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std::poisson_distribution - cppreference.com

template< class IntType = int >
class poisson_distribution;

Produces random non-negative integer values i, distributed according to discrete probability function:

\(P(i | \mu) = \frac{e^{-\mu}\mu^i}{i!}\)P(i|μ) =

The value obtained is the probability of exactly i occurrences of a random event if the expected, mean number of its occurrence under the same conditions (on the same time/space interval) is μ.

std::poisson_distribution satisfies RandomNumberDistribution.

#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());
 
    // If an event occurs 4 times a minute on average, how
    // often is it that it occurs n times in one minute?
    std::poisson_distribution<> d(4);
 
    std::map<int, int> hist;
    for (int n = 0; n != 10000; ++n)
        ++hist[d(gen)];
 
    for (auto [x, y] : hist)
        std::cout << std::hex << x << ' '
                  << std::string(y / 100, '*') << '\n';
}

Possible output:

0 *
1 *******
2 **************
3 *******************
4 *******************
5 ***************
6 **********
7 *****
8 **
9 *
a
b
c
d

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