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, const param_type& parm); 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 P p(1, .5); 41 const int N = 1000000; 42 std::vector<D::result_type> u; 43 for (int i = 0; i < N; ++i) 44 { 45 D::result_type v = d(g, p); 46 assert(d.min() <= v); 47 u.push_back(v); 48 } 49 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 50 double var = 0; 51 double skew = 0; 52 double kurtosis = 0; 53 for (int i = 0; i < u.size(); ++i) 54 { 55 double d = (u[i] - mean); 56 double d2 = sqr(d); 57 var += d2; 58 skew += d * d2; 59 kurtosis += d2 * d2; 60 } 61 var /= u.size(); 62 double dev = std::sqrt(var); 63 skew /= u.size() * dev * var; 64 kurtosis /= u.size() * var * var; 65 kurtosis -= 3; 66 double x_mean = p.b() * std::tgamma(1 + 1/p.a()); 67 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean); 68 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) - 69 3*x_mean*x_var - sqr(x_mean)*x_mean) / 70 (std::sqrt(x_var)*x_var); 71 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) - 72 4*x_skew*x_var*sqrt(x_var)*x_mean - 73 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 74 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 75 assert(std::abs((var - x_var) / x_var) < 0.01); 76 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 77 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 78 } 79 { 80 typedef std::weibull_distribution<> D; 81 typedef D::param_type P; 82 typedef std::mt19937 G; 83 G g; 84 D d(1, .5); 85 P p(2, 3); 86 const int N = 1000000; 87 std::vector<D::result_type> u; 88 for (int i = 0; i < N; ++i) 89 { 90 D::result_type v = d(g, p); 91 assert(d.min() <= v); 92 u.push_back(v); 93 } 94 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 95 double var = 0; 96 double skew = 0; 97 double kurtosis = 0; 98 for (int i = 0; i < u.size(); ++i) 99 { 100 double d = (u[i] - mean); 101 double d2 = sqr(d); 102 var += d2; 103 skew += d * d2; 104 kurtosis += d2 * d2; 105 } 106 var /= u.size(); 107 double dev = std::sqrt(var); 108 skew /= u.size() * dev * var; 109 kurtosis /= u.size() * var * var; 110 kurtosis -= 3; 111 double x_mean = p.b() * std::tgamma(1 + 1/p.a()); 112 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean); 113 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) - 114 3*x_mean*x_var - sqr(x_mean)*x_mean) / 115 (std::sqrt(x_var)*x_var); 116 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) - 117 4*x_skew*x_var*sqrt(x_var)*x_mean - 118 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 119 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 120 assert(std::abs((var - x_var) / x_var) < 0.01); 121 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 122 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 123 } 124 { 125 typedef std::weibull_distribution<> D; 126 typedef D::param_type P; 127 typedef std::mt19937 G; 128 G g; 129 D d(2, 3); 130 P p(.5, 2); 131 const int N = 1000000; 132 std::vector<D::result_type> u; 133 for (int i = 0; i < N; ++i) 134 { 135 D::result_type v = d(g, p); 136 assert(d.min() <= v); 137 u.push_back(v); 138 } 139 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 140 double var = 0; 141 double skew = 0; 142 double kurtosis = 0; 143 for (int i = 0; i < u.size(); ++i) 144 { 145 double d = (u[i] - mean); 146 double d2 = sqr(d); 147 var += d2; 148 skew += d * d2; 149 kurtosis += d2 * d2; 150 } 151 var /= u.size(); 152 double dev = std::sqrt(var); 153 skew /= u.size() * dev * var; 154 kurtosis /= u.size() * var * var; 155 kurtosis -= 3; 156 double x_mean = p.b() * std::tgamma(1 + 1/p.a()); 157 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean); 158 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) - 159 3*x_mean*x_var - sqr(x_mean)*x_mean) / 160 (std::sqrt(x_var)*x_var); 161 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) - 162 4*x_skew*x_var*sqrt(x_var)*x_mean - 163 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3; 164 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 165 assert(std::abs((var - x_var) / x_var) < 0.01); 166 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 167 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 168 } 169 } 170
