[rand.dist.pois.gamma]

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

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

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

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

#### 29.5.9.4.3 Class template gamma_distribution [rand.dist.pois.gamma]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5332)

A gamma_distribution random number distribution
produces random numbers x>0 distributed according to
the probability density function in Formula [29.10](#eq:rand.dist.pois.gamma)[.](#1.sentence-1)

p(x|Î±,Î²)=eâx/Î²Î²Î±âÎ(Î±)âxÎ±â1(29.10)

[ð](#lib:gamma_distribution_)

namespace std {template<class RealType = double>class gamma_distribution {public:// typesusing result_type = RealType; using param_type = *unspecified*; // constructors and reset functions gamma_distribution() : gamma_distribution(1.0) {}explicit gamma_distribution(RealType alpha, RealType beta = 1.0); explicit gamma_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const gamma_distribution& x, const gamma_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 RealType alpha() const;
 RealType beta() 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 gamma_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, gamma_distribution& x); };}

[ð](#lib:gamma_distribution,constructor)

`explicit gamma_distribution(RealType alpha, RealType beta = 1.0);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5394)

*Preconditions*: 0<alpha and 0<beta[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5398)

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

[ð](#lib:alpha,gamma_distribution)

`RealType alpha() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5410)

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

[ð](#lib:beta,gamma_distribution)

`RealType beta() const;
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5422)

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