Defined in header <random>  

template< class IntType = int > class binomial_distribution;  (since C++11) 
Produces random nonnegative integer values i, distributed according to discrete probability function: \(P(it,p) = \binom{t}{i} \cdot p^i \cdot (1p)^{ti}\)P(it,p) =
⎛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.
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 type  Definition 

result_type  IntType 
param_type  the type of the parameter set, see RandomNumberDistribution. 
constructs new distribution (public member function) 

resets the internal state of the distribution (public member function) 

Generation 

generates the next random number in the distribution (public member function) 

Characteristics 

returns the distribution parameters (public member function) 

gets or sets the distribution parameter object (public member function) 

returns the minimum potentially generated value (public member function) 

returns the maximum potentially generated value (public member function) 
compares two distribution objects (function) 

performs stream input and output on pseudorandom number distribution (function template) 
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) { ++hist[d(gen)]; } for (auto p : hist) { std::cout << p.first << ' ' << std::string(p.second/100, '*') << '\n'; } }
Possible output:
0 ****** 1 ************************ 2 ************************************* 3 ************************* 4 ******
Weisstein, Eric W. "Binomial Distribution." From MathWorldA Wolfram Web Resource.
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