# std::binomial_distribution

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< cpp‎ | numeric‎ | random

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:

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

### 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.

### Member types

Member type | Definition
`result_type` (C++11) | IntType
`param_type` (C++11) | the type of the parameter set, see RandomNumberDistribution.

### Member functions

(constructor) (C++11) | constructs new distribution (public member function)
reset (C++11) | resets the internal state of the distribution (public member function)
##### Generation
operator() (C++11) | generates the next random number in the distribution (public member function)
##### Characteristics
p t (C++11) | returns the distribution parameters (public member function)
param (C++11) | gets or sets the distribution parameter object (public member function)
min (C++11) | returns the minimum potentially generated value (public member function)
max (C++11) | returns the maximum potentially generated value (public member function)

### Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20) | compares two distribution objects (function)
operator<<operator>> (C++11) | performs stream input and output on pseudo-random number distribution (function template)

### 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)

Run this code

    #include <iomanip>
    #include <iostream>
    #include <map>
    #include <random>
    #include <string>

    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)
            ++hist[d(gen)];

        for (auto const& [x, y] : hist)
            std::cout << x << ' ' << std::string(y / 100, '*') << '\n';
    }

Possible output:

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

### External links

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

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