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 chi_squared_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::chi_squared_distribution<> D;
34         typedef D::param_type P;
35         typedef std::minstd_rand G;
36         G g;
37         D d(0.5);
38         P p(1);
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.n();
65         double x_var = 2 * p.n();
66         double x_skew = std::sqrt(8 / p.n());
67         double x_kurtosis = 12 / p.n();
68         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
69         assert(std::abs((var - x_var) / x_var) < 0.01);
70         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
71         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
72     }
73     {
74         typedef std::chi_squared_distribution<> D;
75         typedef D::param_type P;
76         typedef std::mt19937 G;
77         G g;
78         D d(1);
79         P p(2);
80         const int N = 1000000;
81         std::vector<D::result_type> u;
82         for (int i = 0; i < N; ++i)
83         {
84             D::result_type v = d(g, p);
85             assert(d.min() < v);
86             u.push_back(v);
87         }
88         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
89         double var = 0;
90         double skew = 0;
91         double kurtosis = 0;
92         for (int i = 0; i < u.size(); ++i)
93         {
94             double d = (u[i] - mean);
95             double d2 = sqr(d);
96             var += d2;
97             skew += d * d2;
98             kurtosis += d2 * d2;
99         }
100         var /= u.size();
101         double dev = std::sqrt(var);
102         skew /= u.size() * dev * var;
103         kurtosis /= u.size() * var * var;
104         kurtosis -= 3;
105         double x_mean = p.n();
106         double x_var = 2 * p.n();
107         double x_skew = std::sqrt(8 / p.n());
108         double x_kurtosis = 12 / p.n();
109         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
110         assert(std::abs((var - x_var) / x_var) < 0.01);
111         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
112         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
113     }
114     {
115         typedef std::chi_squared_distribution<> D;
116         typedef D::param_type P;
117         typedef std::minstd_rand G;
118         G g;
119         D d(2);
120         P p(.5);
121         const int N = 1000000;
122         std::vector<D::result_type> u;
123         for (int i = 0; i < N; ++i)
124         {
125             D::result_type v = d(g, p);
126             assert(d.min() < v);
127             u.push_back(v);
128         }
129         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
130         double var = 0;
131         double skew = 0;
132         double kurtosis = 0;
133         for (int i = 0; i < u.size(); ++i)
134         {
135             double d = (u[i] - mean);
136             double d2 = sqr(d);
137             var += d2;
138             skew += d * d2;
139             kurtosis += d2 * d2;
140         }
141         var /= u.size();
142         double dev = std::sqrt(var);
143         skew /= u.size() * dev * var;
144         kurtosis /= u.size() * var * var;
145         kurtosis -= 3;
146         double x_mean = p.n();
147         double x_var = 2 * p.n();
148         double x_skew = std::sqrt(8 / p.n());
149         double x_kurtosis = 12 / p.n();
150         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
151         assert(std::abs((var - x_var) / x_var) < 0.01);
152         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
153         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
154     }
155 }
156