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 student_t_distribution
14
15// template<class _URNG> result_type operator()(_URNG& g);
16
17#include <random>
18#include <cassert>
19#include <vector>
20#include <numeric>
21
22template <class T>
23inline
24T
25sqr(T x)
26{
27    return x * x;
28}
29
30int main()
31{
32    {
33        typedef std::student_t_distribution<> D;
34        typedef D::param_type P;
35        typedef std::minstd_rand G;
36        G g;
37        D d(5.5);
38        const int N = 1000000;
39        std::vector<D::result_type> u;
40        for (int i = 0; i < N; ++i)
41            u.push_back(d(g));
42        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
43        double var = 0;
44        double skew = 0;
45        double kurtosis = 0;
46        for (int i = 0; i < u.size(); ++i)
47        {
48            double d = (u[i] - mean);
49            double d2 = sqr(d);
50            var += d2;
51            skew += d * d2;
52            kurtosis += d2 * d2;
53        }
54        var /= u.size();
55        double dev = std::sqrt(var);
56        skew /= u.size() * dev * var;
57        kurtosis /= u.size() * var * var;
58        kurtosis -= 3;
59        double x_mean = 0;
60        double x_var = d.n() / (d.n() - 2);
61        double x_skew = 0;
62        double x_kurtosis = 6 / (d.n() - 4);
63        assert(std::abs(mean - x_mean) < 0.01);
64        assert(std::abs((var - x_var) / x_var) < 0.01);
65        assert(std::abs(skew - x_skew) < 0.01);
66        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
67    }
68    {
69        typedef std::student_t_distribution<> D;
70        typedef D::param_type P;
71        typedef std::minstd_rand G;
72        G g;
73        D d(10);
74        const int N = 1000000;
75        std::vector<D::result_type> u;
76        for (int i = 0; i < N; ++i)
77            u.push_back(d(g));
78        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
79        double var = 0;
80        double skew = 0;
81        double kurtosis = 0;
82        for (int i = 0; i < u.size(); ++i)
83        {
84            double d = (u[i] - mean);
85            double d2 = sqr(d);
86            var += d2;
87            skew += d * d2;
88            kurtosis += d2 * d2;
89        }
90        var /= u.size();
91        double dev = std::sqrt(var);
92        skew /= u.size() * dev * var;
93        kurtosis /= u.size() * var * var;
94        kurtosis -= 3;
95        double x_mean = 0;
96        double x_var = d.n() / (d.n() - 2);
97        double x_skew = 0;
98        double x_kurtosis = 6 / (d.n() - 4);
99        assert(std::abs(mean - x_mean) < 0.01);
100        assert(std::abs((var - x_var) / x_var) < 0.01);
101        assert(std::abs(skew - x_skew) < 0.01);
102        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
103    }
104    {
105        typedef std::student_t_distribution<> D;
106        typedef D::param_type P;
107        typedef std::minstd_rand G;
108        G g;
109        D d(100);
110        const int N = 1000000;
111        std::vector<D::result_type> u;
112        for (int i = 0; i < N; ++i)
113            u.push_back(d(g));
114        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
115        double var = 0;
116        double skew = 0;
117        double kurtosis = 0;
118        for (int i = 0; i < u.size(); ++i)
119        {
120            double d = (u[i] - mean);
121            double d2 = sqr(d);
122            var += d2;
123            skew += d * d2;
124            kurtosis += d2 * d2;
125        }
126        var /= u.size();
127        double dev = std::sqrt(var);
128        skew /= u.size() * dev * var;
129        kurtosis /= u.size() * var * var;
130        kurtosis -= 3;
131        double x_mean = 0;
132        double x_var = d.n() / (d.n() - 2);
133        double x_skew = 0;
134        double x_kurtosis = 6 / (d.n() - 4);
135        assert(std::abs(mean - x_mean) < 0.01);
136        assert(std::abs((var - x_var) / x_var) < 0.01);
137        assert(std::abs(skew - x_skew) < 0.01);
138        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
139    }
140}
141