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 IntType = int>
15// class poisson_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::poisson_distribution<> D;
36        typedef std::minstd_rand G;
37        G g;
38        D d(2);
39        const int N = 100000;
40        std::vector<double> u;
41        for (int i = 0; i < N; ++i)
42        {
43            D::result_type v = d(g);
44            assert(d.min() <= v && v <= d.max());
45            u.push_back(v);
46        }
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(var);
61        skew /= u.size() * dev * var;
62        kurtosis /= u.size() * var * var;
63        kurtosis -= 3;
64        double x_mean = d.mean();
65        double x_var = d.mean();
66        double x_skew = 1 / std::sqrt(x_var);
67        double x_kurtosis = 1 / x_var;
68        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
69        assert(std::abs((var - x_var) / x_var) < 0.01);
70        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
71        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
72    }
73    {
74        typedef std::poisson_distribution<> D;
75        typedef std::minstd_rand G;
76        G g;
77        D d(0.75);
78        const int N = 100000;
79        std::vector<double> u;
80        for (int i = 0; i < N; ++i)
81        {
82            D::result_type v = d(g);
83            assert(d.min() <= v && v <= d.max());
84            u.push_back(v);
85        }
86        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
87        double var = 0;
88        double skew = 0;
89        double kurtosis = 0;
90        for (unsigned i = 0; i < u.size(); ++i)
91        {
92            double dbl = (u[i] - mean);
93            double d2 = sqr(dbl);
94            var += d2;
95            skew += dbl * d2;
96            kurtosis += d2 * d2;
97        }
98        var /= u.size();
99        double dev = std::sqrt(var);
100        skew /= u.size() * dev * var;
101        kurtosis /= u.size() * var * var;
102        kurtosis -= 3;
103        double x_mean = d.mean();
104        double x_var = d.mean();
105        double x_skew = 1 / std::sqrt(x_var);
106        double x_kurtosis = 1 / x_var;
107        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
108        assert(std::abs((var - x_var) / x_var) < 0.01);
109        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
110        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
111    }
112    {
113        typedef std::poisson_distribution<> D;
114        typedef std::mt19937 G;
115        G g;
116        D d(20);
117        const int N = 1000000;
118        std::vector<double> u;
119        for (int i = 0; i < N; ++i)
120        {
121            D::result_type v = d(g);
122            assert(d.min() <= v && v <= d.max());
123            u.push_back(v);
124        }
125        double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
126        double var = 0;
127        double skew = 0;
128        double kurtosis = 0;
129        for (unsigned i = 0; i < u.size(); ++i)
130        {
131            double dbl = (u[i] - mean);
132            double d2 = sqr(dbl);
133            var += d2;
134            skew += dbl * d2;
135            kurtosis += d2 * d2;
136        }
137        var /= u.size();
138        double dev = std::sqrt(var);
139        skew /= u.size() * dev * var;
140        kurtosis /= u.size() * var * var;
141        kurtosis -= 3;
142        double x_mean = d.mean();
143        double x_var = d.mean();
144        double x_skew = 1 / std::sqrt(x_var);
145        double x_kurtosis = 1 / x_var;
146        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
147        assert(std::abs((var - x_var) / x_var) < 0.01);
148        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
149        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
150    }
151}
152