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 binomial_distribution
16
17// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
18
19#include <random>
20#include <numeric>
21#include <vector>
22#include <cassert>
23
24template <class T>
25inline
26T
27sqr(T x)
28{
29    return x * x;
30}
31
32int main()
33{
34    {
35        typedef std::binomial_distribution<> D;
36        typedef D::param_type P;
37        typedef std::mt19937_64 G;
38        G g;
39        D d(16, .75);
40        P p(5, .75);
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, p);
46            assert(0 <= v && v <= p.t());
47            u.push_back(v);
48        }
49        double mean = std::accumulate(u.begin(), u.end(),
50                                              double(0)) / u.size();
51        double var = 0;
52        double skew = 0;
53        double kurtosis = 0;
54        for (unsigned i = 0; i < u.size(); ++i)
55        {
56            double dbl = (u[i] - mean);
57            double d2 = sqr(dbl);
58            var += d2;
59            skew += dbl * d2;
60            kurtosis += d2 * d2;
61        }
62        var /= u.size();
63        double dev = std::sqrt(var);
64        skew /= u.size() * dev * var;
65        kurtosis /= u.size() * var * var;
66        kurtosis -= 3;
67        double x_mean = p.t() * p.p();
68        double x_var = x_mean*(1-p.p());
69        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
70        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
71        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
72        assert(std::abs((var - x_var) / x_var) < 0.01);
73        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
74        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
75    }
76    {
77        typedef std::binomial_distribution<> D;
78        typedef D::param_type P;
79        typedef std::mt19937 G;
80        G g;
81        D d(16, .75);
82        P p(30, .03125);
83        const int N = 100000;
84        std::vector<D::result_type> u;
85        for (int i = 0; i < N; ++i)
86        {
87            D::result_type v = d(g, p);
88            assert(0 <= v && v <= p.t());
89            u.push_back(v);
90        }
91        double mean = std::accumulate(u.begin(), u.end(),
92                                              double(0)) / u.size();
93        double var = 0;
94        double skew = 0;
95        double kurtosis = 0;
96        for (unsigned i = 0; i < u.size(); ++i)
97        {
98            double dbl = (u[i] - mean);
99            double d2 = sqr(dbl);
100            var += d2;
101            skew += dbl * d2;
102            kurtosis += d2 * d2;
103        }
104        var /= u.size();
105        double dev = std::sqrt(var);
106        skew /= u.size() * dev * var;
107        kurtosis /= u.size() * var * var;
108        kurtosis -= 3;
109        double x_mean = p.t() * p.p();
110        double x_var = x_mean*(1-p.p());
111        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
112        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
113        assert(std::abs((mean - x_mean) / x_mean) < 0.01);
114        assert(std::abs((var - x_var) / x_var) < 0.01);
115        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
116        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
117    }
118    {
119        typedef std::binomial_distribution<> D;
120        typedef D::param_type P;
121        typedef std::mt19937 G;
122        G g;
123        D d(16, .75);
124        P p(40, .25);
125        const int N = 1000000;
126        std::vector<D::result_type> u;
127        for (int i = 0; i < N; ++i)
128        {
129            D::result_type v = d(g, p);
130            assert(0 <= v && v <= p.t());
131            u.push_back(v);
132        }
133        double mean = std::accumulate(u.begin(), u.end(),
134                                              double(0)) / u.size();
135        double var = 0;
136        double skew = 0;
137        double kurtosis = 0;
138        for (unsigned 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(var);
148        skew /= u.size() * dev * var;
149        kurtosis /= u.size() * var * var;
150        kurtosis -= 3;
151        double x_mean = p.t() * p.p();
152        double x_var = x_mean*(1-p.p());
153        double x_skew = (1-2*p.p()) / std::sqrt(x_var);
154        double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
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) < 0.04);
158        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
159    }
160}
161