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 RealType = double> 15 // class weibull_distribution 16 17 // template<class _URNG> result_type operator()(_URNG& g); 18 19 #include <random> 20 #include <cassert> 21 #include <vector> 22 #include <numeric> 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::weibull_distribution<> D; 36 typedef D::param_type P; 37 typedef std::mt19937 G; 38 G g; 39 D d(0.5, 2); 40 const int N = 1000000; 41 std::vector<D::result_type> u; 42 for (int i = 0; i < N; ++i) 43 { 44 D::result_type v = d(g); 45 assert(d.min() <= v); 46 u.push_back(v); 47 } 48 double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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.b() * std::tgamma(1 + 1/d.a()); 66 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 67 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 68 3*x_mean*x_var - sqr(x_mean)*x_mean) / 69 (std::sqrt(x_var)*x_var); 70 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 71 4*x_skew*x_var*sqrt(x_var)*x_mean - 72 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 73 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 74 assert(std::abs((var - x_var) / x_var) < 0.01); 75 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 76 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 77 } 78 { 79 typedef std::weibull_distribution<> D; 80 typedef D::param_type P; 81 typedef std::mt19937 G; 82 G g; 83 D d(1, .5); 84 const int N = 1000000; 85 std::vector<D::result_type> u; 86 for (int i = 0; i < N; ++i) 87 { 88 D::result_type v = d(g); 89 assert(d.min() <= v); 90 u.push_back(v); 91 } 92 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 93 double var = 0; 94 double skew = 0; 95 double kurtosis = 0; 96 for (int i = 0; i < u.size(); ++i) 97 { 98 double d = (u[i] - mean); 99 double d2 = sqr(d); 100 var += d2; 101 skew += d * d2; 102 kurtosis += d2 * d2; 103 } 104 var /= u.size(); 105 double dev = std::sqrt(var); 106 skew /= u.size() * dev * var; 107 kurtosis /= u.size() * var * var; 108 kurtosis -= 3; 109 double x_mean = d.b() * std::tgamma(1 + 1/d.a()); 110 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 111 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 112 3*x_mean*x_var - sqr(x_mean)*x_mean) / 113 (std::sqrt(x_var)*x_var); 114 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 115 4*x_skew*x_var*sqrt(x_var)*x_mean - 116 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 117 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 118 assert(std::abs((var - x_var) / x_var) < 0.01); 119 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 120 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 121 } 122 { 123 typedef std::weibull_distribution<> D; 124 typedef D::param_type P; 125 typedef std::mt19937 G; 126 G g; 127 D d(2, 3); 128 const int N = 1000000; 129 std::vector<D::result_type> u; 130 for (int i = 0; i < N; ++i) 131 { 132 D::result_type v = d(g); 133 assert(d.min() <= v); 134 u.push_back(v); 135 } 136 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 137 double var = 0; 138 double skew = 0; 139 double kurtosis = 0; 140 for (int i = 0; i < u.size(); ++i) 141 { 142 double d = (u[i] - mean); 143 double d2 = sqr(d); 144 var += d2; 145 skew += d * d2; 146 kurtosis += d2 * d2; 147 } 148 var /= u.size(); 149 double dev = std::sqrt(var); 150 skew /= u.size() * dev * var; 151 kurtosis /= u.size() * var * var; 152 kurtosis -= 3; 153 double x_mean = d.b() * std::tgamma(1 + 1/d.a()); 154 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 155 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 156 3*x_mean*x_var - sqr(x_mean)*x_mean) / 157 (std::sqrt(x_var)*x_var); 158 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 159 4*x_skew*x_var*sqrt(x_var)*x_mean - 160 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 161 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 162 assert(std::abs((var - x_var) / x_var) < 0.01); 163 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 164 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 165 } 166 } 167
