175 lines · cpp
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-exception6//7//===----------------------------------------------------------------------===//8//9// REQUIRES: long_tests10 11// <random>12 13// template<class RealType = double>14// class weibull_distribution15 16// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);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 27template <class T>28inline29T30sqr(T x)31{32 return x * x;33}34 35int main(int, char**)36{37 {38 typedef std::weibull_distribution<> D;39 typedef D::param_type P;40 typedef std::mt19937 G;41 G g;42 D d(0.5, 2);43 P p(1, .5);44 const int N = 1000000;45 std::vector<D::result_type> u;46 for (int i = 0; i < N; ++i)47 {48 D::result_type v = d(g, p);49 assert(d.min() <= v);50 u.push_back(v);51 }52 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();53 double var = 0;54 double skew = 0;55 double kurtosis = 0;56 for (std::size_t i = 0; i < u.size(); ++i)57 {58 double dbl = (u[i] - mean);59 double d2 = sqr(dbl);60 var += d2;61 skew += dbl * d2;62 kurtosis += d2 * d2;63 }64 var /= u.size();65 double dev = std::sqrt(var);66 skew /= u.size() * dev * var;67 kurtosis /= u.size() * var * var;68 kurtosis -= 3;69 double x_mean = p.b() * std::tgamma(1 + 1/p.a());70 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);71 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -72 3*x_mean*x_var - sqr(x_mean)*x_mean) /73 (std::sqrt(x_var)*x_var);74 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -75 4*x_skew*x_var*sqrt(x_var)*x_mean -76 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;77 assert(std::abs((mean - x_mean) / x_mean) < 0.01);78 assert(std::abs((var - x_var) / x_var) < 0.01);79 assert(std::abs((skew - x_skew) / x_skew) < 0.01);80 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);81 }82 {83 typedef std::weibull_distribution<> D;84 typedef D::param_type P;85 typedef std::mt19937 G;86 G g;87 D d(1, .5);88 P p(2, 3);89 const int N = 1000000;90 std::vector<D::result_type> u;91 for (int i = 0; i < N; ++i)92 {93 D::result_type v = d(g, p);94 assert(d.min() <= v);95 u.push_back(v);96 }97 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();98 double var = 0;99 double skew = 0;100 double kurtosis = 0;101 for (std::size_t i = 0; i < u.size(); ++i)102 {103 double dbl = (u[i] - mean);104 double d2 = sqr(dbl);105 var += d2;106 skew += dbl * d2;107 kurtosis += d2 * d2;108 }109 var /= u.size();110 double dev = std::sqrt(var);111 skew /= u.size() * dev * var;112 kurtosis /= u.size() * var * var;113 kurtosis -= 3;114 double x_mean = p.b() * std::tgamma(1 + 1/p.a());115 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);116 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -117 3*x_mean*x_var - sqr(x_mean)*x_mean) /118 (std::sqrt(x_var)*x_var);119 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -120 4*x_skew*x_var*sqrt(x_var)*x_mean -121 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;122 assert(std::abs((mean - x_mean) / x_mean) < 0.01);123 assert(std::abs((var - x_var) / x_var) < 0.01);124 assert(std::abs((skew - x_skew) / x_skew) < 0.01);125 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);126 }127 {128 typedef std::weibull_distribution<> D;129 typedef D::param_type P;130 typedef std::mt19937 G;131 G g;132 D d(2, 3);133 P p(.5, 2);134 const int N = 1000000;135 std::vector<D::result_type> u;136 for (int i = 0; i < N; ++i)137 {138 D::result_type v = d(g, p);139 assert(d.min() <= v);140 u.push_back(v);141 }142 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();143 double var = 0;144 double skew = 0;145 double kurtosis = 0;146 for (std::size_t i = 0; i < u.size(); ++i)147 {148 double dbl = (u[i] - mean);149 double d2 = sqr(dbl);150 var += d2;151 skew += dbl * d2;152 kurtosis += d2 * d2;153 }154 var /= u.size();155 double dev = std::sqrt(var);156 skew /= u.size() * dev * var;157 kurtosis /= u.size() * var * var;158 kurtosis -= 3;159 double x_mean = p.b() * std::tgamma(1 + 1/p.a());160 double x_var = sqr(p.b()) * std::tgamma(1 + 2/p.a()) - sqr(x_mean);161 double x_skew = (sqr(p.b())*p.b() * std::tgamma(1 + 3/p.a()) -162 3*x_mean*x_var - sqr(x_mean)*x_mean) /163 (std::sqrt(x_var)*x_var);164 double x_kurtosis = (sqr(sqr(p.b())) * std::tgamma(1 + 4/p.a()) -165 4*x_skew*x_var*sqrt(x_var)*x_mean -166 6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;167 assert(std::abs((mean - x_mean) / x_mean) < 0.01);168 assert(std::abs((var - x_var) / x_var) < 0.01);169 assert(std::abs((skew - x_skew) / x_skew) < 0.01);170 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);171 }172 173 return 0;174}175