I am trying to use Boost to generate random numbers according to the beta distribution using C++. I have seen many examples online for generating random numbers according to distributions in random.hpp (e.g. this book). However, I cannot seen to translate them to use the beta distribution found in beta.hpp.
Thanks.
You'll first want to draw a random number uniformly from the range (0,1). Given any distribution, you can then plug that number into the distribution's "quantile function," and the result is as if a random value was drawn from the distribution. From here:
A general method to generate random numbers from an arbitrary distribution which has a cdf without jumps is to use the inverse function to the cdf: G(y)=F^{-1}(y). If u(1), ..., u(n) are random numbers from the uniform on (0,1) distribution then G(u(1)), ..., G(u(n)) is a random sample from the distribution with cdf F(x).
So how do we get a quantile function for a beta distribution? The documentation for beta.hpp is here. You should be able to use something like this:
#include <boost/math/distributions.hpp> using namespace boost::math; double alpha, beta, randFromUnif; //parameters and the random value on (0,1) you drew beta_distribution<> dist(alpha, beta); double randFromDist = quantile(dist, randFromUnif); 
randFromUnif floating point number you're passing in doesn't have enough resolution to generate random numbers when passed through the quantile: you'd end up getting quantized output values. So know your problem domain and your quantile function to make sure you're aware of this!According to boost's demo for the random number library Random_demo.cpp and Generating integers with different probabilities
What you should do is to use "variate_generator" class to bind your random number generator and distribution.
An example may look like
#include <iostream> #include "boost/random.hpp" int main(int argc, char *argv[]) { int seed = 2018; typedef boost::random::mt19937 RandomNumberGenerator; typedef boost::random::beta_distribution<> BetaDistribution; typedef boost::variate_generator<RandomNumberGenerator&, BetaDistribution> Generator; RandomNumberGenerator Rng(seed); BetaDistribution distribution(2,5); Generator getRandomNumber(Rng,distribution); for (int idx = 0 ; idx < 1000 ; ++idx) { std::cout << getRandomNumber() << std::endl; } return 0; } However, in the more recent document enter link description here, it seems that boost recommends to directly passing the generator to the distribution obejct. The result from the code below is identical.
#include <iostream> #include "boost/random.hpp" int main(int argc, char *argv[]) { int seed = 2018; typedef boost::random::mt19937 RandomNumberGenerator; typedef boost::random::beta_distribution<> BetaDistribution; RandomNumberGenerator Rng(seed); BetaDistribution distribution(2,5); for (int idx = 0 ; idx < 1000 ; ++idx) { std::cout << distribution(Rng) << std::endl; } return 0; } 