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 gamma_distribution 14 15 // template<class _URNG> result_type operator()(_URNG& g, const param_type& parm); 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::gamma_distribution<> D; 34 typedef D::param_type P; 35 typedef std::mt19937 G; 36 G g; 37 D d(0.5, 2); 38 P p(1, .5); 39 const int N = 1000000; 40 std::vector<D::result_type> u; 41 for (int i = 0; i < N; ++i) 42 { 43 D::result_type v = d(g, p); 44 assert(d.min() < v); 45 u.push_back(v); 46 } 47 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 48 double var = 0; 49 double skew = 0; 50 double kurtosis = 0; 51 for (int i = 0; i < u.size(); ++i) 52 { 53 double d = (u[i] - mean); 54 double d2 = sqr(d); 55 var += d2; 56 skew += d * d2; 57 kurtosis += d2 * d2; 58 } 59 var /= u.size(); 60 double dev = std::sqrt(var); 61 skew /= u.size() * dev * var; 62 kurtosis /= u.size() * var * var; 63 kurtosis -= 3; 64 double x_mean = p.alpha() * p.beta(); 65 double x_var = p.alpha() * sqr(p.beta()); 66 double x_skew = 2 / std::sqrt(p.alpha()); 67 double x_kurtosis = 6 / p.alpha(); 68 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 69 assert(std::abs((var - x_var) / x_var) < 0.01); 70 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 71 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 72 } 73 { 74 typedef std::gamma_distribution<> D; 75 typedef D::param_type P; 76 typedef std::mt19937 G; 77 G g; 78 D d(1, .5); 79 P p(2, 3); 80 const int N = 1000000; 81 std::vector<D::result_type> u; 82 for (int i = 0; i < N; ++i) 83 { 84 D::result_type v = d(g, p); 85 assert(d.min() < v); 86 u.push_back(v); 87 } 88 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 89 double var = 0; 90 double skew = 0; 91 double kurtosis = 0; 92 for (int i = 0; i < u.size(); ++i) 93 { 94 double d = (u[i] - mean); 95 double d2 = sqr(d); 96 var += d2; 97 skew += d * d2; 98 kurtosis += d2 * d2; 99 } 100 var /= u.size(); 101 double dev = std::sqrt(var); 102 skew /= u.size() * dev * var; 103 kurtosis /= u.size() * var * var; 104 kurtosis -= 3; 105 double x_mean = p.alpha() * p.beta(); 106 double x_var = p.alpha() * sqr(p.beta()); 107 double x_skew = 2 / std::sqrt(p.alpha()); 108 double x_kurtosis = 6 / p.alpha(); 109 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 110 assert(std::abs((var - x_var) / x_var) < 0.01); 111 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 112 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 113 } 114 { 115 typedef std::gamma_distribution<> D; 116 typedef D::param_type P; 117 typedef std::mt19937 G; 118 G g; 119 D d(2, 3); 120 P p(.5, 2); 121 const int N = 1000000; 122 std::vector<D::result_type> u; 123 for (int i = 0; i < N; ++i) 124 { 125 D::result_type v = d(g, p); 126 assert(d.min() < v); 127 u.push_back(v); 128 } 129 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 130 double var = 0; 131 double skew = 0; 132 double kurtosis = 0; 133 for (int i = 0; i < u.size(); ++i) 134 { 135 double d = (u[i] - mean); 136 double d2 = sqr(d); 137 var += d2; 138 skew += d * d2; 139 kurtosis += d2 * d2; 140 } 141 var /= u.size(); 142 double dev = std::sqrt(var); 143 skew /= u.size() * dev * var; 144 kurtosis /= u.size() * var * var; 145 kurtosis -= 3; 146 double x_mean = p.alpha() * p.beta(); 147 double x_var = p.alpha() * sqr(p.beta()); 148 double x_skew = 2 / std::sqrt(p.alpha()); 149 double x_kurtosis = 6 / p.alpha(); 150 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 151 assert(std::abs((var - x_var) / x_var) < 0.01); 152 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 153 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 154 } 155 } 156
