< cpp‎ | numeric‎ | random
Pseudo-random number generation
Engines and engine adaptors
Uniform distributions
Bernoulli distributions
Poisson distributions
Normal distributions
Sampling distributions
Seed Sequences
C library
Defined in header <random>
template< class IntType = int >
class binomial_distribution;
(since C++11)

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

P(i|t,p) =


· pi
· (1 − p)t−i

The value obtained is the number of successes in a sequence of t yes/no experiments, each of which succeeds with probability p.

std::binomial_distribution satisfies RandomNumberDistribution


[edit] Template parameters

IntType - The result type generated by the generator. The effect is undefined if this is not one of short, int, long, long long, unsigned short, unsigned int, unsigned long, or unsigned long long.

[edit] Member types

Member type Definition
result_type IntType
param_type the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

constructs new distribution
(public member function) [edit]
resets the internal state of the distribution
(public member function) [edit]
generates the next random number in the distribution
(public member function) [edit]
returns the distribution parameters
(public member function) [edit]
gets or sets the distribution parameter object
(public member function) [edit]
returns the minimum potentially generated value
(public member function) [edit]
returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

compares two distribution objects
(function) [edit]
performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Example

Plot of binomial distribution with probability of success of each trial exactly 0.5, illustrating the relationship with the pascal triangle (the probabilities that none, 1, 2, 3, or all four of the 4 trials will be successful in this case are 1:4:6:4:1)

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
int main()
    std::random_device rd;
    std::mt19937 gen(rd());
    // perform 4 trials, each succeeds 1 in 2 times
    std::binomial_distribution<> d(4, 0.5);
    std::map<int, int> hist;
    for (int n = 0; n < 10000; ++n) {
    for (auto p : hist) {
        std::cout << p.first << ' '
                  << std::string(p.second/100, '*') << '\n';

Possible output:

0 ******
1 ************************
2 *************************************
3 *************************
4 ******

[edit] External links

Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource.