[rand.dist.norm.cauchy]

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

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

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

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

#### 29.5.9.5.4 Class template cauchy_distribution [rand.dist.norm.cauchy]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5964)

A cauchy_distribution random number distribution
produces random numbers x distributed according to
the probability density function in Formula [29.16](#eq:rand.dist.norm.cauchy)[.](#1.sentence-1)

p(x|a,b)=(Ïb(1+(xâab)2))â1(29.16)

[ð](#lib:cauchy_distribution_)

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

[ð](#lib:cauchy_distribution,constructor)

`explicit cauchy_distribution(RealType a, RealType b = 1.0);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6025)

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

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6029)

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

[ð](#lib:a,cauchy_distribution)

`RealType a() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6041)

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

[ð](#lib:b,cauchy_distribution)

`RealType b() const;
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6053)

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