Random Number Generator with Beta Distribution

Question

I need the c or c++ source code of a function like betarand(a,b) that produces random number with beta distribution . I know that I can use boost library but I'm going to port it for CUDA architecture so I need the code. Can somebody help me?
Meantime I have betapdf (Beta Probability density function). But I don't know how to use it for creating random numbers :).

Answer 1

The C++11 random number library doesn't provide a beta distribution. However, a beta distribution can be modelled in terms of two gamma distributions, which the library does provide. I've implemented a beta_distribution in terms of std::gamma_distribution for you. As far as I can tell, it fully conforms with the requirements for a Random Number Distribution.

#include <iostream>
#include <sstream>
#include <string>
#include <random>

namespace sftrabbit {

  template <typename RealType = double>
  class beta_distribution
  {
    public:
      typedef RealType result_type;

      class param_type
      {
        public:
          typedef beta_distribution distribution_type;

          explicit param_type(RealType a = 2.0, RealType b = 2.0)
            : a_param(a), b_param(b) { }

          RealType a() const { return a_param; }
          RealType b() const { return b_param; }

          bool operator==(const param_type& other) const
          {
            return (a_param == other.a_param &&
                    b_param == other.b_param);
          }

          bool operator!=(const param_type& other) const
          {
            return !(*this == other);
          }

        private:
          RealType a_param, b_param;
      };

      explicit beta_distribution(RealType a = 2.0, RealType b = 2.0)
        : a_gamma(a), b_gamma(b) { }
      explicit beta_distribution(const param_type& param)
        : a_gamma(param.a()), b_gamma(param.b()) { }

      void reset() { }

      param_type param() const
      {
        return param_type(a(), b());
      }

      void param(const param_type& param)
      {
        a_gamma = gamma_dist_type(param.a());
        b_gamma = gamma_dist_type(param.b());
      }

      template <typename URNG>
      result_type operator()(URNG& engine)
      {
        return generate(engine, a_gamma, b_gamma);
      }

      template <typename URNG>
      result_type operator()(URNG& engine, const param_type& param)
      {
        gamma_dist_type a_param_gamma(param.a()),
                        b_param_gamma(param.b());
        return generate(engine, a_param_gamma, b_param_gamma); 
      }

      result_type min() const { return 0.0; }
      result_type max() const { return 1.0; }

      result_type a() const { return a_gamma.alpha(); }
      result_type b() const { return b_gamma.alpha(); }

      bool operator==(const beta_distribution<result_type>& other) const
      {
        return (param() == other.param() &&
                a_gamma == other.a_gamma &&
                b_gamma == other.b_gamma);
      }

      bool operator!=(const beta_distribution<result_type>& other) const
      {
        return !(*this == other);
      }

    private:
      typedef std::gamma_distribution<result_type> gamma_dist_type;

      gamma_dist_type a_gamma, b_gamma;

      template <typename URNG>
      result_type generate(URNG& engine,
        gamma_dist_type& x_gamma,
        gamma_dist_type& y_gamma)
      {
        result_type x = x_gamma(engine);
        return x / (x + y_gamma(engine));
      }
  };

  template <typename CharT, typename RealType>
  std::basic_ostream<CharT>& operator<<(std::basic_ostream<CharT>& os,
    const beta_distribution<RealType>& beta)
  {
    os << "~Beta(" << beta.a() << "," << beta.b() << ")";
    return os;
  }

  template <typename CharT, typename RealType>
  std::basic_istream<CharT>& operator>>(std::basic_istream<CharT>& is,
    beta_distribution<RealType>& beta)
  {
    std::string str;
    RealType a, b;
    if (std::getline(is, str, '(') && str == "~Beta" &&
        is >> a && is.get() == ',' && is >> b && is.get() == ')') {
      beta = beta_distribution<RealType>(a, b);
    } else {
      is.setstate(std::ios::failbit);
    }
    return is;
  }

}

Use it like so:

std::random_device rd;
std::mt19937 gen(rd());
sftrabbit::beta_distribution<> beta(2, 2);
for (int i = 0; i < 10000; i++) {
  std::cout << beta(gen) << std::endl;
}

Answer 2

Maybe you can use the code that gsl uses for producing random numbers with the beta distribution. They use a little weird way of produging them, as you have to pass a random number generator to the function, but surely you can get what you need.

Here's the documentation and the web page

Answer 3

Boost "inverse incomplete Beta" is another fast (and simple) way to simulate Betas.

#include <random>
#include <boost/math/special_functions/beta.hpp>
template<typename URNG>
double beta_sample(URNG& engine, double a, double b)
{
  static std::uniform_real_distribution<double> unif(0,1);
  double p = unif(engine);
  return boost::math::ibeta_inv(a, b, p); 
  // Use Boost policies if it's not fast enough
}

Answer 4

Check out the random number generator implementations in NumPy : NumPy distributions source

They are implemented in C, and work very fast.