| //===----------------------------------------------------------------------===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is distributed under the University of Illinois Open Source |
| // License. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| // <random> |
| |
| // template<class IntType = int> |
| // class negative_binomial_distribution |
| |
| // template<class _URNG> result_type operator()(_URNG& g); |
| |
| #include <random> |
| #include <numeric> |
| #include <vector> |
| #include <cassert> |
| |
| template <class T> |
| inline |
| T |
| sqr(T x) |
| { |
| return x * x; |
| } |
| |
| int main() |
| { |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::minstd_rand G; |
| G g; |
| D d(5, .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(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| 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 < 0.01); |
| } |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(30, .03125); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| 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 < 0.01); |
| } |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(40, .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(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| 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); |
| } |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(40, 1); |
| const int N = 1000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| assert(mean == x_mean); |
| assert(var == x_var); |
| } |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(400, 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(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| 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 < 0.04); |
| assert(std::abs(kurtosis - x_kurtosis) / x_kurtosis < 0.05); |
| } |
| { |
| typedef std::negative_binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(1, 0.05); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(0)) / u.size(); |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (int i = 0; i < u.size(); ++i) |
| { |
| double d = (u[i] - mean); |
| double d2 = sqr(d); |
| var += d2; |
| skew += d * 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 = d.k() * (1 - d.p()) / d.p(); |
| double x_var = x_mean / d.p(); |
| double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p())); |
| double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p())); |
| 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 < 0.02); |
| } |
| } |