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std::negative_binomial_distribution - cppreference.com

template< class IntType = int >
class negative_binomial_distribution;

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

\(P(i|k, p) = \binom{k + i - 1}{i} \cdot p^k \cdot (1 - p)^i\)P(i|k,p) =⎛
⎜
⎝k + i − 1
i⎞
⎟
⎠ · pk
· (1 − p)i

The value represents the number of failures in a series of independent yes/no trials (each succeeds with probability p), before exactly k successes occur.

std::negative_binomial_distribution satisfies RandomNumberDistribution.

#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());
    // Pat goes door-to-door selling cookies
    // At each house, there's a 75% chance that she sells one box
    // how many times will she be turned away before selling 5 boxes?
    std::negative_binomial_distribution<> d(5, 0.75);
 
    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

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