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 27 sqr(T x) 28 { 29 return x * x; 30 } 31 32 void 33 test1() 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 (unsigned i = 0; i < u.size(); ++i) 53 { 54 double dbl = (u[i] - mean); 55 double d2 = sqr(dbl); 56 var += d2; 57 skew += dbl * 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 void 76 test2() 77 { 78 typedef std::negative_binomial_distribution<> D; 79 typedef std::mt19937 G; 80 G g; 81 D d(30, .03125); 82 const int N = 1000000; 83 std::vector<D::result_type> u; 84 for (int i = 0; i < N; ++i) 85 { 86 D::result_type v = d(g); 87 assert(d.min() <= v && v <= d.max()); 88 u.push_back(v); 89 } 90 double mean = std::accumulate(u.begin(), u.end(), 91 double(0)) / u.size(); 92 double var = 0; 93 double skew = 0; 94 double kurtosis = 0; 95 for (unsigned i = 0; i < u.size(); ++i) 96 { 97 double dbl = (u[i] - mean); 98 double d2 = sqr(dbl); 99 var += d2; 100 skew += dbl * d2; 101 kurtosis += d2 * d2; 102 } 103 var /= u.size(); 104 double dev = std::sqrt(var); 105 skew /= u.size() * dev * var; 106 kurtosis /= u.size() * var * var; 107 kurtosis -= 3; 108 double x_mean = d.k() * (1 - d.p()) / d.p(); 109 double x_var = x_mean / d.p(); 110 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 111 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 112 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 113 assert(std::abs((var - x_var) / x_var) < 0.01); 114 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 115 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 116 } 117 118 void 119 test3() 120 { 121 typedef std::negative_binomial_distribution<> D; 122 typedef std::mt19937 G; 123 G g; 124 D d(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); 130 assert(d.min() <= v && v <= d.max()); 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 = d.k() * (1 - d.p()) / d.p(); 152 double x_var = x_mean / d.p(); 153 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 154 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 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) < 0.01); 158 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 159 } 160 161 void 162 test4() 163 { 164 typedef std::negative_binomial_distribution<> D; 165 typedef std::mt19937 G; 166 G g; 167 D d(40, 1); 168 const int N = 1000; 169 std::vector<D::result_type> u; 170 for (int i = 0; i < N; ++i) 171 { 172 D::result_type v = d(g); 173 assert(d.min() <= v && v <= d.max()); 174 u.push_back(v); 175 } 176 double mean = std::accumulate(u.begin(), u.end(), 177 double(0)) / u.size(); 178 double var = 0; 179 double skew = 0; 180 double kurtosis = 0; 181 for (unsigned i = 0; i < u.size(); ++i) 182 { 183 double dbl = (u[i] - mean); 184 double d2 = sqr(dbl); 185 var += d2; 186 skew += dbl * d2; 187 kurtosis += d2 * d2; 188 } 189 var /= u.size(); 190 double dev = std::sqrt(var); 191 skew /= u.size() * dev * var; 192 kurtosis /= u.size() * var * var; 193 kurtosis -= 3; 194 double x_mean = d.k() * (1 - d.p()) / d.p(); 195 double x_var = x_mean / d.p(); 196 // double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 197 // double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 198 assert(mean == x_mean); 199 assert(var == x_var); 200 } 201 202 void 203 test5() 204 { 205 typedef std::negative_binomial_distribution<> D; 206 typedef std::mt19937 G; 207 G g; 208 D d(400, 0.5); 209 const int N = 1000000; 210 std::vector<D::result_type> u; 211 for (int i = 0; i < N; ++i) 212 { 213 D::result_type v = d(g); 214 assert(d.min() <= v && v <= d.max()); 215 u.push_back(v); 216 } 217 double mean = std::accumulate(u.begin(), u.end(), 218 double(0)) / u.size(); 219 double var = 0; 220 double skew = 0; 221 double kurtosis = 0; 222 for (unsigned i = 0; i < u.size(); ++i) 223 { 224 double dbl = (u[i] - mean); 225 double d2 = sqr(dbl); 226 var += d2; 227 skew += dbl * d2; 228 kurtosis += d2 * d2; 229 } 230 var /= u.size(); 231 double dev = std::sqrt(var); 232 skew /= u.size() * dev * var; 233 kurtosis /= u.size() * var * var; 234 kurtosis -= 3; 235 double x_mean = d.k() * (1 - d.p()) / d.p(); 236 double x_var = x_mean / d.p(); 237 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 238 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 239 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 240 assert(std::abs((var - x_var) / x_var) < 0.01); 241 assert(std::abs((skew - x_skew) / x_skew) < 0.04); 242 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05); 243 } 244 245 void 246 test6() 247 { 248 typedef std::negative_binomial_distribution<> D; 249 typedef std::mt19937 G; 250 G g; 251 D d(1, 0.05); 252 const int N = 1000000; 253 std::vector<D::result_type> u; 254 for (int i = 0; i < N; ++i) 255 { 256 D::result_type v = d(g); 257 assert(d.min() <= v && v <= d.max()); 258 u.push_back(v); 259 } 260 double mean = std::accumulate(u.begin(), u.end(), 261 double(0)) / u.size(); 262 double var = 0; 263 double skew = 0; 264 double kurtosis = 0; 265 for (unsigned i = 0; i < u.size(); ++i) 266 { 267 double dbl = (u[i] - mean); 268 double d2 = sqr(dbl); 269 var += d2; 270 skew += dbl * d2; 271 kurtosis += d2 * d2; 272 } 273 var /= u.size(); 274 double dev = std::sqrt(var); 275 skew /= u.size() * dev * var; 276 kurtosis /= u.size() * var * var; 277 kurtosis -= 3; 278 double x_mean = d.k() * (1 - d.p()) / d.p(); 279 double x_var = x_mean / d.p(); 280 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 281 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 282 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 283 assert(std::abs((var - x_var) / x_var) < 0.01); 284 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 285 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 286 } 287 288 int main() 289 { 290 test1(); 291 test2(); 292 test3(); 293 test4(); 294 test5(); 295 test6(); 296 } 297
