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 chi_squared_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 <cstddef>
22#include <numeric>
23#include <vector>
24
25#include "test_macros.h"
26
27template <class T>
28inline
29T
30sqr(T x)
31{
32 return x * x;
33}
34
35int main(int, char**)
36{
37 {
38 typedef std::chi_squared_distribution<> D;
39 typedef D::param_type P;
40 typedef std::minstd_rand G;
41 G g;
42 D d(0.5);
43 P p(1);
44 const int N = 1000000;
45 std::vector<D::result_type> u;
46 for (int i = 0; i < N; ++i)
47 {
48 D::result_type v = d(g, p);
49 assert(d.min() < v);
50 u.push_back(v);
51 }
52 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
53 double var = 0;
54 double skew = 0;
55 double kurtosis = 0;
56 for (std::size_t i = 0; i < u.size(); ++i)
57 {
58 double dbl = (u[i] - mean);
59 double d2 = sqr(dbl);
60 var += d2;
61 skew += dbl * d2;
62 kurtosis += d2 * d2;
63 }
64 var /= u.size();
65 double dev = std::sqrt(x: var);
66 skew /= u.size() * dev * var;
67 kurtosis /= u.size() * var * var;
68 kurtosis -= 3;
69 double x_mean = p.n();
70 double x_var = 2 * p.n();
71 double x_skew = std::sqrt(x: 8 / p.n());
72 double x_kurtosis = 12 / p.n();
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::chi_squared_distribution<> D;
80 typedef D::param_type P;
81 typedef std::mt19937 G;
82 G g;
83 D d(1);
84 P p(2);
85 const int N = 1000000;
86 std::vector<D::result_type> u;
87 for (int i = 0; i < N; ++i)
88 {
89 D::result_type v = d(g, p);
90 assert(d.min() < v);
91 u.push_back(v);
92 }
93 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
94 double var = 0;
95 double skew = 0;
96 double kurtosis = 0;
97 for (std::size_t i = 0; i < u.size(); ++i)
98 {
99 double dbl = (u[i] - mean);
100 double d2 = sqr(dbl);
101 var += d2;
102 skew += dbl * d2;
103 kurtosis += d2 * d2;
104 }
105 var /= u.size();
106 double dev = std::sqrt(x: var);
107 skew /= u.size() * dev * var;
108 kurtosis /= u.size() * var * var;
109 kurtosis -= 3;
110 double x_mean = p.n();
111 double x_var = 2 * p.n();
112 double x_skew = std::sqrt(8 / p.n());
113 double x_kurtosis = 12 / p.n();
114 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
115 assert(std::abs((var - x_var) / x_var) < 0.01);
116 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
117 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
118 }
119 {
120 typedef std::chi_squared_distribution<> D;
121 typedef D::param_type P;
122 typedef std::minstd_rand G;
123 G g;
124 D d(2);
125 P p(.5);
126 const int N = 1000000;
127 std::vector<D::result_type> u;
128 for (int i = 0; i < N; ++i)
129 {
130 D::result_type v = d(g, p);
131 assert(d.min() < v);
132 u.push_back(v);
133 }
134 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
135 double var = 0;
136 double skew = 0;
137 double kurtosis = 0;
138 for (std::size_t i = 0; i < u.size(); ++i)
139 {
140 double dbl = (u[i] - mean);
141 double d2 = sqr(dbl);
142 var += d2;
143 skew += dbl * d2;
144 kurtosis += d2 * d2;
145 }
146 var /= u.size();
147 double dev = std::sqrt(x: var);
148 skew /= u.size() * dev * var;
149 kurtosis /= u.size() * var * var;
150 kurtosis -= 3;
151 double x_mean = p.n();
152 double x_var = 2 * p.n();
153 double x_skew = std::sqrt(8 / p.n());
154 double x_kurtosis = 12 / p.n();
155 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
156 assert(std::abs((var - x_var) / x_var) < 0.01);
157 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
158 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
159 }
160
161 return 0;
162}
163

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