[rand.dist.norm.t]

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

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

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

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

#### 29.5.9.5.6 Class template student_t_distribution [rand.dist.norm.t]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6170)

A student_t_distribution random number distribution
produces random numbers x distributed according to
the probability density function in Formula [29.18](#eq:rand.dist.norm.t)[.](#1.sentence-1)

p(x|n)=1ânÏâÎ((n+1)/2)Î(n/2)â(1+x2n)â(n+1)/2(29.18)

[ð](#lib:student_t_distribution_)

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

[ð](#lib:student_t_distribution,constructor)

`explicit student_t_distribution(RealType n);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6231)

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

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6235)

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

[ð](#lib:mean,student_t_distribution)

`RealType n() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L6246)

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