[rand.dist.norm.normal]

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

## 29.5 Random number generation [[rand]](rand#dist.norm.normal)

### 29.5.9 Random number distribution class templates [[rand.dist]](rand.dist#norm.normal)

#### 29.5.9.5 Normal distributions [[rand.dist.norm]](rand.dist.norm#normal)

#### 29.5.9.5.1 Class template normal_distribution [rand.dist.norm.normal]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5663)

A normal_distribution random number distribution
produces random numbers x distributed according to
the probability density function in Formula [29.13](#eq:rand.dist.norm.normal)[.](#1.sentence-1)

p(x|Î¼,Ï)=1Ïâ2Ïâexp(â(xâÎ¼)22Ï2)(29.13)

The distribution parameters Î¼ and Ï are also known as this distribution's [*mean*](#def:mean) and [*standard deviation*](#def:standard_deviation)[.](#1.sentence-2)

[ð](#lib:normal_distribution_)

namespace std {template<class RealType = double>class normal_distribution {public:// typesusing result_type = RealType; using param_type = *unspecified*; // constructors and reset functions normal_distribution() : normal_distribution(0.0) {}explicit normal_distribution(RealType mean, RealType stddev = 1.0); explicit normal_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const normal_distribution& x, const normal_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 mean() const;
 RealType stddev() 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 normal_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, normal_distribution& x); };}

[ð](#lib:normal_distribution,constructor)

`explicit normal_distribution(RealType mean, RealType stddev = 1.0);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5733)

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

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5737)

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

[ð](#lib:mean,normal_distribution)

`RealType mean() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5749)

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

[ð](#lib:stddev,normal_distribution)

`RealType stddev() const;
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5761)

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