# 29 Numerics library [numerics]

## 29.6 Random number generation [rand]

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

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

A bernoulli_­distribution random number distribution produces bool values b distributed according to the discrete probability function

P(b|p)={pifb=true1pifb=false.

```class bernoulli_distribution {
public:
// types
using result_type = bool;
using param_type  = unspecified;

// constructors and reset functions
explicit bernoulli_distribution(double p = 0.5);
explicit bernoulli_distribution(const param_type& parm);
void reset();

// 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;
};```

```explicit bernoulli_distribution(double p = 0.5); ```

Requires: 0p1.

Effects: Constructs a bernoulli_­distribution object; p corresponds to the parameter of the distribution.

```double p() const; ```

Returns: The value of the p parameter with which the object was constructed.

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

A binomial_­distribution random number distribution produces integer values i0 distributed according to the discrete probability function

P(i|t,p)=(ti)pi(1p)ti.

```template<class IntType = int>
class binomial_distribution {
public:
// types
using result_type = IntType;
using param_type  = unspecified;

// constructors and reset functions
explicit binomial_distribution(IntType t = 1, double p = 0.5);
explicit binomial_distribution(const param_type& parm);
void reset();

// 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;
};```

```explicit binomial_distribution(IntType t = 1, double p = 0.5); ```

Requires: 0p1 and 0t.

Effects: Constructs a binomial_­distribution object; 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.

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

A geometric_­distribution random number distribution produces integer values i0 distributed according to the discrete probability function

P(i|p)=p(1p)i.

```template<class IntType = int>
class geometric_distribution {
public:
// types
using result_type = IntType;
using param_type  = unspecified;

// constructors and reset functions
explicit geometric_distribution(double p = 0.5);
explicit geometric_distribution(const param_type& parm);
void reset();

// 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;
};```

```explicit geometric_distribution(double p = 0.5); ```

Requires: 0<p<1.

Effects: Constructs a geometric_­distribution object; p corresponds to the parameter of the distribution.

```double p() const; ```

Returns: The value of the p parameter with which the object was constructed.

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

A negative_­binomial_­distribution random number distribution produces random integers i0 distributed according to the discrete probability function

P(i|k,p)=(k+i1i)pk(1p)i.

[Note: This implies that P(i|k,p) is undefined when p == 1. end note]

```template<class IntType = int>
class negative_binomial_distribution {
public:
// types
using result_type = IntType;
using param_type  = unspecified;

// constructor and reset functions
explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);
explicit negative_binomial_distribution(const param_type& parm);
void reset();

// 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;
};```

```explicit negative_binomial_distribution(IntType k = 1, double p = 0.5); ```

Requires: 0<p1 and 0<k.

Effects: Constructs a negative_­binomial_­distribution object; 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.