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 #include <cstddef> 24 25 template <class T> 26 inline 27 T 28 sqr(T x) 29 { 30 return x * x; 31 } 32 33 int main() 34 { 35 { 36 typedef std::weibull_distribution<> D; 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 (std::size_t 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.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 std::mt19937 G; 81 G g; 82 D d(1, .5); 83 const int N = 1000000; 84 std::vector<D::result_type> u; 85 for (int i = 0; i < N; ++i) 86 { 87 D::result_type v = d(g); 88 assert(d.min() <= v); 89 u.push_back(v); 90 } 91 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 92 double var = 0; 93 double skew = 0; 94 double kurtosis = 0; 95 for (std::size_t 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.b() * std::tgamma(1 + 1/d.a()); 109 double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean); 110 double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) - 111 3*x_mean*x_var - sqr(x_mean)*x_mean) / 112 (std::sqrt(x_var)*x_var); 113 double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) - 114 4*x_skew*x_var*sqrt(x_var)*x_mean - 115 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 116 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 117 assert(std::abs((var - x_var) / x_var) < 0.01); 118 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 119 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 120 } 121 { 122 typedef std::weibull_distribution<> D; 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 (std::size_t 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.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
