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 IntType = int>
13// class binomial_distribution
14
15// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
16
17#include <random>
18#include <numeric>
19#include <vector>
20#include <cassert>
21
22template <class T>
23inline
24T
25sqr(T x)
26{
27    return x * x;
28}
29
30int main()
31{
32    {
33        typedef std::binomial_distribution<> D;
34        typedef D::param_type P;
35        typedef std::mt19937_64 G;
36        G g;
37        D d(16, .75);
38        P p(5, .75);
39        const int N = 1000000;
40        std::vector<D::result_type> u;
41        for (int i = 0; i < N; ++i)
42        {
43            D::result_type v = d(g, p);
44            assert(0 <= v && v <= p.t());
45            u.push_back(v);
46        }
47        double mean = std::accumulate(u.begin(), u.end(),
48                                              double(0)) / u.size();
49        double var = 0;
50        double skew = 0;
51        double kurtosis = 0;
52        for (int i = 0; i < u.size(); ++i)
53        {
54            double d = (u[i] - mean);
55            double d2 = sqr(d);
56            var += d2;
57            skew += d * d2;
58            kurtosis += d2 * d2;
59        }
60        var /= u.size();
61        double dev = std::sqrt(var);
62        skew /= u.size() * dev * var;
63        kurtosis /= u.size() * var * var;
64        kurtosis -= 3;
65        double x_mean = p.t() * p.p();
66        double x_var = x_mean*(1-p.p());
67        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
68        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
69        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
70        assert(std::abs((var - x_var) / x_var) < 0.01);
71        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
72        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
73    }
74    {
75        typedef std::binomial_distribution<> D;
76        typedef D::param_type P;
77        typedef std::mt19937 G;
78        G g;
79        D d(16, .75);
80        P p(30, .03125);
81        const int N = 100000;
82        std::vector<D::result_type> u;
83        for (int i = 0; i < N; ++i)
84        {
85            D::result_type v = d(g, p);
86            assert(0 <= v && v <= p.t());
87            u.push_back(v);
88        }
89        double mean = std::accumulate(u.begin(), u.end(),
90                                              double(0)) / u.size();
91        double var = 0;
92        double skew = 0;
93        double kurtosis = 0;
94        for (int i = 0; i < u.size(); ++i)
95        {
96            double d = (u[i] - mean);
97            double d2 = sqr(d);
98            var += d2;
99            skew += d * d2;
100            kurtosis += d2 * d2;
101        }
102        var /= u.size();
103        double dev = std::sqrt(var);
104        skew /= u.size() * dev * var;
105        kurtosis /= u.size() * var * var;
106        kurtosis -= 3;
107        double x_mean = p.t() * p.p();
108        double x_var = x_mean*(1-p.p());
109        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
110        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
111        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
112        assert(std::abs((var - x_var) / x_var) < 0.01);
113        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
114        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
115    }
116    {
117        typedef std::binomial_distribution<> D;
118        typedef D::param_type P;
119        typedef std::mt19937 G;
120        G g;
121        D d(16, .75);
122        P p(40, .25);
123        const int N = 1000000;
124        std::vector<D::result_type> u;
125        for (int i = 0; i < N; ++i)
126        {
127            D::result_type v = d(g, p);
128            assert(0 <= v && v <= p.t());
129            u.push_back(v);
130        }
131        double mean = std::accumulate(u.begin(), u.end(),
132                                              double(0)) / u.size();
133        double var = 0;
134        double skew = 0;
135        double kurtosis = 0;
136        for (int i = 0; i < u.size(); ++i)
137        {
138            double d = (u[i] - mean);
139            double d2 = sqr(d);
140            var += d2;
141            skew += d * d2;
142            kurtosis += d2 * d2;
143        }
144        var /= u.size();
145        double dev = std::sqrt(var);
146        skew /= u.size() * dev * var;
147        kurtosis /= u.size() * var * var;
148        kurtosis -= 3;
149        double x_mean = p.t() * p.p();
150        double x_var = x_mean*(1-p.p());
151        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
152        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
153        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
154        assert(std::abs((var - x_var) / x_var) < 0.01);
155        assert(std::abs((skew - x_skew) / x_skew) < 0.04);
156        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
157    }
158}
159