text: //===----------------------------------------------------------------------===//
  //
  //                     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 IntType = int>
  // class poisson_distribution
  
  // template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
  
  #include <random>
  #include <cassert>
  #include <vector>
  #include <numeric>
  
  template <class T>
  inline
  T
  sqr(T x)
  {
      return x * x;
  }
  
  int main()
  {
      {
          typedef std::poisson_distribution<> D;
          typedef D::param_type P;
          typedef std::minstd_rand G;
          G g;
          D d(.75);
          P p(2);
          const int N = 100000;
          std::vector<double> u;
          for (int i = 0; i < N; ++i)
          {
              D::result_type v = d(g, p);
              assert(d.min() <= v && v <= d.max());
              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 (int 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 = p.mean();
          double x_var = p.mean();
          double x_skew = 1 / std::sqrt(x_var);
          double x_kurtosis = 1 / x_var;
          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::poisson_distribution<> D;
          typedef D::param_type P;
          typedef std::minstd_rand G;
          G g;
          D d(2);
          P p(.75);
          const int N = 100000;
          std::vector<double> u;
          for (int i = 0; i < N; ++i)
          {
              D::result_type v = d(g, p);
              assert(d.min() <= v && v <= d.max());
              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 (int 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 = p.mean();
          double x_var = p.mean();
          double x_skew = 1 / std::sqrt(x_var);
          double x_kurtosis = 1 / x_var;
          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) < 0.04);
      }
      {
          typedef std::poisson_distribution<> D;
          typedef D::param_type P;
          typedef std::mt19937 G;
          G g;
          D d(2);
          P p(20);
          const int N = 1000000;
          std::vector<double> u;
          for (int i = 0; i < N; ++i)
          {
              D::result_type v = d(g, p);
              assert(d.min() <= v && v <= d.max());
              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 (int 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 = p.mean();
          double x_var = p.mean();
          double x_skew = 1 / std::sqrt(x_var);
          double x_kurtosis = 1 / x_var;
          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);
      }
  }
  