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
24 template <class T>
25 inline
26 T
sqr(T x)27 sqr(T x)
28 {
29 return x * x;
30 }
31
main()32 int 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