# 28 Numerics library [numerics]

## 28.5 Random number generation [rand]

### 28.5.9 Random number distribution class templates [rand.dist]

#### 28.5.9.3.1 Class bernoulli_distribution[rand.dist.bern.bernoulli]

A bernoulli_distribution random number distribution produces bool values b distributed according to the discrete probability function
namespace std { class bernoulli_distribution { public: // types using result_type = bool; using param_type = unspecified; // constructors and reset functions bernoulli_distribution() : bernoulli_distribution(0.5) {} explicit bernoulli_distribution(double p); explicit bernoulli_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const bernoulli_distribution& x, const bernoulli_distribution& y); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const bernoulli_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, bernoulli_distribution& x); }; }
explicit bernoulli_distribution(double p);
Preconditions: .
Remarks: p corresponds to the parameter of the distribution.
double p() const;
Returns: The value of the p parameter with which the object was constructed.

#### 28.5.9.3.2 Class template binomial_distribution[rand.dist.bern.bin]

A binomial_distribution random number distribution produces integer values distributed according to the discrete probability function
namespace std { template<class IntType = int> class binomial_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructors and reset functions binomial_distribution() : binomial_distribution(1) {} explicit binomial_distribution(IntType t, double p = 0.5); explicit binomial_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const binomial_distribution& x, const binomial_distribution& y); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions IntType t() const; double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const binomial_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, binomial_distribution& x); }; }
explicit binomial_distribution(IntType t, double p = 0.5);
Preconditions: and .
Remarks: t and p correspond to the respective parameters of the distribution.
IntType t() const;
Returns: The value of the t parameter with which the object was constructed.
double p() const;
Returns: The value of the p parameter with which the object was constructed.

#### 28.5.9.3.3 Class template geometric_distribution[rand.dist.bern.geo]

A geometric_distribution random number distribution produces integer values distributed according to the discrete probability function
namespace std { template<class IntType = int> class geometric_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructors and reset functions geometric_distribution() : geometric_distribution(0.5) {} explicit geometric_distribution(double p); explicit geometric_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const geometric_distribution& x, const geometric_distribution& y); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const geometric_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, geometric_distribution& x); }; }
explicit geometric_distribution(double p);
Preconditions: .
Remarks: p corresponds to the parameter of the distribution.
double p() const;
Returns: The value of the p parameter with which the object was constructed.

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

A negative_binomial_distribution random number distribution produces random integers distributed according to the discrete probability function
[Note 1:
This implies that P(i|k,p) is undefined when p == 1.
— end note]
namespace std { template<class IntType = int> class negative_binomial_distribution { public: // types using 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 operators friend bool operator==(const negative_binomial_distribution& x, const negative_binomial_distribution& y); // generating functions template<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 extractors template<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); }; }
explicit negative_binomial_distribution(IntType k, double p = 0.5);
Preconditions: and .
Remarks: k and p correspond to the respective parameters of the distribution.
IntType k() const;
Returns: The value of the k parameter with which the object was constructed.
double p() const;
Returns: The value of the p parameter with which the object was constructed.