29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.8 Random number distribution class templates [rand.dist]

29.6.8.4.1 Class template poisson_­distribution[rand.dist.pois.poisson]

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

P(i|μ)=eμμii!.

The distribution parameter μ is also known as this distribution's mean.

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

// constructors and reset functions
explicit poisson_distribution(double mean = 1.0);
explicit poisson_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 mean() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};```

```explicit poisson_distribution(double mean = 1.0); ```

Requires: 0<mean.

Effects: Constructs a poisson_­distribution object; mean corresponds to the parameter of the distribution.

```double mean() const; ```

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

29.6.8.4.2 Class template exponential_­distribution[rand.dist.pois.exp]

An exponential_­distribution random number distribution produces random numbers x>0 distributed according to the probability density function

p(x|λ)=λeλx.

```template<class RealType = double>
class exponential_distribution {
public:
// types
using result_type = RealType;
using param_type  = unspecified;

// constructors and reset functions
explicit exponential_distribution(RealType lambda = 1.0);
explicit exponential_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
RealType lambda() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};```

```explicit exponential_distribution(RealType lambda = 1.0); ```

Requires: 0<lambda.

Effects: Constructs an exponential_­distribution object; lambda corresponds to the parameter of the distribution.

```RealType lambda() const; ```

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

29.6.8.4.3 Class template gamma_­distribution[rand.dist.pois.gamma]

A gamma_­distribution random number distribution produces random numbers x>0 distributed according to the probability density function

p(x|α,β)=ex/ββαΓ(α)xα1.

```template<class RealType = double>
class gamma_distribution {
public:
// types
using result_type = RealType;
using param_type  = unspecified;

// constructors and reset functions
explicit gamma_distribution(RealType alpha = 1.0, RealType beta = 1.0);
explicit gamma_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
RealType alpha() const;
RealType beta() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};```

```explicit gamma_distribution(RealType alpha = 1.0, RealType beta = 1.0); ```

Requires: 0<alpha and 0<beta.

Effects: Constructs a gamma_­distribution object; alpha and beta correspond to the parameters of the distribution.

```RealType alpha() const; ```

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

```RealType beta() const; ```

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

29.6.8.4.4 Class template weibull_­distribution[rand.dist.pois.weibull]

A weibull_­distribution random number distribution produces random numbers x0 distributed according to the probability density function

p(x|a,b)=ab(xb)a1exp((xb)a).

```template<class RealType = double>
class weibull_distribution {
public:
// types
using result_type = RealType;
using param_type  = unspecified;

// constructor and reset functions
explicit weibull_distribution(RealType a = 1.0, RealType b = 1.0);
explicit weibull_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
RealType a() const;
RealType b() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};```

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

Requires: 0<a and 0<b.

Effects: Constructs a weibull_­distribution object; a and b correspond to the respective parameters of the distribution.

```RealType a() const; ```

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

```RealType b() const; ```

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

29.6.8.4.5 Class template extreme_­value_­distribution[rand.dist.pois.extreme]

An extreme_­value_­distribution random number distribution produces random numbers x distributed according to the probability density function274

p(x|a,b)=1bexp(axbexp(axb)).

```template<class RealType = double>
class extreme_value_distribution {
public:
// types
using result_type = RealType;
using param_type  = unspecified;

// constructor and reset functions
explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0);
explicit extreme_value_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
RealType a() const;
RealType b() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};```

```explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0); ```

Requires: 0<b.

Effects: Constructs an extreme_­value_­distribution object; a and b correspond to the respective parameters of the distribution.

```RealType a() const; ```

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

```RealType b() const; ```

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

The distribution corresponding to this probability density function is also known (with a possible change of variable) as the Gumbel Type I, the log-Weibull, or the Fisher-Tippett Type I distribution.