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 IntType = int> 15 // class binomial_distribution 16 17 // template<class _URNG> result_type operator()(_URNG& g, const param_type& parm); 18 19 #include <random> 20 #include <numeric> 21 #include <vector> 22 #include <cassert> 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::binomial_distribution<> D; 36 typedef D::param_type P; 37 typedef std::mt19937_64 G; 38 G g; 39 D d(16, .75); 40 P p(5, .75); 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(0 <= v && v <= p.t()); 47 u.push_back(v); 48 } 49 double mean = std::accumulate(u.begin(), u.end(), 50 double(0)) / u.size(); 51 double var = 0; 52 double skew = 0; 53 double kurtosis = 0; 54 for (int i = 0; i < u.size(); ++i) 55 { 56 double d = (u[i] - mean); 57 double d2 = sqr(d); 58 var += d2; 59 skew += d * d2; 60 kurtosis += d2 * d2; 61 } 62 var /= u.size(); 63 double dev = std::sqrt(var); 64 skew /= u.size() * dev * var; 65 kurtosis /= u.size() * var * var; 66 kurtosis -= 3; 67 double x_mean = p.t() * p.p(); 68 double x_var = x_mean*(1-p.p()); 69 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 70 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 71 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 72 assert(std::abs((var - x_var) / x_var) < 0.01); 73 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 74 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04); 75 } 76 { 77 typedef std::binomial_distribution<> D; 78 typedef D::param_type P; 79 typedef std::mt19937 G; 80 G g; 81 D d(16, .75); 82 P p(30, .03125); 83 const int N = 100000; 84 std::vector<D::result_type> u; 85 for (int i = 0; i < N; ++i) 86 { 87 D::result_type v = d(g, p); 88 assert(0 <= v && v <= p.t()); 89 u.push_back(v); 90 } 91 double mean = std::accumulate(u.begin(), u.end(), 92 double(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 = p.t() * p.p(); 110 double x_var = x_mean*(1-p.p()); 111 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 112 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 113 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 114 assert(std::abs((var - x_var) / x_var) < 0.01); 115 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 116 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 117 } 118 { 119 typedef std::binomial_distribution<> D; 120 typedef D::param_type P; 121 typedef std::mt19937 G; 122 G g; 123 D d(16, .75); 124 P p(40, .25); 125 const int N = 1000000; 126 std::vector<D::result_type> u; 127 for (int i = 0; i < N; ++i) 128 { 129 D::result_type v = d(g, p); 130 assert(0 <= v && v <= p.t()); 131 u.push_back(v); 132 } 133 double mean = std::accumulate(u.begin(), u.end(), 134 double(0)) / u.size(); 135 double var = 0; 136 double skew = 0; 137 double kurtosis = 0; 138 for (int i = 0; i < u.size(); ++i) 139 { 140 double d = (u[i] - mean); 141 double d2 = sqr(d); 142 var += d2; 143 skew += d * 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 = p.t() * p.p(); 152 double x_var = x_mean*(1-p.p()); 153 double x_skew = (1-2*p.p()) / std::sqrt(x_var); 154 double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var; 155 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 156 assert(std::abs((var - x_var) / x_var) < 0.01); 157 assert(std::abs((skew - x_skew) / x_skew) < 0.04); 158 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3); 159 } 160 } 161
