26 Numerics library [numerics]

26.5 Random number generation [rand]

26.5.8 Random number distribution class templates [rand.dist]

26.5.8.4 Poisson distributions [rand.dist.pois]

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

1

A poisson_distribution random number distribution produces integer values i ≥ 0 distributed according to the discrete probability function \[% P(i\,|\,\mu) = \frac{ e^{-\mu} \mu^{i} } { i\,! } \; \mbox{.} \] The distribution parameter μ is also known as this distribution's mean.

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

 // constructors and reset functions
 explicit poisson_distribution(double mean = 1.0);
 explicit poisson_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& 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);

2

Requires: 0 < mean .

3

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

double mean() const;

4

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

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

1

An exponential_distribution random number distribution produces random numbers x > 0 distributed according to the probability density function p(x | λ) = λ e-λ x . 

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

 // constructors and reset functions
 explicit exponential_distribution(RealType lambda = 1.0);
 explicit exponential_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& 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);

2

Requires: 0 < lambda .

3

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

RealType lambda() const;

4

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

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

1

A gamma_distribution random number distribution produces random numbers x > 0 distributed according to the probability density function \[% p(x\,|\,\alpha,\beta) = \frac{e^{-x/\beta}}{\beta^{\alpha} \cdot \Gamma(\alpha)} \, \cdot \, x^{\, \alpha-1} \; \mbox{.} \]

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

 // 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 URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& 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);

2

Requires: 0 < alpha and 0 < beta .

3

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

RealType alpha() const;

4

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

RealType beta() const;

5

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

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

1

A weibull_distribution random number distribution produces random numbers x ≥ 0 distributed according to the probability density function \[% p(x\,|\,a,b) = \frac{a}{b} \cdot \left(\frac{x}{b}\right)^{a-1} \cdot \, \exp\left( -\left(\frac{x}{b}\right)^a\right) \; \mbox{.} \]

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

 // 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 URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& 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);

2

Requires: 0 < a and 0 < b .

3

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

RealType a() const;

4

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

RealType b() const;

5

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

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

1

An extreme_value_distribution random number distribution produces random numbers x distributed according to the probability density function280 \[% p(x\,|\,a,b) = \frac{1}{b} \cdot \exp\left( \frac{a-x}{b} \,-\, \exp\left(\frac{a-x}{b}\right) \right) \; \mbox{.} \]

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

 // 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 URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& 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);

2

Requires: 0 < b .

3

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

RealType a() const;

4

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

RealType b() const;

5

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

279)

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.