[rand.dist.bern.negbin]

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

## 29.5 Random number generation [[rand]](rand#dist.bern.negbin)

### 29.5.9 Random number distribution class templates [[rand.dist]](rand.dist#bern.negbin)

#### 29.5.9.3 Bernoulli distributions [[rand.dist.bern]](rand.dist.bern#negbin)

#### 29.5.9.3.4 Class template negative_binomial_distribution [rand.dist.bern.negbin]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5038)

A negative_binomial_distribution random number distribution
produces random integers i â¥ 0 distributed according to
the discrete probability function in Formula [29.7](#eq:rand.dist.bern.negbin)[.](#1.sentence-1)

P(i|k,p)=(k+iâ1i)âpkâ(1âp)i(29.7)

[*Note [1](#note-1)*:

This implies that P(i | k,p) is undefined when p == 1[.](#1.sentence-2)

â *end note*]

[ð](#lib:negative_binomial_distribution_)

namespace std {template<class IntType = int>class negative_binomial_distribution {public:// typesusing result_type = IntType; using param_type = *unspecified*; // constructor and reset functions negative_binomial_distribution() : negative_binomial_distribution(1) {}explicit negative_binomial_distribution(IntType k, double p = 0.5); explicit negative_binomial_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const negative_binomial_distribution& x, const negative_binomial_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 IntType k() const; double p() 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 negative_binomial_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, negative_binomial_distribution& x); };}

[ð](#lib:negative_binomial_distribution,constructor)

`explicit negative_binomial_distribution(IntType k, double p = 0.5);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5103)

*Preconditions*: 0<pâ¤1 and 0<k[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5108)

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

[ð](#lib:k,negative_binomial_distribution)

`IntType k() const;
`

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5120)

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

[ð](#lib:p,negative_binomial_distribution)

`double p() const;
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L5132)

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