1 //===----------------------------------------------------------------------===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 // 9 // REQUIRES: long_tests 10 11 // <random> 12 13 // template<class RealType = double> 14 // class chi_squared_distribution 15 16 // template<class _URNG> result_type operator()(_URNG& g); 17 18 #include <random> 19 #include <cassert> 20 #include <cmath> 21 #include <cstddef> 22 #include <numeric> 23 #include <vector> 24 25 #include "test_macros.h" 26 27 template <class T> 28 inline 29 T 30 sqr(T x) 31 { 32 return x * x; 33 } 34 35 int main(int, char**) 36 { 37 { 38 typedef std::chi_squared_distribution<> D; 39 typedef std::minstd_rand G; 40 G g; 41 D d(0.5); 42 const int N = 1000000; 43 std::vector<D::result_type> u; 44 for (int i = 0; i < N; ++i) 45 { 46 D::result_type v = d(g); 47 assert(d.min() < v); 48 u.push_back(v); 49 } 50 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 51 double var = 0; 52 double skew = 0; 53 double kurtosis = 0; 54 for (std::size_t i = 0; i < u.size(); ++i) 55 { 56 double dbl = (u[i] - mean); 57 double d2 = sqr(dbl); 58 var += d2; 59 skew += dbl * 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 = d.n(); 68 double x_var = 2 * d.n(); 69 double x_skew = std::sqrt(8 / d.n()); 70 double x_kurtosis = 12 / d.n(); 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::chi_squared_distribution<> D; 78 typedef std::minstd_rand G; 79 G g; 80 D d(1); 81 const int N = 1000000; 82 std::vector<D::result_type> u; 83 for (int i = 0; i < N; ++i) 84 { 85 D::result_type v = d(g); 86 assert(d.min() < v); 87 u.push_back(v); 88 } 89 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 90 double var = 0; 91 double skew = 0; 92 double kurtosis = 0; 93 for (std::size_t i = 0; i < u.size(); ++i) 94 { 95 double dbl = (u[i] - mean); 96 double d2 = sqr(dbl); 97 var += d2; 98 skew += dbl * d2; 99 kurtosis += d2 * d2; 100 } 101 var /= u.size(); 102 double dev = std::sqrt(var); 103 skew /= u.size() * dev * var; 104 kurtosis /= u.size() * var * var; 105 kurtosis -= 3; 106 double x_mean = d.n(); 107 double x_var = 2 * d.n(); 108 double x_skew = std::sqrt(8 / d.n()); 109 double x_kurtosis = 12 / d.n(); 110 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 111 assert(std::abs((var - x_var) / x_var) < 0.01); 112 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 113 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 114 } 115 { 116 typedef std::chi_squared_distribution<> D; 117 typedef std::mt19937 G; 118 G g; 119 D d(2); 120 const int N = 1000000; 121 std::vector<D::result_type> u; 122 for (int i = 0; i < N; ++i) 123 { 124 D::result_type v = d(g); 125 assert(d.min() < v); 126 u.push_back(v); 127 } 128 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 129 double var = 0; 130 double skew = 0; 131 double kurtosis = 0; 132 for (std::size_t i = 0; i < u.size(); ++i) 133 { 134 double dbl = (u[i] - mean); 135 double d2 = sqr(dbl); 136 var += d2; 137 skew += dbl * d2; 138 kurtosis += d2 * d2; 139 } 140 var /= u.size(); 141 double dev = std::sqrt(var); 142 skew /= u.size() * dev * var; 143 kurtosis /= u.size() * var * var; 144 kurtosis -= 3; 145 double x_mean = d.n(); 146 double x_var = 2 * d.n(); 147 double x_skew = std::sqrt(8 / d.n()); 148 double x_kurtosis = 12 / d.n(); 149 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 150 assert(std::abs((var - x_var) / x_var) < 0.01); 151 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 152 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 153 } 154 155 return 0; 156 } 157