[rand.dist.pois.poisson]

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

## 29.5 Random number generation [[rand]](rand#dist.pois.poisson)

### 29.5.9 Random number distribution class templates [[rand.dist]](rand.dist#pois.poisson)

#### 29.5.9.4 Poisson distributions [[rand.dist.pois]](rand.dist.pois#poisson)

#### 29.5.9.4.1 Class template poisson_distribution [rand.dist.pois.poisson]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5157)

A poisson_distribution random number distribution
produces integer values i â¥ 0 distributed according to
the discrete probability function in Formula [29.8](#eq:rand.dist.pois.poisson)[.](#1.sentence-1)

P(i|Î¼)=eâÎ¼Î¼ii!(29.8)

The distribution parameter Î¼ is also known as this distribution's [*mean*](#def:mean)[.](#1.sentence-2)

[ð](#lib:poisson_distribution_)

namespace std {template<class IntType = int>class poisson_distribution {public:// typesusing result_type = IntType; using param_type = *unspecified*; // constructors and reset functions poisson_distribution() : poisson_distribution(1.0) {}explicit poisson_distribution(double mean); explicit poisson_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const poisson_distribution& x, const poisson_distribution& y); // generating functionstemplate<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functionsdouble mean() 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 poisson_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, poisson_distribution& x); };}

[ð](#lib:poisson_distribution,constructor)

`explicit poisson_distribution(double mean);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5218)

*Preconditions*: 0<mean[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5222)

*Remarks*: mean corresponds to the parameter of the distribution[.](#3.sentence-1)

[ð](#lib:mean,poisson_distribution)

`double mean() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5233)

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