| //===----------------------------------------------------------------------===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is dual licensed under the MIT and the University of Illinois Open |
| // Source Licenses. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // REQUIRES: long_tests |
| |
| // <random> |
| |
| // template<class RealType = double> |
| // class lognormal_distribution |
| |
| // template<class _URNG> result_type operator()(_URNG& g); |
| |
| #include <random> |
| #include <cassert> |
| #include <vector> |
| #include <numeric> |
| |
| template <class T> |
| inline |
| T |
| sqr(T x) |
| { |
| return x * x; |
| } |
| |
| void |
| test1() |
| { |
| typedef std::lognormal_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(-1./8192, 0.015625); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(v > 0); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (unsigned i = 0; i < u.size(); ++i) |
| { |
| double dbl = (u[i] - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= u.size(); |
| double dev = std::sqrt(var); |
| skew /= u.size() * dev * var; |
| kurtosis /= u.size() * var * var; |
| kurtosis -= 3; |
| double x_mean = std::exp(d.m() + sqr(d.s())/2); |
| double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); |
| double x_skew = (std::exp(sqr(d.s())) + 2) * |
| std::sqrt((std::exp(sqr(d.s())) - 1)); |
| double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + |
| 3*std::exp(2*sqr(d.s())) - 6; |
| assert(std::abs((mean - x_mean) / x_mean) < 0.01); |
| assert(std::abs((var - x_var) / x_var) < 0.01); |
| assert(std::abs((skew - x_skew) / x_skew) < 0.05); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25); |
| } |
| |
| void |
| test2() |
| { |
| typedef std::lognormal_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(-1./32, 0.25); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(v > 0); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (unsigned i = 0; i < u.size(); ++i) |
| { |
| double dbl = (u[i] - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= u.size(); |
| double dev = std::sqrt(var); |
| skew /= u.size() * dev * var; |
| kurtosis /= u.size() * var * var; |
| kurtosis -= 3; |
| double x_mean = std::exp(d.m() + sqr(d.s())/2); |
| double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); |
| double x_skew = (std::exp(sqr(d.s())) + 2) * |
| std::sqrt((std::exp(sqr(d.s())) - 1)); |
| double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + |
| 3*std::exp(2*sqr(d.s())) - 6; |
| assert(std::abs((mean - x_mean) / x_mean) < 0.01); |
| assert(std::abs((var - x_var) / x_var) < 0.01); |
| assert(std::abs((skew - x_skew) / x_skew) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); |
| } |
| |
| void |
| test3() |
| { |
| typedef std::lognormal_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(-1./8, 0.5); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(v > 0); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (unsigned i = 0; i < u.size(); ++i) |
| { |
| double dbl = (u[i] - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= u.size(); |
| double dev = std::sqrt(var); |
| skew /= u.size() * dev * var; |
| kurtosis /= u.size() * var * var; |
| kurtosis -= 3; |
| double x_mean = std::exp(d.m() + sqr(d.s())/2); |
| double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); |
| double x_skew = (std::exp(sqr(d.s())) + 2) * |
| std::sqrt((std::exp(sqr(d.s())) - 1)); |
| double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + |
| 3*std::exp(2*sqr(d.s())) - 6; |
| assert(std::abs((mean - x_mean) / x_mean) < 0.01); |
| assert(std::abs((var - x_var) / x_var) < 0.01); |
| assert(std::abs((skew - x_skew) / x_skew) < 0.02); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05); |
| } |
| |
| void |
| test4() |
| { |
| typedef std::lognormal_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d; |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(v > 0); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (unsigned i = 0; i < u.size(); ++i) |
| { |
| double dbl = (u[i] - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= u.size(); |
| double dev = std::sqrt(var); |
| skew /= u.size() * dev * var; |
| kurtosis /= u.size() * var * var; |
| kurtosis -= 3; |
| double x_mean = std::exp(d.m() + sqr(d.s())/2); |
| double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); |
| double x_skew = (std::exp(sqr(d.s())) + 2) * |
| std::sqrt((std::exp(sqr(d.s())) - 1)); |
| double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + |
| 3*std::exp(2*sqr(d.s())) - 6; |
| assert(std::abs((mean - x_mean) / x_mean) < 0.01); |
| assert(std::abs((var - x_var) / x_var) < 0.02); |
| assert(std::abs((skew - x_skew) / x_skew) < 0.08); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4); |
| } |
| |
| void |
| test5() |
| { |
| typedef std::lognormal_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(-0.78125, 1.25); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(v > 0); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (unsigned i = 0; i < u.size(); ++i) |
| { |
| double dbl = (u[i] - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= u.size(); |
| double dev = std::sqrt(var); |
| skew /= u.size() * dev * var; |
| kurtosis /= u.size() * var * var; |
| kurtosis -= 3; |
| double x_mean = std::exp(d.m() + sqr(d.s())/2); |
| double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); |
| double x_skew = (std::exp(sqr(d.s())) + 2) * |
| std::sqrt((std::exp(sqr(d.s())) - 1)); |
| double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + |
| 3*std::exp(2*sqr(d.s())) - 6; |
| assert(std::abs((mean - x_mean) / x_mean) < 0.01); |
| assert(std::abs((var - x_var) / x_var) < 0.04); |
| assert(std::abs((skew - x_skew) / x_skew) < 0.2); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7); |
| } |
| |
| int main() |
| { |
| test1(); |
| test2(); |
| test3(); |
| test4(); |
| test5(); |
| } |