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);
16
17 #include <random>
18 #include <numeric>
19 #include <vector>
20 #include <cassert>
21
22 template <class T>
23 inline
24 T
sqr(T x)25 sqr(T x)
26 {
27 return x * x;
28 }
29
main()30 int main()
31 {
32 {
33 typedef std::binomial_distribution<> D;
34 typedef std::mt19937_64 G;
35 G g;
36 D d(5, .75);
37 const int N = 1000000;
38 std::vector<D::result_type> u;
39 for (int i = 0; i < N; ++i)
40 {
41 D::result_type v = d(g);
42 assert(d.min() <= v && v <= d.max());
43 u.push_back(v);
44 }
45 double mean = std::accumulate(u.begin(), u.end(),
46 double(0)) / u.size();
47 double var = 0;
48 double skew = 0;
49 double kurtosis = 0;
50 for (int i = 0; i < u.size(); ++i)
51 {
52 double d = (u[i] - mean);
53 double d2 = sqr(d);
54 var += d2;
55 skew += d * d2;
56 kurtosis += d2 * d2;
57 }
58 var /= u.size();
59 double dev = std::sqrt(var);
60 skew /= u.size() * dev * var;
61 kurtosis /= u.size() * var * var;
62 kurtosis -= 3;
63 double x_mean = d.t() * d.p();
64 double x_var = x_mean*(1-d.p());
65 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
66 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
67 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
68 assert(std::abs((var - x_var) / x_var) < 0.01);
69 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
70 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
71 }
72 {
73 typedef std::binomial_distribution<> D;
74 typedef std::mt19937 G;
75 G g;
76 D d(30, .03125);
77 const int N = 100000;
78 std::vector<D::result_type> u;
79 for (int i = 0; i < N; ++i)
80 {
81 D::result_type v = d(g);
82 assert(d.min() <= v && v <= d.max());
83 u.push_back(v);
84 }
85 double mean = std::accumulate(u.begin(), u.end(),
86 double(0)) / u.size();
87 double var = 0;
88 double skew = 0;
89 double kurtosis = 0;
90 for (int i = 0; i < u.size(); ++i)
91 {
92 double d = (u[i] - mean);
93 double d2 = sqr(d);
94 var += d2;
95 skew += d * d2;
96 kurtosis += d2 * d2;
97 }
98 var /= u.size();
99 double dev = std::sqrt(var);
100 skew /= u.size() * dev * var;
101 kurtosis /= u.size() * var * var;
102 kurtosis -= 3;
103 double x_mean = d.t() * d.p();
104 double x_var = x_mean*(1-d.p());
105 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
106 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
107 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
108 assert(std::abs((var - x_var) / x_var) < 0.01);
109 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
110 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
111 }
112 {
113 typedef std::binomial_distribution<> D;
114 typedef std::mt19937 G;
115 G g;
116 D d(40, .25);
117 const int N = 100000;
118 std::vector<D::result_type> u;
119 for (int i = 0; i < N; ++i)
120 {
121 D::result_type v = d(g);
122 assert(d.min() <= v && v <= d.max());
123 u.push_back(v);
124 }
125 double mean = std::accumulate(u.begin(), u.end(),
126 double(0)) / u.size();
127 double var = 0;
128 double skew = 0;
129 double kurtosis = 0;
130 for (int i = 0; i < u.size(); ++i)
131 {
132 double d = (u[i] - mean);
133 double d2 = sqr(d);
134 var += d2;
135 skew += d * d2;
136 kurtosis += d2 * d2;
137 }
138 var /= u.size();
139 double dev = std::sqrt(var);
140 skew /= u.size() * dev * var;
141 kurtosis /= u.size() * var * var;
142 kurtosis -= 3;
143 double x_mean = d.t() * d.p();
144 double x_var = x_mean*(1-d.p());
145 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
146 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
147 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
148 assert(std::abs((var - x_var) / x_var) < 0.01);
149 assert(std::abs((skew - x_skew) / x_skew) < 0.03);
150 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
151 }
152 {
153 typedef std::binomial_distribution<> D;
154 typedef std::mt19937 G;
155 G g;
156 D d(40, 0);
157 const int N = 100000;
158 std::vector<D::result_type> u;
159 for (int i = 0; i < N; ++i)
160 {
161 D::result_type v = d(g);
162 assert(d.min() <= v && v <= d.max());
163 u.push_back(v);
164 }
165 double mean = std::accumulate(u.begin(), u.end(),
166 double(0)) / u.size();
167 double var = 0;
168 double skew = 0;
169 double kurtosis = 0;
170 for (int i = 0; i < u.size(); ++i)
171 {
172 double d = (u[i] - mean);
173 double d2 = sqr(d);
174 var += d2;
175 skew += d * d2;
176 kurtosis += d2 * d2;
177 }
178 var /= u.size();
179 double dev = std::sqrt(var);
180 // In this case:
181 // skew computes to 0./0. == nan
182 // kurtosis computes to 0./0. == nan
183 // x_skew == inf
184 // x_kurtosis == inf
185 // These tests are commented out because UBSan warns about division by 0
186 // skew /= u.size() * dev * var;
187 // kurtosis /= u.size() * var * var;
188 // kurtosis -= 3;
189 double x_mean = d.t() * d.p();
190 double x_var = x_mean*(1-d.p());
191 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
192 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
193 assert(mean == x_mean);
194 assert(var == x_var);
195 // assert(skew == x_skew);
196 // assert(kurtosis == x_kurtosis);
197 }
198 {
199 typedef std::binomial_distribution<> D;
200 typedef std::mt19937 G;
201 G g;
202 D d(40, 1);
203 const int N = 100000;
204 std::vector<D::result_type> u;
205 for (int i = 0; i < N; ++i)
206 {
207 D::result_type v = d(g);
208 assert(d.min() <= v && v <= d.max());
209 u.push_back(v);
210 }
211 double mean = std::accumulate(u.begin(), u.end(),
212 double(0)) / u.size();
213 double var = 0;
214 double skew = 0;
215 double kurtosis = 0;
216 for (int i = 0; i < u.size(); ++i)
217 {
218 double d = (u[i] - mean);
219 double d2 = sqr(d);
220 var += d2;
221 skew += d * d2;
222 kurtosis += d2 * d2;
223 }
224 var /= u.size();
225 double dev = std::sqrt(var);
226 // In this case:
227 // skew computes to 0./0. == nan
228 // kurtosis computes to 0./0. == nan
229 // x_skew == -inf
230 // x_kurtosis == inf
231 // These tests are commented out because UBSan warns about division by 0
232 // skew /= u.size() * dev * var;
233 // kurtosis /= u.size() * var * var;
234 // kurtosis -= 3;
235 double x_mean = d.t() * d.p();
236 double x_var = x_mean*(1-d.p());
237 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
238 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
239 assert(mean == x_mean);
240 assert(var == x_var);
241 // assert(skew == x_skew);
242 // assert(kurtosis == x_kurtosis);
243 }
244 {
245 typedef std::binomial_distribution<> D;
246 typedef std::mt19937 G;
247 G g;
248 D d(400, 0.5);
249 const int N = 100000;
250 std::vector<D::result_type> u;
251 for (int i = 0; i < N; ++i)
252 {
253 D::result_type v = d(g);
254 assert(d.min() <= v && v <= d.max());
255 u.push_back(v);
256 }
257 double mean = std::accumulate(u.begin(), u.end(),
258 double(0)) / u.size();
259 double var = 0;
260 double skew = 0;
261 double kurtosis = 0;
262 for (int i = 0; i < u.size(); ++i)
263 {
264 double d = (u[i] - mean);
265 double d2 = sqr(d);
266 var += d2;
267 skew += d * d2;
268 kurtosis += d2 * d2;
269 }
270 var /= u.size();
271 double dev = std::sqrt(var);
272 skew /= u.size() * dev * var;
273 kurtosis /= u.size() * var * var;
274 kurtosis -= 3;
275 double x_mean = d.t() * d.p();
276 double x_var = x_mean*(1-d.p());
277 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
278 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
279 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
280 assert(std::abs((var - x_var) / x_var) < 0.01);
281 assert(std::abs(skew - x_skew) < 0.01);
282 assert(std::abs(kurtosis - x_kurtosis) < 0.01);
283 }
284 {
285 typedef std::binomial_distribution<> D;
286 typedef std::mt19937 G;
287 G g;
288 D d(1, 0.5);
289 const int N = 100000;
290 std::vector<D::result_type> u;
291 for (int i = 0; i < N; ++i)
292 {
293 D::result_type v = d(g);
294 assert(d.min() <= v && v <= d.max());
295 u.push_back(v);
296 }
297 double mean = std::accumulate(u.begin(), u.end(),
298 double(0)) / u.size();
299 double var = 0;
300 double skew = 0;
301 double kurtosis = 0;
302 for (int i = 0; i < u.size(); ++i)
303 {
304 double d = (u[i] - mean);
305 double d2 = sqr(d);
306 var += d2;
307 skew += d * d2;
308 kurtosis += d2 * d2;
309 }
310 var /= u.size();
311 double dev = std::sqrt(var);
312 skew /= u.size() * dev * var;
313 kurtosis /= u.size() * var * var;
314 kurtosis -= 3;
315 double x_mean = d.t() * d.p();
316 double x_var = x_mean*(1-d.p());
317 double x_skew = (1-2*d.p()) / std::sqrt(x_var);
318 double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
319 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
320 assert(std::abs((var - x_var) / x_var) < 0.01);
321 assert(std::abs(skew - x_skew) < 0.01);
322 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
323 }
324 {
325 typedef std::binomial_distribution<> D;
326 typedef std::mt19937 G;
327 G g;
328 D d(0, 0.005);
329 const int N = 100000;
330 std::vector<D::result_type> u;
331 for (int i = 0; i < N; ++i)
332 {
333 D::result_type v = d(g);
334 assert(d.min() <= v && v <= d.max());
335 u.push_back(v);
336 }
337 double mean = std::accumulate(u.begin(), u.end(),
338 double(0)) / u.size();
339 double var = 0;
340 double skew = 0;
341 double kurtosis = 0;
342 for (int i = 0; i < u.size(); ++i)
343 {
344 double d = (u[i] - mean);
345 double d2 = sqr(d);
346 var += d2;
347 skew += d * d2;
348 kurtosis += d2 * d2;
349 }
350 var /= u.size();
351 double dev = std::sqrt(var);
352 // In this case:
353 // skew computes to 0./0. == nan
354 // kurtosis computes to 0./0. == nan
355 // x_skew == inf
356 // x_kurtosis == inf
357 // These tests are commented out because UBSan warns about division by 0
358 // skew /= u.size() * dev * var;
359 // kurtosis /= u.size() * var * var;
360 // kurtosis -= 3;
361 double x_mean = d.t() * d.p();
362 double x_var = x_mean*(1-d.p());
363 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
364 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
365 assert(mean == x_mean);
366 assert(var == x_var);
367 // assert(skew == x_skew);
368 // assert(kurtosis == x_kurtosis);
369 }
370 {
371 typedef std::binomial_distribution<> D;
372 typedef std::mt19937 G;
373 G g;
374 D d(0, 0);
375 const int N = 100000;
376 std::vector<D::result_type> u;
377 for (int i = 0; i < N; ++i)
378 {
379 D::result_type v = d(g);
380 assert(d.min() <= v && v <= d.max());
381 u.push_back(v);
382 }
383 double mean = std::accumulate(u.begin(), u.end(),
384 double(0)) / u.size();
385 double var = 0;
386 double skew = 0;
387 double kurtosis = 0;
388 for (int i = 0; i < u.size(); ++i)
389 {
390 double d = (u[i] - mean);
391 double d2 = sqr(d);
392 var += d2;
393 skew += d * d2;
394 kurtosis += d2 * d2;
395 }
396 var /= u.size();
397 double dev = std::sqrt(var);
398 // In this case:
399 // skew computes to 0./0. == nan
400 // kurtosis computes to 0./0. == nan
401 // x_skew == inf
402 // x_kurtosis == inf
403 // These tests are commented out because UBSan warns about division by 0
404 // skew /= u.size() * dev * var;
405 // kurtosis /= u.size() * var * var;
406 // kurtosis -= 3;
407 double x_mean = d.t() * d.p();
408 double x_var = x_mean*(1-d.p());
409 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
410 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
411 assert(mean == x_mean);
412 assert(var == x_var);
413 // assert(skew == x_skew);
414 // assert(kurtosis == x_kurtosis);
415 }
416 {
417 typedef std::binomial_distribution<> D;
418 typedef std::mt19937 G;
419 G g;
420 D d(0, 1);
421 const int N = 100000;
422 std::vector<D::result_type> u;
423 for (int i = 0; i < N; ++i)
424 {
425 D::result_type v = d(g);
426 assert(d.min() <= v && v <= d.max());
427 u.push_back(v);
428 }
429 double mean = std::accumulate(u.begin(), u.end(),
430 double(0)) / u.size();
431 double var = 0;
432 double skew = 0;
433 double kurtosis = 0;
434 for (int i = 0; i < u.size(); ++i)
435 {
436 double d = (u[i] - mean);
437 double d2 = sqr(d);
438 var += d2;
439 skew += d * d2;
440 kurtosis += d2 * d2;
441 }
442 var /= u.size();
443 double dev = std::sqrt(var);
444 // In this case:
445 // skew computes to 0./0. == nan
446 // kurtosis computes to 0./0. == nan
447 // x_skew == -inf
448 // x_kurtosis == inf
449 // These tests are commented out because UBSan warns about division by 0
450 // skew /= u.size() * dev * var;
451 // kurtosis /= u.size() * var * var;
452 // kurtosis -= 3;
453 double x_mean = d.t() * d.p();
454 double x_var = x_mean*(1-d.p());
455 // double x_skew = (1-2*d.p()) / std::sqrt(x_var);
456 // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
457 assert(mean == x_mean);
458 assert(var == x_var);
459 // assert(skew == x_skew);
460 // assert(kurtosis == x_kurtosis);
461 }
462 }
463