generating poisson variables in c++

Question

I implemented this function to generate a poisson random variable

typedef long unsigned int luint;
luint poisson(luint lambda) {
    double L = exp(-double(lambda));
    luint k = 0;
    double p = 1;
    do {
        k++;
        p *= mrand.rand();
    } while( p > L);
    return (k-1);
}

where mrand is the MersenneTwister random number generator. I find that, as I increase lambda, the expected distribution is going to be wrong, with a mean that saturates at around 750. Is it due to numerical approximations or did I make any mistakes?

Answer 1

If you go the "existing library" route, your compiler may already support the C++11 std::random package. Here is how you use it:

#include <random>
#include <ctime>
#include <iostream>

std::mt19937 mrand(std::time(0));  // seed however you want

typedef long unsigned int luint;

luint poisson(luint lambda)
{
    std::poisson_distribution<luint> d(lambda);
    return d(mrand);
}

int main()
{
    std::cout << poisson(750) << '\n';
    std::poisson_distribution<luint> d(750);
    std::cout << d(mrand) << '\n';
    std::cout << d(mrand) << '\n';
}

I've used it two ways above:

1. I tried to imitate your existing interface.

2. If you create a std::poisson_distribution with a mean, it is more efficient to use that distribution over and over for the same mean (as done in main()).

Here is sample output for me:

751
730
779