
76         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
77     }
78     {
79         typedef std::weibull_distribution<> D;
80         typedef D::param_type P;
81         typedef std::mt19937 G;
82         G g;
83         D d(1, .5);
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);
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 = d.b() * std::tgamma(1 + 1/d.a());
110         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
111         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.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(d.b())) * std::tgamma(1 + 4/d.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) < 0.01);
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         const int N = 1000000;
129         std::vector<D::result_type> u;
130         for (int i = 0; i < N; ++i)
131         {
132             D::result_type v = d(g);
133             assert(d.min() <= v);
134             u.push_back(v);
135         }
136         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
137         double var = 0;
138         double skew = 0;
139         double kurtosis = 0;
140         for (int i = 0; i < u.size(); ++i)
141         {
142             double d = (u[i] - mean);
143             double d2 = sqr(d);
144             var += d2;
145             skew += d * d2;
146             kurtosis += d2 * d2;
147         }
148         var /= u.size();
149         double dev = std::sqrt(var);
150         skew /= u.size() * dev * var;
151         kurtosis /= u.size() * var * var;
152         kurtosis -= 3;
153         double x_mean = d.b() * std::tgamma(1 + 1/d.a());
154         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
155         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) -
156                         3*x_mean*x_var - sqr(x_mean)*x_mean) /
157                         (std::sqrt(x_var)*x_var);
158         double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) -
159                        4*x_skew*x_var*sqrt(x_var)*x_mean -
160                        6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
161         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
162         assert(std::abs((var - x_var) / x_var) < 0.01);
163         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
164         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
165     }
166 }
167