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 IntType = int> 13 // class binomial_distribution 14 15 // template<class _URNG> result_type operator()(_URNG& g, const param_type& parm); 16 17 #include <random> 18 #include <numeric> 19 #include <vector> 20 #include <cassert> 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::binomial_distribution<> D; 34 typedef D::param_type P; 35 typedef std::mt19937_64 G; 36 G g; 37 D d(16, .75); 38 P p(5, .75); 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(0 <= v && v <= p.t()); 45 u.push_back(v); 46 } 47 double mean = std::accumulate(u.begin(), u.end(), 48 double(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 = p.t() * p.p(); 66 double x_var = x_mean*(1-p.p()); 67 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 68 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 69 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 70 assert(std::abs((var - x_var) / x_var) < 0.01); 71 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 72 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04); 73 } 74 { 75 typedef std::binomial_distribution<> D; 76 typedef D::param_type P; 77 typedef std::mt19937 G; 78 G g; 79 D d(16, .75); 80 P p(30, .03125); 81 const int N = 100000; 82 std::vector<D::result_type> u; 83 for (int i = 0; i < N; ++i) 84 { 85 D::result_type v = d(g, p); 86 assert(0 <= v && v <= p.t()); 87 u.push_back(v); 88 } 89 double mean = std::accumulate(u.begin(), u.end(), 90 double(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 = p.t() * p.p(); 108 double x_var = x_mean*(1-p.p()); 109 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 110 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 111 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 112 assert(std::abs((var - x_var) / x_var) < 0.01); 113 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 114 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 115 } 116 { 117 typedef std::binomial_distribution<> D; 118 typedef D::param_type P; 119 typedef std::mt19937 G; 120 G g; 121 D d(16, .75); 122 P p(40, .25); 123 const int N = 1000000; 124 std::vector<D::result_type> u; 125 for (int i = 0; i < N; ++i) 126 { 127 D::result_type v = d(g, p); 128 assert(0 <= v && v <= p.t()); 129 u.push_back(v); 130 } 131 double mean = std::accumulate(u.begin(), u.end(), 132 double(0)) / u.size(); 133 double var = 0; 134 double skew = 0; 135 double kurtosis = 0; 136 for (int i = 0; i < u.size(); ++i) 137 { 138 double d = (u[i] - mean); 139 double d2 = sqr(d); 140 var += d2; 141 skew += d * d2; 142 kurtosis += d2 * d2; 143 } 144 var /= u.size(); 145 double dev = std::sqrt(var); 146 skew /= u.size() * dev * var; 147 kurtosis /= u.size() * var * var; 148 kurtosis -= 3; 149 double x_mean = p.t() * p.p(); 150 double x_var = x_mean*(1-p.p()); 151 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 152 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 153 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 154 assert(std::abs((var - x_var) / x_var) < 0.01); 155 assert(std::abs((skew - x_skew) / x_skew) < 0.04); 156 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3); 157 } 158 } 159
