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 negative_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 25 sqr(T x) 26 { 27 return x * x; 28 } 29 30 int main() 31 { 32 { 33 typedef std::negative_binomial_distribution<> D; 34 typedef std::minstd_rand G; 35 G g; 36 D d(5, .25); 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.k() * (1 - d.p()) / d.p(); 64 double x_var = x_mean / d.p(); 65 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 66 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (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) < 0.02); 71 } 72 { 73 typedef std::negative_binomial_distribution<> D; 74 typedef std::mt19937 G; 75 G g; 76 D d(30, .03125); 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 = d.k() * (1 - d.p()) / d.p(); 104 double x_var = x_mean / d.p(); 105 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 106 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (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) < 0.01); 111 } 112 { 113 typedef std::negative_binomial_distribution<> D; 114 typedef std::mt19937 G; 115 G g; 116 D d(40, .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 = d.k() * (1 - d.p()) / d.p(); 144 double x_var = x_mean / d.p(); 145 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 146 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (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) < 0.03); 151 } 152 { 153 typedef std::negative_binomial_distribution<> D; 154 typedef std::mt19937 G; 155 G g; 156 D d(40, 1); 157 const int N = 1000; 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 = d.k() * (1 - d.p()) / d.p(); 184 double x_var = x_mean / d.p(); 185 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 186 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 187 assert(mean == x_mean); 188 assert(var == x_var); 189 } 190 { 191 typedef std::negative_binomial_distribution<> D; 192 typedef std::mt19937 G; 193 G g; 194 D d(400, 0.5); 195 const int N = 1000000; 196 std::vector<D::result_type> u; 197 for (int i = 0; i < N; ++i) 198 { 199 D::result_type v = d(g); 200 assert(d.min() <= v && v <= d.max()); 201 u.push_back(v); 202 } 203 double mean = std::accumulate(u.begin(), u.end(), 204 double(0)) / u.size(); 205 double var = 0; 206 double skew = 0; 207 double kurtosis = 0; 208 for (int i = 0; i < u.size(); ++i) 209 { 210 double d = (u[i] - mean); 211 double d2 = sqr(d); 212 var += d2; 213 skew += d * d2; 214 kurtosis += d2 * d2; 215 } 216 var /= u.size(); 217 double dev = std::sqrt(var); 218 skew /= u.size() * dev * var; 219 kurtosis /= u.size() * var * var; 220 kurtosis -= 3; 221 double x_mean = d.k() * (1 - d.p()) / d.p(); 222 double x_var = x_mean / d.p(); 223 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 224 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 225 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 226 assert(std::abs((var - x_var) / x_var) < 0.01); 227 assert(std::abs((skew - x_skew) / x_skew) < 0.04); 228 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05); 229 } 230 { 231 typedef std::negative_binomial_distribution<> D; 232 typedef std::mt19937 G; 233 G g; 234 D d(1, 0.05); 235 const int N = 1000000; 236 std::vector<D::result_type> u; 237 for (int i = 0; i < N; ++i) 238 { 239 D::result_type v = d(g); 240 assert(d.min() <= v && v <= d.max()); 241 u.push_back(v); 242 } 243 double mean = std::accumulate(u.begin(), u.end(), 244 double(0)) / u.size(); 245 double var = 0; 246 double skew = 0; 247 double kurtosis = 0; 248 for (int i = 0; i < u.size(); ++i) 249 { 250 double d = (u[i] - mean); 251 double d2 = sqr(d); 252 var += d2; 253 skew += d * d2; 254 kurtosis += d2 * d2; 255 } 256 var /= u.size(); 257 double dev = std::sqrt(var); 258 skew /= u.size() * dev * var; 259 kurtosis /= u.size() * var * var; 260 kurtosis -= 3; 261 double x_mean = d.k() * (1 - d.p()) / d.p(); 262 double x_var = x_mean / d.p(); 263 double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); 264 double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); 265 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 266 assert(std::abs((var - x_var) / x_var) < 0.01); 267 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 268 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 269 } 270 } 271