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 negative_binomial_distribution
16 
17 // template<class _URNG> result_type operator()(_URNG& g);
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::negative_binomial_distribution<> D;
36         typedef std::minstd_rand G;
37         G g;
38         D d(5, .25);
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);
44             assert(d.min() <= v && v <= d.max());
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 = d.k() * (1 - d.p()) / d.p();
66         double x_var = x_mean / d.p();
67         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
68         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
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) < 0.02);
73     }
74     {
75         typedef std::negative_binomial_distribution<> D;
76         typedef std::mt19937 G;
77         G g;
78         D d(30, .03125);
79         const int N = 1000000;
80         std::vector<D::result_type> u;
81         for (int i = 0; i < N; ++i)
82         {
83             D::result_type v = d(g);
84             assert(d.min() <= v && v <= d.max());
85             u.push_back(v);
86         }
87         double mean = std::accumulate(u.begin(), u.end(),
88                                               double(0)) / u.size();
89         double var = 0;
90         double skew = 0;
91         double kurtosis = 0;
92         for (int i = 0; i < u.size(); ++i)
93         {
94             double d = (u[i] - mean);
95             double d2 = sqr(d);
96             var += d2;
97             skew += d * d2;
98             kurtosis += d2 * d2;
99         }
100         var /= u.size();
101         double dev = std::sqrt(var);
102         skew /= u.size() * dev * var;
103         kurtosis /= u.size() * var * var;
104         kurtosis -= 3;
105         double x_mean = d.k() * (1 - d.p()) / d.p();
106         double x_var = x_mean / d.p();
107         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
108         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
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) < 0.01);
113     }
114     {
115         typedef std::negative_binomial_distribution<> D;
116         typedef std::mt19937 G;
117         G g;
118         D d(40, .25);
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 && v <= d.max());
125             u.push_back(v);
126         }
127         double mean = std::accumulate(u.begin(), u.end(),
128                                               double(0)) / u.size();
129         double var = 0;
130         double skew = 0;
131         double kurtosis = 0;
132         for (int i = 0; i < u.size(); ++i)
133         {
134             double d = (u[i] - mean);
135             double d2 = sqr(d);
136             var += d2;
137             skew += d * d2;
138             kurtosis += d2 * d2;
139         }
140         var /= u.size();
141         double dev = std::sqrt(var);
142         skew /= u.size() * dev * var;
143         kurtosis /= u.size() * var * var;
144         kurtosis -= 3;
145         double x_mean = d.k() * (1 - d.p()) / d.p();
146         double x_var = x_mean / d.p();
147         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
148         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
149         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
150         assert(std::abs((var - x_var) / x_var) < 0.01);
151         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
152         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
153     }
154     {
155         typedef std::negative_binomial_distribution<> D;
156         typedef std::mt19937 G;
157         G g;
158         D d(40, 1);
159         const int N = 1000;
160         std::vector<D::result_type> u;
161         for (int i = 0; i < N; ++i)
162         {
163             D::result_type v = d(g);
164             assert(d.min() <= v && v <= d.max());
165             u.push_back(v);
166         }
167         double mean = std::accumulate(u.begin(), u.end(),
168                                               double(0)) / u.size();
169         double var = 0;
170         double skew = 0;
171         double kurtosis = 0;
172         for (int i = 0; i < u.size(); ++i)
173         {
174             double d = (u[i] - mean);
175             double d2 = sqr(d);
176             var += d2;
177             skew += d * d2;
178             kurtosis += d2 * d2;
179         }
180         var /= u.size();
181         double dev = std::sqrt(var);
182         skew /= u.size() * dev * var;
183         kurtosis /= u.size() * var * var;
184         kurtosis -= 3;
185         double x_mean = d.k() * (1 - d.p()) / d.p();
186         double x_var = x_mean / d.p();
187         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
188         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
189         assert(mean == x_mean);
190         assert(var == x_var);
191     }
192     {
193         typedef std::negative_binomial_distribution<> D;
194         typedef std::mt19937 G;
195         G g;
196         D d(400, 0.5);
197         const int N = 1000000;
198         std::vector<D::result_type> u;
199         for (int i = 0; i < N; ++i)
200         {
201             D::result_type v = d(g);
202             assert(d.min() <= v && v <= d.max());
203             u.push_back(v);
204         }
205         double mean = std::accumulate(u.begin(), u.end(),
206                                               double(0)) / u.size();
207         double var = 0;
208         double skew = 0;
209         double kurtosis = 0;
210         for (int i = 0; i < u.size(); ++i)
211         {
212             double d = (u[i] - mean);
213             double d2 = sqr(d);
214             var += d2;
215             skew += d * d2;
216             kurtosis += d2 * d2;
217         }
218         var /= u.size();
219         double dev = std::sqrt(var);
220         skew /= u.size() * dev * var;
221         kurtosis /= u.size() * var * var;
222         kurtosis -= 3;
223         double x_mean = d.k() * (1 - d.p()) / d.p();
224         double x_var = x_mean / d.p();
225         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
226         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
227         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
228         assert(std::abs((var - x_var) / x_var) < 0.01);
229         assert(std::abs((skew - x_skew) / x_skew) < 0.04);
230         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
231     }
232     {
233         typedef std::negative_binomial_distribution<> D;
234         typedef std::mt19937 G;
235         G g;
236         D d(1, 0.05);
237         const int N = 1000000;
238         std::vector<D::result_type> u;
239         for (int i = 0; i < N; ++i)
240         {
241             D::result_type v = d(g);
242             assert(d.min() <= v && v <= d.max());
243             u.push_back(v);
244         }
245         double mean = std::accumulate(u.begin(), u.end(),
246                                               double(0)) / u.size();
247         double var = 0;
248         double skew = 0;
249         double kurtosis = 0;
250         for (int i = 0; i < u.size(); ++i)
251         {
252             double d = (u[i] - mean);
253             double d2 = sqr(d);
254             var += d2;
255             skew += d * d2;
256             kurtosis += d2 * d2;
257         }
258         var /= u.size();
259         double dev = std::sqrt(var);
260         skew /= u.size() * dev * var;
261         kurtosis /= u.size() * var * var;
262         kurtosis -= 3;
263         double x_mean = d.k() * (1 - d.p()) / d.p();
264         double x_var = x_mean / d.p();
265         double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
266         double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
267         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
268         assert(std::abs((var - x_var) / x_var) < 0.01);
269         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
270         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
271     }
272 }
273