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 geometric_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::geometric_distribution<> D;
34 typedef std::mt19937 G;
35 G g;
36 D d(.03125);
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 = (1 - d.p()) / d.p();
64 double x_var = x_mean / d.p();
65 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
66 double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
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) < 0.01);
71 }
72 {
73 typedef std::geometric_distribution<> D;
74 typedef std::mt19937 G;
75 G g;
76 D d(0.05);
77 const int N = 1000000;
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 = (1 - d.p()) / d.p();
104 double x_var = x_mean / d.p();
105 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
106 double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
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) < 0.03);
111 }
112 {
113 typedef std::geometric_distribution<> D;
114 typedef std::minstd_rand G;
115 G g;
116 D d(.25);
117 const int N = 1000000;
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 = (1 - d.p()) / d.p();
144 double x_var = x_mean / d.p();
145 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
146 double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
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) < 0.01);
150 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
151 }
152 {
153 typedef std::geometric_distribution<> D;
154 typedef std::mt19937 G;
155 G g;
156 D d(0.5);
157 const int N = 1000000;
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 skew /= u.size() * dev * var;
181 kurtosis /= u.size() * var * var;
182 kurtosis -= 3;
183 double x_mean = (1 - d.p()) / d.p();
184 double x_var = x_mean / d.p();
185 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
186 double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
187 assert(std::abs((mean - x_mean) / x_mean) < 0.01);
188 assert(std::abs((var - x_var) / x_var) < 0.01);
189 assert(std::abs((skew - x_skew) / x_skew) < 0.01);
190 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
191 }
192 {
193 typedef std::geometric_distribution<> D;
194 typedef std::mt19937 G;
195 G g;
196 D d(0.75);
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 = (1 - d.p()) / d.p();
224 double x_var = x_mean / d.p();
225 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
226 double x_kurtosis = 6 + sqr(d.p()) / (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) < 0.01);
230 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
231 }
232 {
233 typedef std::geometric_distribution<> D;
234 typedef std::mt19937 G;
235 G g;
236 D d(0.96875);
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 = (1 - d.p()) / d.p();
264 double x_var = x_mean / d.p();
265 double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
266 double x_kurtosis = 6 + sqr(d.p()) / (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) < 0.02);
271 }
272 }
273