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 student_t_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 24template <class T> 25inline 26T 27sqr(T x) 28{ 29 return x * x; 30} 31 32int main() 33{ 34 { 35 typedef std::student_t_distribution<> D; 36 typedef D::param_type P; 37 typedef std::minstd_rand G; 38 G g; 39 D d(5.5); 40 const int N = 1000000; 41 std::vector<D::result_type> u; 42 for (int i = 0; i < N; ++i) 43 u.push_back(d(g)); 44 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 45 double var = 0; 46 double skew = 0; 47 double kurtosis = 0; 48 for (unsigned i = 0; i < u.size(); ++i) 49 { 50 double dbl = (u[i] - mean); 51 double d2 = sqr(dbl); 52 var += d2; 53 skew += dbl * d2; 54 kurtosis += d2 * d2; 55 } 56 var /= u.size(); 57 double dev = std::sqrt(var); 58 skew /= u.size() * dev * var; 59 kurtosis /= u.size() * var * var; 60 kurtosis -= 3; 61 double x_mean = 0; 62 double x_var = d.n() / (d.n() - 2); 63 double x_skew = 0; 64 double x_kurtosis = 6 / (d.n() - 4); 65 assert(std::abs(mean - x_mean) < 0.01); 66 assert(std::abs((var - x_var) / x_var) < 0.01); 67 assert(std::abs(skew - x_skew) < 0.01); 68 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2); 69 } 70 { 71 typedef std::student_t_distribution<> D; 72 typedef D::param_type P; 73 typedef std::minstd_rand G; 74 G g; 75 D d(10); 76 const int N = 1000000; 77 std::vector<D::result_type> u; 78 for (int i = 0; i < N; ++i) 79 u.push_back(d(g)); 80 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 81 double var = 0; 82 double skew = 0; 83 double kurtosis = 0; 84 for (unsigned i = 0; i < u.size(); ++i) 85 { 86 double dbl = (u[i] - mean); 87 double d2 = sqr(dbl); 88 var += d2; 89 skew += dbl * d2; 90 kurtosis += d2 * d2; 91 } 92 var /= u.size(); 93 double dev = std::sqrt(var); 94 skew /= u.size() * dev * var; 95 kurtosis /= u.size() * var * var; 96 kurtosis -= 3; 97 double x_mean = 0; 98 double x_var = d.n() / (d.n() - 2); 99 double x_skew = 0; 100 double x_kurtosis = 6 / (d.n() - 4); 101 assert(std::abs(mean - x_mean) < 0.01); 102 assert(std::abs((var - x_var) / x_var) < 0.01); 103 assert(std::abs(skew - x_skew) < 0.01); 104 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04); 105 } 106 { 107 typedef std::student_t_distribution<> D; 108 typedef D::param_type P; 109 typedef std::minstd_rand G; 110 G g; 111 D d(100); 112 const int N = 1000000; 113 std::vector<D::result_type> u; 114 for (int i = 0; i < N; ++i) 115 u.push_back(d(g)); 116 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 117 double var = 0; 118 double skew = 0; 119 double kurtosis = 0; 120 for (unsigned i = 0; i < u.size(); ++i) 121 { 122 double dbl = (u[i] - mean); 123 double d2 = sqr(dbl); 124 var += d2; 125 skew += dbl * d2; 126 kurtosis += d2 * d2; 127 } 128 var /= u.size(); 129 double dev = std::sqrt(var); 130 skew /= u.size() * dev * var; 131 kurtosis /= u.size() * var * var; 132 kurtosis -= 3; 133 double x_mean = 0; 134 double x_var = d.n() / (d.n() - 2); 135 double x_skew = 0; 136 double x_kurtosis = 6 / (d.n() - 4); 137 assert(std::abs(mean - x_mean) < 0.01); 138 assert(std::abs((var - x_var) / x_var) < 0.01); 139 assert(std::abs(skew - x_skew) < 0.01); 140 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02); 141 } 142} 143