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 RealType = double> 13 // class weibull_distribution 14 15 // template<class _URNG> result_type operator()(_URNG& g); 16 17 #include <random> 18 #include <cassert> 19 #include <vector> 20 #include <numeric> 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::weibull_distribution<> D; 34 typedef D::param_type P; 35 typedef std::mt19937 G; 36 G g; 37 D d(0.5, 2); 38 const int N = 1000000; 39 std::vector<D::result_type> u; 40 for (int i = 0; i < N; ++i) 41 { 42 D::result_type v = d(g); 43 assert(d.min() <= v); 44 u.push_back(v); 45 } 46 double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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.b() * std::tgamma(1 + 1/d.a()); 64 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 65 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 66 3*x_mean*x_var - sqr(x_mean)*x_mean) / 67 (std::sqrt(x_var)*x_var); 68 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 69 4*x_skew*x_var*sqrt(x_var)*x_mean - 70 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 71 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 72 assert(std::abs((var - x_var) / x_var) < 0.01); 73 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 74 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 75 } 76 { 77 typedef std::weibull_distribution<> D; 78 typedef D::param_type P; 79 typedef std::mt19937 G; 80 G g; 81 D d(1, .5); 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); 88 u.push_back(v); 89 } 90 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 91 double var = 0; 92 double skew = 0; 93 double kurtosis = 0; 94 for (int i = 0; i < u.size(); ++i) 95 { 96 double d = (u[i] - mean); 97 double d2 = sqr(d); 98 var += d2; 99 skew += d * d2; 100 kurtosis += d2 * d2; 101 } 102 var /= u.size(); 103 double dev = std::sqrt(var); 104 skew /= u.size() * dev * var; 105 kurtosis /= u.size() * var * var; 106 kurtosis -= 3; 107 double x_mean = d.b() * std::tgamma(1 + 1/d.a()); 108 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 109 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 110 3*x_mean*x_var - sqr(x_mean)*x_mean) / 111 (std::sqrt(x_var)*x_var); 112 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 113 4*x_skew*x_var*sqrt(x_var)*x_mean - 114 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 115 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 116 assert(std::abs((var - x_var) / x_var) < 0.01); 117 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 118 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 119 } 120 { 121 typedef std::weibull_distribution<> D; 122 typedef D::param_type P; 123 typedef std::mt19937 G; 124 G g; 125 D d(2, 3); 126 const int N = 1000000; 127 std::vector<D::result_type> u; 128 for (int i = 0; i < N; ++i) 129 { 130 D::result_type v = d(g); 131 assert(d.min() <= v); 132 u.push_back(v); 133 } 134 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 135 double var = 0; 136 double skew = 0; 137 double kurtosis = 0; 138 for (int i = 0; i < u.size(); ++i) 139 { 140 double d = (u[i] - mean); 141 double d2 = sqr(d); 142 var += d2; 143 skew += d * 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.b() * std::tgamma(1 + 1/d.a()); 152 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 153 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 154 3*x_mean*x_var - sqr(x_mean)*x_mean) / 155 (std::sqrt(x_var)*x_var); 156 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 157 4*x_skew*x_var*sqrt(x_var)*x_mean - 158 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 159 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 160 assert(std::abs((var - x_var) / x_var) < 0.01); 161 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 162 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 163 } 164 } 165
