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 gamma_distribution
15
16// template<class _URNG> result_type operator()(_URNG& g);
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::gamma_distribution<> D;
38 typedef std::mt19937 G;
39 G g;
40 D d(0.5, 2);
41 const int N = 1000000;
42 std::vector<D::result_type> u;
43 for (int i = 0; i < N; ++i)
44 {
45 D::result_type v = d(g);
46 assert(d.min() < v);
47 u.push_back(v);
48 }
49 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
50 double var = 0;
51 double skew = 0;
52 double kurtosis = 0;
53 for (unsigned i = 0; i < u.size(); ++i)
54 {
55 double dbl = (u[i] - mean);
56 double d2 = sqr(dbl);
57 var += d2;
58 skew += dbl * d2;
59 kurtosis += d2 * d2;
60 }
61 var /= u.size();
62 double dev = std::sqrt(x: var);
63 skew /= u.size() * dev * var;
64 kurtosis /= u.size() * var * var;
65 kurtosis -= 3;
66 double x_mean = d.alpha() * d.beta();
67 double x_var = d.alpha() * sqr(d.beta());
68 double x_skew = 2 / std::sqrt(x: d.alpha());
69 double x_kurtosis = 6 / d.alpha();
70 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
71 assert(std::abs((var - x_var) / x_var) < 0.01);
72 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
73 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
74 }
75 {
76 typedef std::gamma_distribution<> D;
77 typedef std::mt19937 G;
78 G g;
79 D d(1, .5);
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 (unsigned i = 0; i < u.size(); ++i)
93 {
94 double dbl = (u[i] - mean);
95 double d2 = sqr(dbl);
96 var += d2;
97 skew += dbl * d2;
98 kurtosis += d2 * d2;
99 }
100 var /= u.size();
101 double dev = std::sqrt(x: var);
102 skew /= u.size() * dev * var;
103 kurtosis /= u.size() * var * var;
104 kurtosis -= 3;
105 double x_mean = d.alpha() * d.beta();
106 double x_var = d.alpha() * sqr(d.beta());
107 double x_skew = 2 / std::sqrt(d.alpha());
108 double x_kurtosis = 6 / d.alpha();
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) < 0.03);
113 }
114 {
115 typedef std::gamma_distribution<> D;
116 typedef std::mt19937 G;
117 G g;
118 D d(2, 3);
119 const int N = 1000000;
120 std::vector<D::result_type> u;
121 for (int i = 0; i < N; ++i)
122 {
123 D::result_type v = d(g);
124 assert(d.min() < v);
125 u.push_back(v);
126 }
127 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
128 double var = 0;
129 double skew = 0;
130 double kurtosis = 0;
131 for (unsigned i = 0; i < u.size(); ++i)
132 {
133 double dbl = (u[i] - mean);
134 double d2 = sqr(dbl);
135 var += d2;
136 skew += dbl * d2;
137 kurtosis += d2 * d2;
138 }
139 var /= u.size();
140 double dev = std::sqrt(x: var);
141 skew /= u.size() * dev * var;
142 kurtosis /= u.size() * var * var;
143 kurtosis -= 3;
144 double x_mean = d.alpha() * d.beta();
145 double x_var = d.alpha() * sqr(d.beta());
146 double x_skew = 2 / std::sqrt(d.alpha());
147 double x_kurtosis = 6 / d.alpha();
148 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
149 assert(std::abs((var - x_var) / x_var) < 0.01);
150 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
151 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
152 }
153
154 return 0;
155}
156

source code of libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval.pass.cpp