29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.8 Random number distribution class templates [rand.dist]

29.6.8.4 Poisson distributions [rand.dist.pois]

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

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

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: .
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 distributed according to the probability density function

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: .
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 distributed according to the probability density function

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: and .
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 distributed according to the probability density function

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: and .
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 function277

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: .
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.