NAME¶

std::binomial_distribution - std::binomial_distribution

Synopsis¶

Defined in header <random>
template< class IntType = int > (since C++11)
class binomial_distribution;

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¶

The result type generated by the generator. The effect is undefined if
IntType - 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 IntType
param_type(C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions¶

constructor constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

p returns the distribution parameters
t (public member function)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

operator==
operator!= compares two distribution objects
(C++11) (function)
(C++11)(removed in C++20)
operator<< performs stream input and output on pseudo-random number
operator>> distribution
(C++11) (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 <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) {
++hist[d(gen)];
}
for (auto p : hist) {
std::cout << p.first << ' '
<< std::string(p.second/100, '*') << '\n';
}
}

Possible output:¶

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

External links¶

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