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