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 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
