[rand.dist.bern.bin]

# 29 Numerics library [[numerics]](./#numerics)

## 29.5 Random number generation [[rand]](rand#dist.bern.bin)

### 29.5.9 Random number distribution class templates [[rand.dist]](rand.dist#bern.bin)

#### 29.5.9.3 Bernoulli distributions [[rand.dist.bern]](rand.dist.bern#bin)

#### 29.5.9.3.2 Class template binomial_distribution [rand.dist.bern.bin]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L4848)

A binomial_distribution random number distribution
produces integer values i â¥ 0 distributed according to
the discrete probability function in Formula [29.5](#eq:rand.dist.bern.bin)[.](#1.sentence-1)

P(i|t,p)=(ti)âpiâ(1âp)tâi(29.5)

[ð](#lib:binomial_distribution_)

namespace std {template<class IntType = int>class binomial_distribution {public:// typesusing result_type = IntType; using param_type = *unspecified*; // constructors and reset functions binomial_distribution() : binomial_distribution(1) {}explicit binomial_distribution(IntType t, double p = 0.5); explicit binomial_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const binomial_distribution& x, const binomial_distribution& y); // generating functionstemplate<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions IntType t() const; double p() const;
 param_type param() const; void param(const param_type& parm);
 result_type min() const;
 result_type max() const; // inserters and extractorstemplate<class charT, class traits>friend basic_ostream<charT, traits>&operator<<(basic_ostream<charT, traits>& os, const binomial_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, binomial_distribution& x); };}

[ð](#lib:binomial_distribution,constructor)

`explicit binomial_distribution(IntType t, double p = 0.5);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L4910)

*Preconditions*: 0 â¤ p â¤ 1 and 0 â¤ t[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L4914)

*Remarks*: t and p correspond to the respective parameters of the distribution[.](#3.sentence-1)

[ð](#lib:t,binomial_distribution)

`IntType t() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L4925)

*Returns*: The value of the t parameter
 with which the object was constructed[.](#4.sentence-1)

[ð](#lib:p,binomial_distribution)

`double p() const;
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L4937)

*Returns*: The value of the p parameter
 with which the object was constructed[.](#5.sentence-1)
