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 chi_squared_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
24template <class T>
25inline
26T
27sqr(T x)
28{
29    return x * x;
30}
31
32int main()
33{
34    {
35        typedef std::chi_squared_distribution<> D;
36        typedef D::param_type P;
37        typedef std::minstd_rand G;
38        G g;
39        D d(0.5);
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.n();
66        double x_var = 2 * d.n();
67        double x_skew = std::sqrt(8 / d.n());
68        double x_kurtosis = 12 / d.n();
69        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
70        assert(std::abs((var - x_var) / x_var) < 0.01);
71        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
72        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
73    }
74    {
75        typedef std::chi_squared_distribution<> D;
76        typedef D::param_type P;
77        typedef std::minstd_rand G;
78        G g;
79        D d(1);
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);
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 = d.n();
106        double x_var = 2 * d.n();
107        double x_skew = std::sqrt(8 / d.n());
108        double x_kurtosis = 12 / d.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::mt19937 G;
118        G g;
119        D d(2);
120        const int N = 1000000;
121        std::vector<D::result_type> u;
122        for (int i = 0; i < N; ++i)
123        {
124            D::result_type v = d(g);
125            assert(d.min() < v);
126            u.push_back(v);
127        }
128        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
129        double var = 0;
130        double skew = 0;
131        double kurtosis = 0;
132        for (int i = 0; i < u.size(); ++i)
133        {
134            double d = (u[i] - mean);
135            double d2 = sqr(d);
136            var += d2;
137            skew += d * d2;
138            kurtosis += d2 * d2;
139        }
140        var /= u.size();
141        double dev = std::sqrt(var);
142        skew /= u.size() * dev * var;
143        kurtosis /= u.size() * var * var;
144        kurtosis -= 3;
145        double x_mean = d.n();
146        double x_var = 2 * d.n();
147        double x_skew = std::sqrt(8 / d.n());
148        double x_kurtosis = 12 / d.n();
149        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
150        assert(std::abs((var - x_var) / x_var) < 0.01);
151        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
152        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
153    }
154}
155