1//===----------------------------------------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// REQUIRES: long_tests
10
11// <random>
12
13// template<class RealType = double>
14// class student_t_distribution
15
16// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
17
18#include <random>
19#include <cassert>
20#include <cmath>
21#include <numeric>
22#include <vector>
23
24#include "test_macros.h"
25
26template <class T>
27inline
28T
29sqr(T x)
30{
31 return x * x;
32}
33
34int main(int, char**)
35{
36 {
37 typedef std::student_t_distribution<> D;
38 typedef D::param_type P;
39 typedef std::minstd_rand G;
40 G g;
41 D d;
42 P p(5.5);
43 const int N = 1000000;
44 std::vector<D::result_type> u;
45 for (int i = 0; i < N; ++i)
46 u.push_back(d(g, p));
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 (unsigned i = 0; i < u.size(); ++i)
52 {
53 double dbl = (u[i] - mean);
54 double d2 = sqr(dbl);
55 var += d2;
56 skew += dbl * d2;
57 kurtosis += d2 * d2;
58 }
59 var /= u.size();
60 double dev = std::sqrt(x: var);
61 skew /= u.size() * dev * var;
62 kurtosis /= u.size() * var * var;
63 kurtosis -= 3;
64 double x_mean = 0;
65 double x_var = p.n() / (p.n() - 2);
66 double x_skew = 0;
67 double x_kurtosis = 6 / (p.n() - 4);
68 assert(std::abs(mean - x_mean) < 0.01);
69 assert(std::abs((var - x_var) / x_var) < 0.01);
70 assert(std::abs(skew - x_skew) < 0.05);
71 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
72 }
73 {
74 typedef std::student_t_distribution<> D;
75 typedef D::param_type P;
76 typedef std::minstd_rand G;
77 G g;
78 D d;
79 P p(10);
80 const int N = 1000000;
81 std::vector<D::result_type> u;
82 for (int i = 0; i < N; ++i)
83 u.push_back(d(g, p));
84 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
85 double var = 0;
86 double skew = 0;
87 double kurtosis = 0;
88 for (unsigned i = 0; i < u.size(); ++i)
89 {
90 double dbl = (u[i] - mean);
91 double d2 = sqr(dbl);
92 var += d2;
93 skew += dbl * d2;
94 kurtosis += d2 * d2;
95 }
96 var /= u.size();
97 double dev = std::sqrt(x: var);
98 skew /= u.size() * dev * var;
99 kurtosis /= u.size() * var * var;
100 kurtosis -= 3;
101 double x_mean = 0;
102 double x_var = p.n() / (p.n() - 2);
103 double x_skew = 0;
104 double x_kurtosis = 6 / (p.n() - 4);
105 assert(std::abs(mean - x_mean) < 0.01);
106 assert(std::abs((var - x_var) / x_var) < 0.01);
107 assert(std::abs(skew - x_skew) < 0.05);
108 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
109 }
110 {
111 typedef std::student_t_distribution<> D;
112 typedef D::param_type P;
113 typedef std::minstd_rand G;
114 G g;
115 D d;
116 P p(100);
117 const int N = 1000000;
118 std::vector<D::result_type> u;
119 for (int i = 0; i < N; ++i)
120 u.push_back(d(g, p));
121 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
122 double var = 0;
123 double skew = 0;
124 double kurtosis = 0;
125 for (unsigned i = 0; i < u.size(); ++i)
126 {
127 double dbl = (u[i] - mean);
128 double d2 = sqr(dbl);
129 var += d2;
130 skew += dbl * d2;
131 kurtosis += d2 * d2;
132 }
133 var /= u.size();
134 double dev = std::sqrt(x: var);
135 skew /= u.size() * dev * var;
136 kurtosis /= u.size() * var * var;
137 kurtosis -= 3;
138 double x_mean = 0;
139 double x_var = p.n() / (p.n() - 2);
140 double x_skew = 0;
141 double x_kurtosis = 6 / (p.n() - 4);
142 assert(std::abs(mean - x_mean) < 0.01);
143 assert(std::abs((var - x_var) / x_var) < 0.01);
144 assert(std::abs(skew - x_skew) < 0.005);
145 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
146 }
147
148 return 0;
149}
150

source code of libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval_param.pass.cpp